solve for x. Round your answer to the nearest tenth.

Solve For X. Round Your Answer To The Nearest Tenth.

Answers

Answer 1

The length of the side opposite to the 42 degree angle in the right triangle is approximately 3.4 units.

Describe Triangle?

The angles of a triangle are the angles formed by its sides. The sum of the angles of a triangle is always 180 degrees, which is a fundamental property of this shape. There are different types of triangles, based on their side lengths and angle measures. For example:

A scalene triangle has three sides of different lengths and three different angles.

An isosceles triangle has two sides of equal length and two equal angles.

An equilateral triangle has three sides of equal length and three equal angles.

A right triangle has one angle that measures 90 degrees (a right angle), and the side opposite to it is called the hypotenuse.

Triangles have many important properties and applications in mathematics, physics, and engineering. They can be used to calculate distances, angles, areas, volumes, and many other quantities. Triangles are also used in the construction of buildings, bridges, and other structures, as well as in art, design, and other fields.

We can use the trigonometric ratio of sine to solve for x:

sin(42) = opposite/hypotenuse

sin(42) = x/5

To solve for x, we can multiply both sides by 5 and simplify:

x = 5*sin(42)

x ≈ 3.4 (rounded to the nearest tenth)

Therefore, the length of the side opposite to the 42 degree angle in the right triangle is approximately 3.4 units.

To know more about hypotenuse visit:

https://brainly.com/question/2613216

#SPJ1


Related Questions

A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.


Ice Cream Candy Cake Pie Cookies
81 9 72 36 27


Which statement is the best prediction about the scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.

Answers

Option D : Based on the given data, the best prediction for the number of students who prefer ice cream at the college, which is approximately 1,440 students.

To make prediction of the number of students who prefer ice cream, we need to use the proportion of students who prefer ice cream from the sample to the entire population of 4,000 students.

Based on the given data, 81 out of 225 students prefer ice cream. To estimate the number of students who prefer ice cream in the entire college, we can use the ratio of students who prefer ice cream in the sample to the total number of students in the college.

The total number of students in the college is 4,000, so we can set up a proportion:

81/225 = x/4000

Solving for x, we get:

x = (81/225) * 4000 = 1,440

Therefore, the best prediction for the number of students who prefer ice cream in the entire college is 1,440.

To learn more about prediction please click on below link        

https://brainly.com/question/28202475

#SPJ1

A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.

Ice Cream Candy Cake Pie Cookies

81 9 72 36 27

Which statement is the best prediction about the scoops of ice cream the college will need?

A. The college will have about 480 students who prefer ice cream.

B. The college will have about 640 students who prefer ice cream.

C. The college will have about 1,280 students who prefer ice cream.

D. The college will have about 1,440 students who prefer ice cream.

The circles have the same center. What is the area of the shaded region?

Answers

Answer: 160.14

Explanation: the inner circle has an area of 153.86 in.^2. The outer circle as a whole has an area of 314 in.^2. Subtract the area of the inner circle(153.86) from the area of the total of the bigger circle(314) to get the area of the shaded region of the circle.

Answer:

The area of the shaded region is 160.2 in² (to the nearest tenth).

Step-by-step explanation:

The area of the shaded region can be calculated by subtracting the area of the inner circle from the area of the outer circle.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a circle}\\\\$A=\pi r^2 $\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]

If the circles have the same center, and the inner circle has a radius of 7 in, then the outer circle has a radius of:

[tex]\implies r = 7 + 3 = 10\; \sf in[/tex]

Therefore, the area of the shaded region is:

[tex]\begin{aligned}\sf Area_{shaded\;region}&=\sf Area_{outer\;circle}-Area_{inner\;circle}\\&=\pi \cdot 10^2 - \pi \cdot 7^2\\&=100\pi - 49 \pi\\&=51 \pi\\& = 160.221225...\\&=160.2\; \sf in^2\;(nearest\;tenth)\end{aligned}[/tex]

6 cm. Find its area to the nearest tenth.

Answers

The area of the rectangle is 35.1 cm²

How to determine the area of the rectangle

To find the area of a rectangle, you need to multiply its length by its width.

Given that the dimensions of the rectangle are 5.85 cm and 6 cm, respectively, the area of the rectangle is:

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

Area = 5.85 cm x 6 cm

Evaluate the product

Area  = 35.1 cm²

Hence, the area of the rectangle to the nearest tenth is 35.1 cm²

Read more about area at

https://brainly.com/question/24487155

#SPJ1

Complete question

The dimension of a rectangle is 5.85 cm by 6 cm. Find its area to the nearest tenth.

A ship travels east from Port Lincoln 24 miles before turning north. When the ship becomes disabled
and radios for help, the rescue boat needs to know the fastest route to the ship. The rescue boat navigator
finds that the shortest route from Port Lincoln is 48 miles long. At what angle off of due east should the
rescue boat travel to take the shortest route to the ship? Round your answer to the nearest whole degree.

Answers

Answer:

Rounding to the nearest whole degree, the rescue boat should travel at an angle of approximately 41 degrees off of due east to take the shortest route to the ship.

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram to represent the situation:

            A (rescue boat)

              | \

              |   \

              |     \ C (disabled ship)

   24 mi |       \

              |        \

              |          \

              |θ          \

              B-----------D (Port Lincoln)

               48 mi

In the diagram, point B represents Port Lincoln, point C represents the disabled ship, and point A represents the rescue boat. Point D is the intersection of the eastward path and the northward path taken by the ship.

We are given that BD = 24 miles and CD = 48 miles. We want to find the angle θ, which is the angle between the line segments AB and AD.

To find θ, we can use the law of cosines:

cos(θ) = (BD² + CD² - AD²) / (2 x BD x CD)

Substituting the given values, we get:

cos(θ) = (24² + 48² - AD²) / (2 x 24 x 48)

Simplifying, we get:

cos(θ) = 0.75

To solve for θ, we can take the inverse cosine of both sides:

θ = cos⁻¹(0.75)

Using a calculator, we get:

θ ≈ 41.41°

Rounding to the nearest whole degree, the rescue boat should travel at an angle of approximately 41 degrees off of due east to take the shortest route to the ship.

what is written history ​

Answers

A written history ​means the writing of history, such as the writing of history based on the critical examination of sources which is also known as historiography.

How can we define written history?

Also known as recorded history describes the historical events that have been recorded in a written form or other documented communication which are subsequently evaluated by historians using the historical method.

Historiography also includes the theory and history of historical writing. Modern historians strive to reconstruct a record of human activities and gain a deeper understanding of them.

Read more about historiography

brainly.com/question/18837262

#SPJ1

PLEASE HELP ASAP will give brainliest

Answers

Let's use variables to represent the width and length of the rectangle:

Let w be the width of the rectangle (in cm)

Then, the length of the rectangle can be expressed as 5w - 18 (since it is 18 cm less than five times its width).

The area of the rectangle can be calculated as:

A = w * (5w - 18)

We are given that the area of the rectangle is 35 square cm. Substituting this value into the equation above, we get:

35 = w * (5w - 18)

Expanding the right-hand side, we get:

35 = 5w^2 - 18w

Rearranging the terms and setting the equation equal to zero, we get:

5w^2 - 18w - 35 = 0

To solve for w, we can use the quadratic formula:

w = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -18, and c = -35.

Plugging in the values, we get:

w = (-(-18) ± sqrt((-18)^2 - 4(5)(-35))) / 2(5)

w = (18 ± sqrt(784)) / 10

w = (18 ± 28) / 10

So w = 2.6 or w = -1.4

Since the width cannot be negative, we reject the solution w = -1.4.

Therefore, the width of the rectangle is approximately 2.6 cm.

To find the length, we can use the expression we derived earlier:

length = 5w - 18

length = 5(2.6) - 18

length = 13 - 18

length = -5

Since the length cannot be negative, we know that there is an error in our calculation. We made an assumption that the width is less than the length, which is not necessarily true. We should check our work and try again using the positive root instead of the negative one.

Using the positive root for the width, we get:

w = (18 + 28) / 10

So w = 4.6

Therefore, the width of the rectangle is 4.6 cm.

To find the length, we can use the expression we derived earlier:

length = 5w - 18

length = 5(4.6) - 18

length = 23 - 18

length = 5

So the length of the rectangle is 5 cm.

Therefore, the dimensions of the rectangle are width = 4.6 cm and length = 5 cm.

A light display for a festival consists of a string of 1,000 lightbulbs in the colors red, yellow, green, and blue repeated consecutively in that order for the entire display. The 543rd lightbulb needs to be replaced.

If the first lightbulb is red, what is the color of the lightbulb that needs to be replaced?

Answers

Using the pattern given, we found that the colour of the lightbulb in the 543rd position of a string of lightbulbs is green.

What is meant by the pattern?

A recurring arrangement of numbers, shapes, colours and other elements is known as a pattern. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series. The number of patterns can be limitless or finite. There are many distinct kinds of number patterns, including geometric, Fibonacci, and algebraic or arithmetic patterns. In mathematics, number patterns are quite prevalent.

Given,

The number of lights on a string of lights = 1000

The order in which the lights repeat is red, yellow, green and blue.

After every four lights, the order repeats.

We can get the pattern as follows.

The blue lights are in positions 4,8,12,........,4n.

We have to find the multiple of 4 close to 543.

Now we can check if 542 is a multiple of 4.

542/4 = 135.5

So it is not a multiple of 4.

Now check if 544 is a multiple of 4.

544/4 = 136

So the bulb in the 544th position is blue.

Then the bulb in the 543rd position should be green.

Therefore using the pattern given, we found that the colour of the lightbulb in the 543rd position of a string of lightbulbs is green.

To learn more about patterns, follow the link.

https://brainly.com/question/28580633

#SPJ1

The first three terms of a geometric sequence are as follows

-5,-20,-80
Find the next two terms of this sequence; give an exact value (not decimals)

Answers

Answer: -1280

Step-by-step explanation:

in a geometric sequence it either multiplies or divides negatively or positively, in this case -5 to -20 is multiplied 4 positively and so is -20 to -80

then -80x4= -320

-320x4= -1280

find the area when the circumference = 6 pi

Answers

Answer:

Step-by-step explanation:

if the circumference=6π, then you can solve for the radius. C=2πr

6π=2πr

Divide 2π from both sides to get r=3

Area=πr^2

A=π*9

Area= 9π

A PVC pipe has an inner diameter of 5 cm and an outer diameter of 6.5 cm. The PVC has a density of 1.38 g/cm³. What is the mass of a pipe that is 30 cm long in grams? Round to the nearest hundredth.​

Answers

Hence, in answering the stated question, we may say that As a result, the  function mass of the 30 cm long PVC pipe is roughly 733.48 grammes, rounded to the nearest tenth.

what is function?

Mathematicians investigate numbers and their variants, equations and associated structures, forms and their locations, and prospective locations for these things. The term "function" refers to the relationship between a group of inputs, each with its own output. A function is a connection of inputs and outputs in which each input results in a single, distinct outcome. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four basic types of accessible functions.

The volume of the PVC pipe can be estimated by subtracting the volumes of the outer and inner cylinders:

V = π/4 × (D² - d²) × L

where V denotes volume, is the mathematical constant pi (roughly equivalent to 3.14159), D denotes outer diameter, d denotes inner diameter, and L denotes pipe length.

V = π/4 × (6.5² - 5²) × 30\sV = 531.13 cm³

PVC pipe mass can be estimated by multiplying its volume by its density:

m = V × ρ

With the provided density, we get:

1.38 g/cm3 m = 733.48 g m = 531.13 cm3

As a result, the mass of the 30 cm long PVC pipe is roughly 733.48 grammes, rounded to the nearest tenth.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

pls someone help asap

Answers

Answer:

2x+15

Step-by-step explanation:

Answer:

2x + 15

Step-by-step explanation:

First, we are doubling x.

We know that doubling is the same thing as multiplying by 2:

2x

Next, we are adding fifteen:

2x + 15

I will mark you brainiest!

Which of the following pairs of quadrilaterals have diagonals that are congruent?

A) Rhombus and a rectangle
B) A parallelogram and a square
C) a rectangle and a square
D) a life and a trapezoid

Answers

The only pair of quadrilaterals that have congruent diagonals is a rectangle and a square, and the answer is C.

What distinguishes a quadrilateral?

These attributes are:

There are four of them.There are four of them.360° is the total of all interior angles.There are two diagonals in them.Both regular and irregular quadrilaterals exist. A regular quadrilateral must have four equal sides, four equal angles, and diagonals that cross each other in a bisecting direction.

C) A rectangle and a square: A rectangle's diagonals are congruent, and a square's diagonals are also congruent. The solution is C because a square is a particular case of a rectangle in which all sides are congruent.

Hence, a rectangle and a square are the only pair of quadrilaterals with congruent diagonals, and the answer is C.

To know more about quadrilaterals visit:

https://brainly.com/question/29934440

#SPJ1

Help with math problems

Answers

The solutions to the absolute value inequalities 1 to 20 are shown below

Solving the absolute value inequalities

|x + 8| < 16

So, we have

-16 < x + 8 < 16

-24 < x < 8

|r + 1| ≤ 2

So, we have

-2 ≤ r + 1 ≤ 2

-3 ≤ r ≤ 1

|2c - 1| ≤ 7

So, we have

-7 ≤ 2c - 1 ≤ 7

-6 ≤ 2c ≤ 8

-3 ≤ r ≤ 4

Using the above as a guide, the solution to the other inequalities are

-3 < h < 5No solutionNo solutionr < -8 and r > 4k < 1 and k > 7h ≤ -3 and h ≥ 6p ≤ -3 and h ≥ 2No solutionAll set of real valuesn ≤ -5.25 and n ≥ 3.75-0.8 ≤ t ≤ 1.6-6 < h < 5p ≤ -14 and p ≥ 22No solutionAll set of real values-3 < r < 1p < -4 and p > -1

Read more about inequalities at

https://brainly.com/question/30390162


#SPJ1

a₁ = -3,
an=3an-1+5
for
n>2

Answers

The sum of the first 10 terms in the sequence is 195.The sequence given above is an arithmetic sequence.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each successive number is found by adding a fixed number, called the common difference, to the previous number in the sequence. The common difference is the same for each pair of consecutive numbers.

An arithmetic sequence is a sequence of numbers where each successive number is obtained by adding a fixed amount, the common difference, to the preceding number. In this particular sequence, the common difference is 5.

The first term in the sequence is a₁ = -3, and the general term is an = 3an-1 + 5, where n > 2. To find any term in the sequence, we can use the formula an = a₁ + (n - 1)d, where d is the common difference. In this case, a₁ = -3 and d = 5, so the formula becomes an = -3 + (n - 1)5.

To find the 9th term in the sequence, we can substitute n = 9 into the above formula and solve for an. This gives us an = -3 + (9 - 1)5 = -3 + 40 = 37. Therefore, the 9th term in the sequence is 37.

To find the sum of the first 10 terms in the sequence, we can use the formula Sₙ = (n/2)(2a₁ + (n - 1)d). In this case, a₁ = -3 and d = 5, so the formula becomes Sₙ = (n/2)(2(-3) + (n - 1)5). Substituting n = 10 into the formula gives us Sₙ = (10/2)(2(-3) + (10 - 1)5) = (10/2)(-6 + 45) = (10/2)(39) = 195. Therefore, the sum of the first 10 terms in the sequence is 195.

For more questions related to consecutive numbers

brainly.com/question/1764265

#SPJ9

Right Question:-

a₁ = -3,

an=3an-1+5

for

n>2.

For given sequence, Find the sum of first 10 terms?

Help please also please explain bc I truly do not get it

Answers

Therefore, the solutions for θ in the interval 0° ≤ θ ≤ 360° are approximately 131.81° and 228.19°.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It is used to study and analyze various phenomena that involve periodic functions, such as waves, oscillations, and sound. Trigonometry also has practical applications in fields such as physics, engineering, navigation, and surveying. It involves the use of trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent to calculate the sides and angles of triangles and other geometric figures.

Here,

Let's solve for θ:

First, let's substitute u = cos(θ), so we have:

3u² - 5u - 4 = 0

Now we can use the quadratic formula:

u = [ -(-5) ± √((-5)² - 4(3)(-4))] / (2*3)

u = [ 5 ± √(49) ] / 6

u1 = (5 + 7) / 6 = 2

u2 = (5 - 7) / 6 = -2/3

Since the cosine function has a range of -1 ≤ cos(θ) ≤ 1, we can discard the solution u1 = 2.

Now we can solve for θ:

cos(θ) = u2 = -2/3

θ = cos⁻¹(-2/3) ≈ 131.81°  

θ = 360° - cos⁻¹(-2/3) ≈ 228.19°

To know more about trigonometry,

https://brainly.com/question/26719838

#SPJ1

Use a calculator to find the measure of

Answers

The measure of the angle A as required to be determined in the task content is; 16.7°.

What is the measure of angel A?

It follows from the task content that the measure of the angle A is to be determined.

By using the trigonometric ratio;

tan (A) = BC / AC

Hence, by substitution; it follows that;

tan (A) = 6 / 20

Hence, by simplification; we have that;

tan A = 3/10

tan A = 0.3

Therefore, to determine A;

A = tan-¹ (0.3)

A = 16.7°.

Ultimately the measure of angle A as required to be determined is; 16.7°.

Read more on trigonometric ratios;

https://brainly.com/question/24349828

#SPJ1

Check here for instructional material to complete this problem.
Evaluate the formula z =
X-μ
0
√n
when μ = 123, n = 26, x= 127, and o=7.
Z= (Round to three decimal places as needed.)

Answers

Answer:

Z = 2.91

Step-by-step explanation:

Mean:  123

Sample Size:  26

Standard Deviation:  7

x = 127

z = (x - μ) / (σ / [tex]\sqrt{n}[/tex] )

[tex]z=\frac{127-123}{\frac{7}{\sqrt{26} } } \\z= 2.91[/tex]

**If this is a z-table question, then P (x = 127) = P (z = 2.91) = 0.9982.**

i-Ready
Find the surface area of the box shown.
S.A. =
Nets and Surface Area- Instruction-Level F
in.²
3 in
12 in
10 in
X

Answers

The surface area of the box shown is 186 square inches (186 in²).

What is surface area?

Surface area is the measure of the area on a two-dimensional surface. It is the sum of the areas of all the shapes that make up a two-dimensional object. It can be used to calculate the area of a sphere, a cylinder, a rectangular prism, and more.

The box shown is a three-dimensional rectangular prism. The surface area (S.A.) of a rectangular prism is calculated by adding the area of each of its six faces. The area of each face is calculated by multiplying the length of the face by its width.

For the box shown, the length is 3 inches (3 in), the width is 12 inches (12 in), and the height is 10 inches (10 in). To find the surface area, we need to calculate the area of each face and add them together. The surface area of this box is calculated as follows:

Front and back faces: 3 in x 10 in = 30 in²

Left and right faces: 12 in x 10 in = 120 in²

Top and bottom faces: 3 in x 12 in = 36 in²

Total surface area: 30 in² + 120 in² + 36 in² = 186 in²

Therefore, the surface area of the box shown is 186 square inches (186 in²).

For more questions related to prism,

https://brainly.com/question/23963432

#SPJ1

twice a number plus three times a second number is negative one. the first number plus four times the second number is two

Answers

Answer:

Step-by-step explanation:

Let [tex]x,y[/tex] be the two numbers. Then we get

    [tex]2x+3y=-1[/tex]     [tex](a)[/tex]

       [tex]x+4y=2[/tex]       [tex](b)[/tex]

We solve equations [tex](a)[/tex] and [tex](b)[/tex] simultaneously:

    equation [tex](b)\times2[/tex] :

       [tex]2x+8y=4[/tex]        [tex](c)[/tex]  

   [tex](c)-(a)[/tex] gives:

       [tex]5y=5\rightarrow y=1[/tex]

    Sub [tex]y=1[/tex] into [tex](a)[/tex] :  

       [tex]2x+3\times1=-1\rightarrow2x=-4\rightarrow x=-2[/tex]

The solution is -2,1

Lin has 27 marbles. He divides them into 3 equal groups and gives 1 group to Jill. Jill then gives 2 of hers away. How many marbles does Jill have now?

Answers

Answer: 7 marbles

Step-by-step explanation:

Lin starts with 27 and creates 3 equal groups.

When separating, you divide.

27 divided by 3 is 9.

Each group has 9 marbles.

This means that by giving one group to Jill, she receives 9 marbles.

Jill gives away 2 of her 9 marbles, thus leaving her with 7 marbles.

9-2=7.

Evaluate each expression for the given values.

4 |m - n|
If m = -7 and n=2

Answers

The expression will give 36 after evaluating.

What is an Expression?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated or simplified. An expression may contain one or more terms, which are separated by operators such as addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^).

Expressions can represent various mathematical concepts, such as equations, inequalities, functions, and polynomials.

Given:  m = -7 and n = 2,

We know that, the mode function converts the function into positive value.

So, |m - n| = |-7 - 2| = 9

Now,

4 |m - n| = 4 * 9 = 36

So the expression 4 |m - n| evaluates to 36 when m = -7 and n = 2.

To learn more about Expression, visit the link:

https://brainly.com/question/1859113

#SPJ1

Evaluate f(x) = 3x + 2 when x = -4.

Answers

Answer:

-10

Step-by-step explanation:

[tex]f(x) = 3x + 2[/tex]

Replace x in the function with the given value x = -4:

[tex]f( - 4) = 3 \times ( - 4) + 2 = - 12 + 2 = - 10[/tex]

The perimeter of a rectangular table is 18 feet The table is 42 inches wide

Answers

Width of the table = 3.5 feet , Length of the table = 5.5 feet and Perimeter of the table = 18 feet

What is Rectangle ?

A rectangle is a 2-dimensional shape with four straight sides, where opposite sides are parallel and equal in length. It has four right angles and its diagonals bisect each other. It is a type of quadrilateral, and its area is calculated by multiplying the length and width of the rectangle. It is commonly found in many geometric shapes and everyday objects such as doors, windows, and computer screens.

Let's convert all measurements to the same unit for easier calculation. Since the table width is given in inches, we can convert it to feet by dividing by 12 (since 1 foot = 12 inches).

Table width: 42 inches = 42÷12 = 3.5 feet

Let's denote the length of the table as 'l' feet. The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (Length + Width)

Given that the perimeter is 18 feet, we can substitute the values into the formula:

18 = 2 * (l + 3.5)

Now, we can solve for 'l':

18 = 2l + 7 (distributing 2 to both terms in the parentheses)

2l = 18 - 7 (subtracting 7 from both sides)

2l = 11 (simplifying)

l = 11÷2 (dividing both sides by 2)

Therefore, Width of the table = 3.5 feet , Length of the table = 5.5 feet

and Perimeter of the table = 18 feet

To learn more about Rectangle from given link.

https://brainly.com/question/15238546

#SPJ1

A rectangle is 16 feet long and 12 feet wide. How long is the diagonal from one corner to the other?

Answers

The length οf the diagοnal is 20 feet.

What is a rectangle?

A rectangle is a type οf quadrilateral with parallel sides that are equal tο οne anοther and fοur vertices that are all 90 degrees apart. It is alsο knοwn as an equiangular quadrilateral fοr this reasοn. The term "parallelοgram" can alsο be used tο describe a rectangle because the οppοsing sides are equal and parallel.

Given that 16 feet and 12 feet make up a rectangle.

The diagοnal and twο cοnsecutive sides οf a rectangle make a right-angled triangle.

Tο find the diagοnal apply Pythagοrean theοrem.

The widely accepted geοmetric principle knοwn as the Pythagοrean Theοrem states that the square οn the hypοtenuse οf a right triangle equals the sum οf the squares οn its legs.

Draw a rectangle:

Cοnsider △ABC:

AB² + BC² = AC²

12² + 16² =AC²

AC² = 144+ 256

AC² = 400

Take square rοοt οn bοth sides:

AC = 20

To learn more about diagonal,

https://brainly.com/question/14413639

#SPJ1

PLEASE HELP !! :( QUESTION 17

Answers

Answer:

b) The graph will shift down 5 units from its parent graph.

Step-by-step explanation:

Your answer is in the image.

Solving Square Root Equations



Solve the following equations. Be sure to label any extraneous solutions.

Answers

Answer:

Step-by-step explanation:

1) To solve the equation √(6x) = x, we can first square both sides of the equation to eliminate the square root:

(√(6x))^2 = x^2

6x = x^2

Next, we can rearrange the equation into standard quadratic form by subtracting 6x from both sides:

x^2 - 6x = 0

Now, we can factor out an x from the left-hand side of the equation:

x(x - 6) = 0

Setting each factor equal to zero, we find two solutions:

x = 0 or x - 6 = 0

Therefore, the solutions to the equation √(6x) = x are x = 0 and x = 6.

2)To solve √(5x-6) = x, we can square both sides of the equation:

(√(5x-6))^2 = x^2

5x-6 = x^2

Rearranging this quadratic equation to the standard form ax^2 + bx + c = 0, we get:

x^2 - 5x + 6 = 0

This can be factored into:

(x - 2)(x - 3) = 0

Therefore, the solutions to the equation √(5x-6) = x are x = 2 and x = 3.

We should check if these solutions satisfy the original equation:

When x=2: √(5x-6) = √(5(2)-6) = √4 = 2, which satisfies the equation.

When x=3: √(5x-6) = √(5(3)-6) = √9 = 3, which also satisfies the equation.

Therefore, the solutions are x = 2 and x = 3.

3) To solve the equation √(2x-1) = x-3, we can square both sides of the equation to eliminate the square root:

(√(2x-1))^2 = (x-3)^2

Simplifying the left-hand side gives:

2x-1 = (x-3)^2

Expanding the right-hand side gives:

2x-1 = x^2 - 6x + 9

Rearranging the equation gives:

x^2 - 8x + 10 = 0

We can solve this quadratic equation :

x^2 - 8x + 10 = 0

Now we can solve this quadratic equation by using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = -8, and c = 10. Substituting these values into the formula:

x = (-(-8) ± √((-8)^2 - 4(1)(10))) / 2(1)

Simplifying:

x = (8 ± √(64 - 40)) / 2

x = (8 ± √24) / 2

x = 4 ± √6

Therefore, the solutions to the equation √(2x - 1) = x - 3 are x = 4 + √6 and x = 4 - √6.

4) has no real solutions.

when you have to remove the square root you have to power the both sides of the equation.

1)6x= x^2

 0 = x^2 - 6x

0= x(x-6)

x=0 or x-6=0

            x=6

2) [tex]\sqrt{5x-6}[/tex] = x

   5x-6=x^2

   x^2 -5x+6=0

   (x-3)(x-2)=0

    x-3=0 or x-2= 0

    x=3 or x=2

3)

[tex]\sqrt{2x-1}[/tex] = x-3

2x-1 = (x-3)^2

2x-1= x^2 - 6x +9

x^2 -8x +10=0

this equation can't solve by factoring method easily. so we have to use the completing square method.

x^2-8x+10=0

x^2-8x= -10

x^2 - 8x+(-4)^2 = -10+ ( -4)^2

(x-4)^2 = 6

[tex]x= 4 +\sqrt{6}[/tex] or  [tex]x= 4 -\sqrt{6}[/tex]

4) [tex]x= 2 + \sqrt{2x-11}[/tex]

x^2= 4+4 [tex]\sqrt{2x-11}[/tex] + 2x-11

x^2= 7+ 2x +4[tex]\sqrt{2x-11}[/tex]

x^2-2x-7= 4[tex]\sqrt{2x-11}[/tex]

(x^2-2x-7)^2= 16 (2x-11)

x^4 +4x^2 +49-4x^3 + 28x - 14x^2 = 32x-176

x^4 - 4x^3 - 10x^2 - 4x + 225= 0

x(x^3 -4x^2 - 10x-4)+225=0

this is a power 4 th equation this equation can solve by normal steps.

The last time Ms. Ward's car tank was filled, the odometer reading was 7,998 miles. The next time she filled up her vehicle with gas, the odometer reading was 8,308.

What was Ms. Ward's cost per mile for the time period? (remember, money always rounds to 2 decimal places!)

Answers

Answer:

$0.14

Step-by-step explanation:

[tex]8,308 - 7,998 = 310 \: miles[/tex]

We don't have information on how many gallons of gas Ms. Ward purchased, so we can't calculate the exact cost per mile. However, we can use the average fuel efficiency of her car to estimate the cost. Let's assume her car gets an average of 25 miles per gallon, which is a common fuel efficiency for a compact car.

To calculate how many gallons of gas she used, we can divide the number of miles driven by the fuel efficiency:

[tex]\frac{310 \: miles}{25 \: miles _{gallon} } = 12.4 \: gallons[/tex]

Assuming that the cost of gas was $3.50 per gallon, we can multiply the number of gallons used by the cost per gallon to find the total cost of gas:

[tex]12.4 \: gallons \times $3.50_{gallon} = $43.40[/tex]

To find the cost per mile, we can divide the total cost of gas by the number of miles driven:

[tex]\frac{$43.40}{310 \: miles} = $0.14_{mile} [/tex]

So Ms. Ward's cost per mile for this time period was approximately $0.14.

Answer:

Step-by-step explanation:

Miles travelled = 8,308 - 7,998 = 310 miles

Total cost = $26.79

Cost per mile[tex]=\frac{26.79}{310}[/tex] =0.0864

Ms. Ward's cost per mile is $0.09 (rounded to nearest cent).

70 divided by 33.8 plsss I have to do my hw

Answers

Answer:

Step-by-step explanation:

70/33.8=2.07100592

A bandana is in the shape of a triangle. The base of the bandana is 30 in. wide and the height is 12 in.

What is the area of the bandana?
_______________________________
(reporting spams/wrong answers)
(no picture is needed for this question)
(giving brainliest to the correct answer)
_______________________________

Answers

Answer:

180 in^2

Step-by-step explanation:

A bandana is in the shape of a triangle. The base of the bandana is 30 in. wide and the height is 12 in.

Triangle Area = 1/2 b x h

substitute the values

1/2 30 x 12 =

15 x 12 = 180 in^2

Which two pairs of measurements are equal?

Answers

Answer:

cm³ and ml

m³ and litre

This is the all you will need to know

Other Questions
A pyrotechnician plans for two fireworks to explode together at the same height in the air. They travel at speeds shown below. Firework B is launched 0.25 s beforeFirework A. How many seconds after Firework B launches will both fireworks explode?Firework A : 320 ft/sFirework B : 220 ft/sBoth fireworks will explode ___ seconds after Firework B launches.(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.) HURRY!!!! What did famous Georgians Richard Russell and Carl Vinson have in common?A. They strongly supported civil rights through their careers.B. They served as governors of Georgia during periods of social unrest.C. They played crucial roles in creating jobs for Georgians during world war ll.D. They supported American isolationism and resisted committing in the country to war. A project is expected to have annual cash flows of $36,800, $24,600, and $9,200 for Years 1 to 3, respectively. The initial cash outlay is $44,500 and the discount rate is 11 percent. What is the modified IRR? which of the following circumstances will not cause a partnership to close its tax year early? a.the business activity of the partnership permanently ceases. b.a new partner enters the partnership. c.the partnership terminates by agreement of the partners. d.all the partners decide to retire, permanently close their stores and stop conducting business. How do you know when to use cos, tan, or sin when trying to find a segment of a trignagle. Example:I had to use cos for this and had to find segment AB and AC. i just need a better understanding. Genetic testing accessible to the public has become much more accurate and reasonably priced because of the use of independent online laboratories.True False Analyze the data about nitrogenous base content of DNA from various species. Percentages of Bases in Five Organisms Source of DNA A T G C Streptococcus 29. 8 31. 6 20. 5 18. 0 Yeast 31. 3 32. 9 18. 7 17. 1 Herring 27. 8 27. 5 22. 2 22. 6 Human 30. 9 29. 4 19. 9 19. 8 E. Coli 24. 7 23. 6 26. 0 25. 7 Which of these statements are supported by the data? Select all that apply. A. In any one species, the amount of adenine closely approximates that of thymine. B. In any one species, the amount of guanine closely approximates that of cytosine. C. The amounts of A, T, G, and C in DNA is constant across species. D. The amounts of A, T, G, and C in DNA varies from species to species the diagram shows the price paid by two groups of people visiting a fair. assume that each adult pays the same price and each child pays the same price which of the following options correctly describe the inscribed polygon method for predicting aromaticity? select all that apply. multiple select question. place the polygon with one of its flat sides down and draw a circle that touches all the vertices. mos below the center of the circle are bonding orbitals, and mos above the center are antibonding orbitals. where each vertex touches the circle, draw a line corresponding to a molecular orbital. aromatic systems have all bonding mos and homos completely filled with no unpaired electrons. place one electron in each bonding orbital, then pair up. explain the difference between a mixture of a element and a compound made of elements. Write about atom in your answer \begin{tabular}{|c|c|c|} \hline \multirow{2}{*}{Time in Seconds } & Run \#1 & \multicolumn{1}{|c|}{ Run \#2 } \\ \cline { 2 - 3 } & Position in Centimetres & Position in Centimetres \\ \hline0.0&0 cm&0 cm\\ \hline0.1&2 cm&2.3 cm\\ \hline0.2&4 cm&4.8 cm\\ \hline0.3&6.2 cm&7.3 cm\\ \hline0.4&8.3 cm&9.7 cm\\ \hline0.5&10.6 cm&12.3 cm\\ \hline0.6&13 cm&14.9 cm\\ \hline0.7&15.4 cm&17.6 cm\\ \hline0.8&17.8 cm&20.3 cm\\ \hline0.9&20.3 cm&22.8 cm\\ \hline1.0&22.4 cm&24.8 cm\\ \hline \end{tabular} 2. Compute the slope of each line, showing calculations: Run \#1 Run \#2 Slope=Slope=Be sure to include the units. 3. Write an equation for each line: Run \#1 Run \#2 What are the transformations of the function? Select all the correct answers read this passage taken from how the Spaniards came to shung-opovi how they built a mission and how the Hopi destroy the mission which two of these elements are found in the Hopi story In general, neurocognitive disorders tend to be caused by a. environmental factors. b. psychological factors. c. biological factors. d. prenatal factors. which statement is prepared for only one date? A recipe for vegetable fritata calls for 10 chard leaves for evry 6 eggs. Eggs are available either by the dozen for $3. 20 or by the half-dozen for $1. 70. Marissa wants to use 25 chard leaves to make a fritata. What is the minimum she should spend on eggs to use all of her chard leaves while keeping the recipe in the correct proportion Owen's Muffin Extravaganza recorded how many of each type of muffin it recently sold.bran muffins 25blueberry muffins 12poppy seed muffins 3chocolate chip muffins 10Considering this data, how many of the next 16 muffins sold would you expect to be bran muffins? A system of two objects has Ktot = 6 J and Uint = -3 J Examine the scenario below. Determine the goal the responding international agency is trying to achieve if they intervene in this issue.Two European countries are at war, and are using their navies to attack one another in an area in which cruise ships frequently travel. NATO has decided to intervene, to help protect the cruise passengers from being attacked.ResponsesHuman RightsSpread DemocracyNational SecurityEconomic Growth What is the connection between the men of the whale ship Essex and the audience walker is addressing