Consider the following trapezoid.
Find the value of X.

(Helpful for math-space users)

Answer; y = 108

Explanation;
x + 72 = 180
X=180-72

All right angles are congruent which is determined by the definitions of a right angle and congruent angles.

Congruent angles are two or more angles that are identical to each other. As a result, the measurements of these angles are equivalent.

Given that ∠1 and ∠2 are right angles.

By the definition of right angles i.e. right angle is one that is exactly 90 degrees. It is precisely one-quarter of a circle. When a pie is divided into four equal pieces, the tip of each slice forms a straight angle.

⇒ m ∠1 =90° ; m ∠2 = 90°

By the substitution to get

⇒ m ∠1 = m ∠2

Therefore, ∠1 ≅ ∠2

Hence, all right angles are congruent which is determined by the definitions of a right angle and congruent angles.

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The measurement pairs that could be the dimensions of rectangle B include:

A. 6cm by 1.5cm

D. 18cm by 4.5vm

F. 80cm by 20cm

From the information, Rectangle A measures 12 cm by 3cm. Therefore, it should be noted that the scale factor is:

= 12/3

= 4/1

Therefore, the options should also have that same constant of 4:1

In this case, 6cm by 1.5cm, 18cm by 4.5cm, and 80cm by 20cm all possess this. This illustrates the concept of equivalent dimensions since they all have a ratio of 4:1.

The complete question is written below.

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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.

A. 6 cm by 1.5 cm

B.10 cm by 2 cm

C. 13 cm by 4 cm

D.18 cm by 4.5 cm

E.80 cm by 20 cm

ANSWER:
94.2m^3

STEP BY STEP:

V = 1/3 x PI x R^2 x h = 1/3 x 3.14 x 3^2 x 10 =94.2^3

Answer:

V = 94.25m³

I don't have enough time to show work because I have to go, but I hope this helped.

The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.

The allocation of weights to the relevant variables that produce the calculation's equilibrium is referred to as a consequence.

A connection between two or more factors results in a linear model when displayed on a graph. The variable will have a degree of one.

The linear equations are given below.

y = -3x + 9        ...1

3y = -9x + 9     ...2

Divide the equation 2 by 3, then the equation will become.

y = -3x + 3

The slope of the lines is the same but the lines are separated by a distance.

The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.

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<EOG =90° AS INDICATED IN THE DIAGRAM

<EOF+<FOG=<EOG(THEY MAKE THE ANGLE)

[tex]27 + 3y = 90 \\ 3y = 90 - 27 \\ 3y = 63 \\ \frac{3y}{3} = \frac{63}{3} \\ y= 21[/tex]

<AOB =180°( STRAIGHT LINE )

<AOE+EOF+<FOG+<GOB=<AOB(THWY MAKE THE ANGLE)

[tex]x + 27 + 3(21) + 8x + 18 = 180[/tex]

[tex]x + 27 + 63 + 8x + 18 = 180 \\ x + 8x + 27 + 63 + 18 = 180 \\ 9x - + 108 = 180 \\ 9x = 180 - 108 \\ 9x =72 \\ \frac{9x}{9} = \frac{72}{8} \\ x = 9[/tex]

ATTACHED IS THE SOLUTION

The table that represents a linear function is Table 1. Thus, the correct option is A.

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c.

Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.

We know that, slope m= (y2-y1)/(x2-x1)

Table 1:

Put (x1, y1)=(1, 5) and (x2, y2)=(2, 9) in slope formula

That is, (9-5)/(2-1)

= 4

Similarly, the slope between last two points is (9-5)/(4-1)

=4

Table 2:

Put (x1, y1)=(1, -5) and (x2, y2)=(2, 10) in slope formula

That is, (10+5)/(2-1)

= 15

Similarly, slope between last two points (20+15)/(4-3)

=35

Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.

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Answer: You could assume that X=8 and y=0

Step-by-step explanation:

Answer:

Solutions below.

Step-by-step explanation:

This Question involves the concept of intercepts of a graph.

Intercepts of a graph are namely the x-intercept and y-intercept.

x-intercept is when y = 0. Example: (3,0)

y-intercept is when x = 0. Example: (0,9)

We are given the equation: x + 4y = 8

To find x-intercept, we can substitute y = 0 into the equation to obtain the value of x.

x + 4(0) = 8

x + 0 = 8

x = 8

Coordinates: (8, 0)

To fins y-intercept, we can substitute x = 0 into the equation to obtain the value of y.

0 + 4y = 8

4y = 8

y = 8 ÷ 4

y = 2

Coordinates: (0, 2)

Answer:

The rule is. the nth term  aₙ is given by

aₙ = n² + 1

Step-by-step explanation:

The following is the summary of n, aₙ

n            aₙ      In terms of n

1             2        1² + 1

2            5        2² + 1

3            10       3² + 1

4            17        4² + 1

5            26       5² + 1

6            37       6² + 1

So the nth term is given by
n² + 1

Answer:

9

Step-by-step explanation:

t < 13 - 4

t < 9

again as far as it goes

Answer: (2, 5/2)

Step-by-step explanation:

CD=(2, 4),(2, 1)

((2+2)/2, (4+1)/2)=

(4/2, 5/2)=(2, 5/2)

D

1) Taking the function g(x)= (x+1) (x-2) (x+5), as we can see this a 3rd degree ploynomial

g (x)= (x+1) (x-2) (x+5)

g(x) =x³+4x²-7x-10

As the coefficient is positive, then we'll have

Examining the options, we have as the roots S={-5,-1,2} So the answer is D

The length of the guy wire to the nearest foot is 42 feet.

The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.

The situations forms a right angle triangle.

Therefore, the length of the guy wire can be found as follows:

Using trigonometric ratios, we can find the angle the guy wire made with the ground.

tan ∅ = opposite / adjacent

tan ∅ = 5 / 15

∅ = tan ⁻¹ 1 / 3

∅ = 18.4349488057

∅ = 18.43°

Therefore, let's find the length of the guy wire using the angle.

cos 18.43° =  adjacent / hypotenuse

0.94871060813 = 40 / h

h = 40 / 0.94871060813

h = 42.162488395

Therefore,

length of the guy wire = 42 feet

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The equation that relates M to R is M = 13 - R

From the question, we have the following parameters:

The total number of new magazines is the sum of the number of magazines read and the number of magazines left

This is represented as

Total number of new magazines = Number of magazines read + Number of magazines left

Substitute the known values in the above equation

13 = R +M

Make M the subject

M = 13 - R

Hence, the equation is M = 13 - R

See attachment for the graph

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Answer: 14

Step-by-step explanation:

87.5% of 105 is 91.875 (91)

105-91=14

Answer:

37

Step-by-step explanation:

Use PEMDAS, in this case, start with multiplication: (2)(-7), don't forget there is a minus sign in front of the two which is important later, then move on to dividing (-9) by (-3). Then you are left with 20-(-14)+3, which is the same as 20+14+3, which equals 37.

The value that Sarah must she get on the third test to have at least 90% test average is represented by the inequality x ≥ 96.

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.

In this case, Sarah has 85 and 89 on her first two math 23 tests.

Let the third test be represented as x. This will be illustrated as:

(85 + 89 + x) / 3 ≥ 90

Cross multiply

85 + 89 + x ≥ 90 × 3

174 + x ≥ 270

Collect like terms

x ≥ 270 - 174

x ≥ 96

The value is x ≥ 96.

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The equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3

The line is passing through the point = (-6,-3)

The slope of the line = 0

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

(y-(-3)) = 0×(x-(-6))

We have to convert this equation the slope intercept form

Slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

(y-(-3)) = 0×(x-(-6))

y+3 = 0×(x+6)

y+3 = 0

y = -3

Hence, the equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3.

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Answer:96

Step-by-step explanation: Answer is 96 because you can do 16 times 3 which is 48 so for the fifth seat to the end will be 96 ways.

Hope this helps! :)

Hello there. To solve this question, we'll have to remember some properties about trigonometric functions and the right triangle.

We want to find x such that:

We'll use the second right triangle to show what we want.

First, given a triangle:

We know that the hypotenuse will be:

But most importantly, the tangent of the angles α and β can be calculated by only using the legs of the triangle: it is the ratio between the opposite side and the adjacent side to an angle.

and

Now look at the triangle we have:

We can easily check that:

So it would be good to find something that relates the ratio between those two numbers: the tangent of 60º!!

Therefore, we have:

And the solution to x is:

Answer:

  x = 3⁴

Step-by-step explanation:

You want the exponential form of log₃(x) = 4.

It can be helpful to remember that a logarithm is an exponent of the base of the logarithm.

  log₃(x) = 4   ⇔   x = 3⁴

The exponential form is x = 3⁴.

265 students at this college have taken a course in either calculus or discrete mathematics.

Let X = number of students who have taken a course in calculus

Y = number of students who have taken a course in discrete mathematics

To determine the number of students who have taken a course in calculus only, subtract 135 from 324.

Only X = X - X∩Y

Only X = 324 - 135

Only X = 189

To determine the number of students who have taken a course in discrete mathematics only, subtract 135 from 211.

Only Y = Y - X∩Y

Only Y = 211 - 135

Only Y = 76

To determine the number of students who have taken a course in either calculus or discrete mathematics, add 189 and 76.

either X or Y = only X + only Y

either X or Y = 189 + 76

either X or Y = 265

To better illustrate the X and Y, see the attached photo of the Venn Diagram.

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A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

Bean advertised footwear on 29 of its 192 catalog pages.

we randomly survey 20 pages

the random variable X is

X = The number of pages that advertise footwear

It is given that 20 pages have been surveyed

so, X = 1, 2, 3.....20

The average value for binomial distribution can be calculated as follows

μ = np

= 20 (29/192)

= 580/192

=3.02

On average 3.02 pages expect to advertise footwear on them

Therefore, A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

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The 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521

In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. Exponential decay differs from linear decay in that the decay factor depends on a percentage of the initial sum, meaning that the amount by which the original sum may be lowered will fluctuate over time as opposed to a linear function, which reduces the original sum by the same amount each time.

Given,

10 hour decay factor = 0.2722

Let us calculate the one-hour decay factor first,

One-hour decay factor = (10 hour decay factor)^1/10 = (0.2722)^1/10 = 0.8779

Now, Calculating the 5-hour decay factor,

5 hour decay factor = ( 1 hour decay factor )^5 = (0.8779)^5 = 0.521

Hence, the 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521

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4x^4-10x^3-15x^2+27x

(use foiling)

The resulting value for the quotient of 21 and a equals 30 is 7/10.

The result of dividing two numbers is known as the quotient. Six divided by two results in the number three.

Latin's "how many times" is the meaning of the word "quotient." That is really logical. For instance, the quotient of a and b is a/b

Given the statement "the quotient of 21 and a equals 30", this can be written mathematically as;

21/a = 30

Cross multiply

30a = 21

Divide both sides by 30

30a/30 = 21/30

a = 21/30

a = 7/10

Hence the value of a from the equivalent expression is 7/10.

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A proportion is an equation in which two ratios are set equal to each other. No option is satisfying the proportion

Ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

A proportion is an equation in which two ratios are set equal to each other.

In the given question, rayon drove 320 miles in 5 hours to complete the first part of his trip. 12 hours to drive 768 miles.

we can write this

320miles/5 = 768 miles/12

320miles/768 miles=5/12

In option d the values are not given in a correct way. It doesnot hold for the proportion.

Hence no option is correct.

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The transformation from the graph of B to the graph of P is a vertical stretch by a scale factor of 2

From the question, the function definitions are given as

B(m) = 5m

P(m) = 10m

Rewrite the function P(m) as follows

P(m) = 2 x 5m

Substitute B(m) = 5m in the equation P(m) = 2 x 5m

P(m) = 2 x B(m)

When a function is represented as

f(x) = kg(x), then the transformation is a vertical stretch by k

Hence. the transformation a vertical stretch by 2

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a) Number of employees that prefer coffee are [tex]\frac{3}{7}[/tex].

b) Percentage of employees don't like either tea or coffee is 30.4%

c) Number of employees that prefer tea are [tex]\frac{28}{105}[/tex]

The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively. A fraction only informs us of the number of parts that make up the whole. The slash that is inserted between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. [tex]\frac{1}{2}[/tex], for instance, is a fraction.

Given Data

In a work survey, it was found that:

28 employees preferred tea

45 employees preferred coffee

32 didn't like either

a) Number of employees that prefer coffee

= 45

Fraction:

= [tex]\frac{45}{105}[/tex]

= [tex]\frac{3}{7}[/tex]

b) Percentage of employees don't like either tea or coffee

= [tex]\frac{32}{105}[/tex] × 100

= 30.4%

c) Number of employees that prefer tea.

= 28

= [tex]\frac{28}{105}[/tex]

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