The length of the diagonal of a Rectangle is 14cm,and it forms a 30 degree angle in one corner of the rectangle.What is the area of the rectangle.(A=LxW)

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Find the equation of the line that passes through the points (7,5) and (−9,5)

Hard

Updated on : 2022-09-05

Solution

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Correct option is A)

Since slope of line passing through two points (x

1

,y

1

) and (x

2

,y

2

) is m=

x

2

−x

1

y

2

−y

1

We now find the slope of the line passing through the points (7,5) and (−9,5) as shown below:

m=

−9−7

5−5

=

−16

0

=0

Therefore, the slope of the line is 0.

Now use the slope and either of the two points to find the y-intercept.

y=mx+b

5=(0)(7)+b

b=5

Write the equation in slope intercept form as:

y=mx+b

y=(0)x+5

y=5

Hence, the equation of the line is y=5.

Find the corresponding possitive angle by adding to the angle t 2pi:

Identify the coordiantes using a unit circle:

Solution

We are asked to factorize the following questions

Question F:

Question G:

Final Answer

The answers to questions F and G are:

I have 42 dimes in my piggy bank according to the given condition of 66 coins and amount $10.20 and used the system of equation as well as substitution method.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system. A group of two or more equations that share the same variables is known as a system of equations. A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations.

Finding the value of any variable from one equation in terms of another variable is the first step in the substitution method. For instance, if there are two equations, x+y=7 and x-y=8, we can deduce that x=7-y from the first equation. Applying the substitution method begins with this.

Here,

x+y=66    ......(1)

1 dime values 10 cents.

1 quarter values 25 cents.

10x+25y=1020       ........(2)

x=66-y

10(66-y)+25y=1020

660-10y+25y=1020

15y=360

y=360/15

y=24

x=66-24

x=42

I used the system of equations and the substitution method to determine that I have 42 dime coins in my piggy bank in accordance with the requirement of 66 coins totaling $10.20.

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The coterminal of angle with measure x is x + 360 degrees

Example:

If x = 30 degrees, then

The coterminal of x is 30 + 360 = 390 degrees

The coterminal of 128 degrees is 128 + 360 = 488 degrees

Then the answer is D

To find the square root of a negative number use the next:

For -6:

You can write -6 as the product of 6 and -1:

The square root of a product is the same as the product of the square root if each of the factors:

As the square root of 6 is not a exact number (it has many decimals) you leave the square root of 6 as it is. The square root of -1 is i; then, the square root of -6 is:

The standard deviation for a total of 200 games is 5.3735.

Let X = number of home runs of this player in 200 games played by him.

p = probability that a this player hits a home run in a single game and this is given to be 0.175.

Where np = Mean of X and √{np(1 - p)} is the standard deviation of X.

Here n = 200 and p = 0.175. So, the standard deviation for a total of 200 games is the standard deviation for a total of X

= √(200 x 0.175 x 0.825) / 2

= 5.3735

The value is 5.3735.

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Probability that Deandre missed at least 1 day is;

Write out the values of each probability and sum them

Hence,

The probability that Deandre missed at least 1 day is 0.93

Multiplication of coefficients and variable

It's given the expression:

You have the following numbrs:

897

12,000

8190

327

In order to determine if the previous numbers are divisibles for numbers between 2 and 10, you take into account the following points:

- If last two digits are divisible by a number, and the part of the number without the last units is divisible too, you can consider that the complete number is divisible too.

- If the last digit is 0, then the number is divisible by 2 and 5 and 10.

- If the number is even, it is dividible by 2.

- In case a number ends in varios zeros you can consider if the digits before the zeros are divisible by a specific number.

- 897 is divisible by 3, because 97 is divisible by 3 and 800 too.

- 12,000 is divisible by 2, 3, 4, 5, 6, 8 and 10, because it is an even number, ends in 0 and the first digits are divisible by 3, 4, 6.

- 8190 is divisible by 2, 3, 5, 6, and 10, becaues it is even, ends in 0 and the number of last two digits is divisible by 3 and 6 and 8100 too.

- 327 is divisible by 3, because number of last two digits is divisible by 3 and 300 too.

The symmetry of a quadratic equation is given by the line that passes through its vertex, so in order to find the axis of symmetry we need to find the coordinate of the vertex, which is done below.

Where "a" is the number multiplying the square factor and "b" is the number multiplying the factor that isn't squared. To find these two constants we need to expand the equation given.

We have that a = 1 and b = 4, therefore:

The axis of symmetry for this quadratic equation is x=-2.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

The visual depiction of numbers, such as fractions, integers, and whole numbers, spread out uniformly along a single horizontal line is known as a number line. A number line can be used as a tool for operations like addition and subtraction as well as comparison and sorting of numbers.

Given:

As from the Figure we have

-1 3/4 = -7/4 = -1.75, which is represented by point 1 on the number line.

and, 14/8 = 1.75, which is represented by point 7 on the number line.

and, 1.125, which is represented by point 6 on the number line.

and, -0.875, which is represented by point 4 on the number line.

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There are 4 quarts in a gallon so the price of one gallon that they have given us has to be split into four so $4.76/4 =$1. 19/quart

Question:

Solution:

This computer program carries out a single mathematical operation in

then, to complete 2.5 x 10^3 mathematical operations the program will take a time of:

thus, the correct answer is:

To round the nearest hundred the digit in the hundred column and test digit in the tens column.

To round the nearest hundred the digit in the hundred column is rounding digit and the digit in the tens column is test digit.

We find the rounding digit in hundred column is 3. Then we look out the test digit 2 to the right of the 3 in the tens column. Because 2<5 we round down and leave the 3 in the hundred column. Then replace the two rightmost digits with 0's.

The 9,321 rounded to the nearest hundred is 9,300.

SOLUTION

The Point of a co-ordinate is always written as

Giving a point

For instance x=2 and y=2, the point will be

If the coordinate of x and y are reversed, the point will remain the same

Hence

the points with the same x- and y-coordinates will give the same location if the coordinate is reversed.

Therefore The Third option is correct (c)

Answer: i donno

Step-by-step explanation:

ask Professor Ahmad Shaoki

Volume of object = 42 cubic cm

Surface area of object = 96 square cm

The given figure is a triangular prism.The formula for calculating its volume is expressed as:

where:

B is the base area

H is the height of prism

Determine the surface area of the prism

The surface area if the sum of all the faces of the prism.The faces consists of 3 rectangles and 2 triangles. The surface area is calculated as:

Hence the surface area of the object shown is 96 square cm

Answer: nonic

Step-by-step explanation:

Answer:

[tex]\frac{5}{2}[/tex] or 2.5cm

Step-by-step explanation:

Hello! Let's help you with your question here!

Let's start by working out what we know and what we need. So, we know that P is a circle and Q is the shape of a quarter circle with a radius of 20cm. The area of Q is 9 times the area of P and we must find the radius of P.

To start, we're looking for area, so we should at least start looking at the area of a circle, given radius, which is:

[tex]A=\pi r^2[/tex]

Now, we don't necessarily know r (radius) and the area either. However, we can try to use the quarter circle as our guide for the full circle. So, we want to find the area of the quarter circle, we can do that by using this formula!

[tex]A=\frac{1}{4} \pi r^2[/tex]

The reason why we put a [tex]\frac{1}{4}[/tex] at the front of [tex]\pi r^{2}[/tex] is because we're only solving for a quarter of a circle instead of the entire circle.

Now that we have our formula! We can calculate the area of the quarter circle as follows:

[tex]A=\frac{1}{4}\pi 15^2[/tex]

[tex]A=\frac{\pi 15^2}{4}[/tex]   -We combine the fraction [tex]\frac{1}{4}[/tex] into the rest of the equation.

[tex]A=\frac{225\pi }{4}[/tex]   - Evaluating [tex]15^2[/tex]

Now that we have the area of the quarter circle, we can now work on the full circle. What we know is that the area of A is 9 times of B, since we're finding the radius of B, we can essentially plug in the area and solve for the radius of the full circle. That would be as such:

[tex]A=9\pi r^2[/tex]   -We're using the area of circle A to find the radius of B.

[tex]\frac{225\pi }{4} =9\pi r^2[/tex]   - Plugging in the area of the quarter circle.

[tex]\frac{225\pi }{4}/9\pi =\frac{9\pi r^2}{9\pi }[/tex]   - We divide [tex]9\pi[/tex] to get rid of it on the right side.

[tex]\frac{25}{4} =r^2[/tex] - When dividing by [tex]\pi[/tex], the numerator [tex]\pi[/tex] gets cancelled out.

[tex]\sqrt{\frac{25}{4} }=r[/tex]   -We square root to get rid of the squared.

[tex]\frac{5}{2}=r[/tex]    - Square rooted both numerator and denominator.

And there we have it! We finally get a radius of [tex]\frac{5}{2}[/tex] or 2.5cm.

Given the two sets:

we can write the product set of A and B in the following form:

next, we have that the number of elements in A is 2 and the number of elements in B is 3, then, we have:

finally, the equation that involves the numerals of the previous parts is:

where n(A) and n(B) represents the number of elements in A and B respectively.

We have a rigth triangle, where we have to find the measure of x.

We can use trigonometric ratios to relate the lengths of the sides and the measure of x.

The lengths we know are from the hypotenuse and the adyacent side of x, so we can use the following trigonometric ratio:

Answer: x = 51.4°

Answer;

Explanation;

Here, we want to get a number

Since the number is not known at the moment, we can start by identifying the number with an a;phabet

Let us call this n

If 1 is added to the number

mathematical representation;

And the sum is tripled;

The result is 5 more than the number

5 more than the number is simply;

So, we equate this to what we had initially as follows;

We can now solve this equation for n

Given:

A pound of chocolate costs 7 dollars.

To find:

The equation represents the total cost c for buying p pounds of chocolate.

Solution:

It is given that a pound of chocolate costs 7 dollars. So,

Since the cost of p pounds of chocolate is c. So,

Thus, the answer is c = 7p.

Answer:

Step-by-step explanation:

According to the given data we have the following function:

f(x)=3x-6

To determine f(8)​ we would have to plug in into the equation the 8 and then proceed to calculate it, so:

If f(x)=3x-6

Then, f(8)=3(8)-6

f(8)=24-6

f(8)=18

Given:

• Slope, m = 1/5

• y-intercept = 13

Let's write the equation of the line.

To write the equation of the line, apply the slope-intercept equation of a line:

Where:

m is the slope

b is the y-intercept.

Thus, we have:

m = 1/5

b = 13

Plug in the values in the equation:

Therefore, the equation of the line is:

Given:

Passing grade = 70

Formula for adjusted grade, A:

Given a passing adjusted grade of 70, let's find the raw score, R.

To solve for R, substitute 70 for A and solve for R.

We have:

Divide both sides by 10:

Take the square of both sides:

Therefore, the raw score a student would need to have a passing adjusted grade of 70 is 49

ANSWER:

49