The length of a rectangle is 4yd longer than its width.
If the perimeter of the rectangle is 68yd, find its length and width.

Answer:

Average= [tex]\frac{25}{72}[/tex]

Step-by-step explanation:

o find the average add up the values and divide the sum by the number of values.

Rewriting all values as fractions, rewriting any negatives if necessary and, setting up as an addition problem

The least common denominator (LCD) is: 24.

Rewriting as equivalent fractions with the LCD:

Rewriting numerators over the common denominator,

Totaling the numerator:

= [tex]\frac{25}{24}[/tex]

Dividing by the number of values: 3

[tex]\frac{25}{24}[/tex] ÷3 =[tex]\frac{25}{24}[/tex] ×[tex]\frac{1}{3}[/tex] = [tex]\frac{25}{72}[/tex]

Average of the fractions is:

Average= [tex]\frac{25}{72}[/tex]

Answer: 120 ==> scale

8.4 m==> longer side

Step-by-step explanation:

6 m=

6*100 cm=600 cm

600/5=120 ==> scale

7*120=840 cm

840 cm=

840/100 m=8.4 m ==> longer side

Answer: 10

Step-by-step explanation: First you decide that each container can fill 3/4 of a cup. You have 8 cups so you need to divide 8 by 3/4 which will give you the answer of 10.666 repeating so the answer is you can only fill up 10 containers.

Answer:

172.78

Step-by-step explanation:

The geometric transformation which will not  produce the image ∆A'B'C' is an option (B) reflection across the x-axis followed by a reflection across the y-axis

In this question, we have been given a triangle ABC and the transformed triangle A'B'C'

Also, in the graph the first triangle is at A(-3, 0), B(-2, 3), C(- 1, 1) and the Second triangle is at A prime (0, -3), B prime (3, -2), C prime (1, -1).

Consider the graph as shown below.

From the coordinates of vertex of triangle ABC and triangle A'B'C' we can observe that,

A(-3, 0) -> A'(0, -3)

B(-2, 3) -> B'(3, -2)

C(-1, 1) -> C'(1, -1)

For each vertex,

x coordinate of triangle ABC = y coordinate of triangle A'B'C'

and y coordinate of triangle ABC = x coordinate of triangle A'B'C'

This means, the geometric transformation of triangle ABC is reflection across the line y = x

But the reflection across the x-axis followed by a reflection across the y-axis.

Therefore, the geometric transformation which will not  produce the image ∆A'B'C' is an option (B) reflection across the x-axis followed by a reflection across the y-axis

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The amount that decreased in dollars is equal to $ 645 and the money left in the account at the end of the year is $ 7955.

The amount of investment that Abdul opened an account with = $ 8600

The amount decreased by 7.5 %.

So, the amount left will be calculated by first using the percentage to find the amount that decreased.

Amount decreased = 7.5 % of 8600

Amount decreased = 0.075 × 8600

Amount decreased = $ 645

Amount left at the end of the year = $ 8600 - $ 645

Amount left at the end of the year = $ 7955

Therefore, the amount that decreased in dollars is equal to $ 645 and the money left in the account at the end of the year is $ 7955.

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Answer:

63 and 16,000

Step-by-step explanation:

The value of st is 30.4

As S is the point in RT, it implies that RS+st=Rt. Therefore according to the question,

3x+6x-5=58

⟹9x=58-5

or

9x=53

⟹x=5.9

RS = 3×5.9=17.7

st=(6×5.9)-5=35.4-5=30.4

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The slope of the line is 1.

The slope of a line is the ratio of the amount that y increases as x increases some amount

To calculate the slope of the graph, we use the formula below.

Formula:

From the question,

Given:

Substitute these values into equation 1

Hence, the slope of the line is 1.

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Answer:

Step-by-step explanation:

sin(A)=2/5

[tex]cos^2(A) +sin^2(A)=1\\cos^2(A)+[\frac{2}{5}]^2=1\\cos^2(A)+\frac{4}{25}=1\\ cos^2(A)=1-\frac{4}{25}\\ cos^2(A)=\frac{21}{25}\\ cosA=\frac{\sqrt{21} }{5}[/tex]

The equation that represents Diego's cash flow is cash flow = $3,000-$2,715.

Cash flow is the difference between cash inflows and cash outflows. Cash inflow are additions to the cash flow. An example of cash inflow is monthly income. Cash outflow would reduce the cash flow. An example of cash inflow is expenses.

Cash inflow = income - expense

$3,000 - $2,715

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The value of the expression 2x - 17 is 3

The expression is given as

-3x + 6 = -24

Subtract 6 from both sides

-3x = -30

Divide both sides by -3

x = 10

Multiply by 2

2x = 20

Subtract 17 from the sides

2x - 17 = 3

Hence, the value of the expression 2x - 17 is 3

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The sum of the given infinite geometric series is; 32

The general formula for finding the sum of an infinite geometric series is s = a₁/(1 - r)

where;

s is the sum

a₁ is the first term of the series

r is the common ratio.

To find the common ratio, use the formula: r = a2⁄a1

where a2 is the second term in the series and a1 is the first term in the series.

Thus;

r = 2²/4²

r = 1/2

Thus;

S = 4²/(1 - 1/2)

S = 16/(1/2)

S = 32

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Solution :

solve by considering data :

The perimeter of a rectangular pool is 56 meters. If the length of the pool is 16 meters, then find its width.

Here the perimeter and the length of the rectangular pool are given. We have to find the width of the pool.

The perimeter P of a rectangle is given by the formula, P=2l+2w, where l is the length and w is the width of the rectangle.

Given that, the perimeter is 56 meters and the length is 16 meters. So, substitute these values into the formula.

56=2(16)+2w

Simplify.

56=32+2w

Subtract 32 from both sides.

24=2w

Divide each side by 2 .

12=w

Therefore, the width of the rectangular pool is 12 meters.

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Table is attached below-

1) 1 m² = 10.75 tiles

2) 10 m² = 107.5 tiles

3) 9.3 m² of tiles = 100 tiles

4) a m² = 10.5a tiles

We have been given that

Every square meter of ceiling requires 10.75 tiles.

we have find missing values in the table.

We know,

1 square meter of ceiling =  10.75 tiles.      ...(i)

1. Therefore, the number of tiles corresponding to 1 square meter of         ceiling is 10.75.

Multiply both sides by 10.

10×1 square meter of ceiling =  10×10.75 tiles.

10 square meter of ceiling =  107.5 tiles.

2. Therefore, the number of tiles corresponding to 10 square meter of ceiling is 107.5.

Divide both sides by 10.75 in (i).

(1/10.75) square meter of ceiling = 1 tile.

Multiply both sides by 100.

(100/10.75) square meter of ceiling = 100 tiles.

On approximating the value, we get

9.3 square meter of ceiling = 100 tiles.

3. Therefore, the square meters of ceiling corresponding to 100 tiles is about 9.3.

Multiply both sides by a in (i).

a×1 square meter of ceiling =  a×10.75 tiles.

a square meter of ceiling =  10.75a tiles.

4. Therefore, the number of tiles corresponding to a square meter of ceiling is 10.75a.

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The answer is 24 - 22i

The answer we got is a complex number.

We are asked to find out the multiplication of a complex number and a real number.

The general form of a complex number is a + bi.

If we need to find the product of a complex number and a real number,

then, we need to multiply the real and imaginary parts by the real number and write down the answer.

The real number given is 2.

And the complex number given is 12 - 11i.

The real part of the complex number is 12.

And the imaginary part of the complex number is -11.

When the real part of the complex number is multiplied by the real number, we get 12 × 2 = 24.

When the imaginary part of the complex number is multiplied by the real number, we get (-11) × 2 = -22

Therefore, the required complex number is 24 - 22i

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Answer:

I think it is -5

Step-by-step explanation:

Answer:

For the first question:

For the second question:

Step-by-step explanation:

Hope it helps! =D

==================================================

Explanation:

x = cost of one dinner

4x = cost of four dinners

50-4x = the difference in the cost of $50 vs 4x dollars

To ensure this difference is never negative, we use absolute value to form the expression |50-4x|

Set this equal to 5 since we want this distance or difference to be 5 units above or below 50

|50-4x| = 5

|50 - 4x| - 5 = 0

Answer:

l 50 - 4x l - 5 = 0

Step-by-step explanation:

Answer:

TRUE

Step-by-step explanation:
na sa inyo na answer

Answer:

Add your questions

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

a=A/8

Step-by-step explanation:

This MIGHT be the answer, I am 99% sure!

Answer:

12 People

Step-by-step explanation:

To start you have 8 people for sure. Then you know that there are 4 fewer children. So then you subtract 4 from 8 and get four. Four plus eight is twelve!

The number of people in line will be 12.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

There are 8 adults in line for a ride. The line has 4 fewer children than adults. Then the number of children will be

⇒ 8 - 4

⇒ 4 children

Then the number of people in line will be

⇒ 8 + 4

⇒ 12

The number of people in line will be 12.

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Answer:

147 different choices.

Step-by-step explanation:

(7)(3)(7) = 147

Hope this helps

Answer:

1.05 dollars per popsicle

Step-by-step explanation:

x is the price per popsicle. In order for you to make 6 dollars of profit, each box is going to cost 10.50 dollars because 4.50 is your amount of expenses.  

Profie= revenue-expenses

6= revenue-4.5

revenue=10.5

If you charge 10.5 per box, and each box has 10 popsicles, then one popsicle is 10.5/10=1.05 dollars per popsicle.

There are 20 bicycles at the Main Street station.

According to question statement, A bicycle-sharing station on Main Street has 5 times as many bicycles as a station on Park Avenue. There are 24 bicycles at the given two stations.

We are supposed to know the number of bicycles at the Main Street station.

Let us assume that the number of bicycles at the Park Avenue station is "x". Then, number of bicycles at the Main Street station will be "5x".

We will have to form a Linear Equation of single variable "x" as per the conditions based in the question statement, and solving for x, we will obtain our desired answer.

As there are 24 bicycles at the two stations therefore,

[tex]x + 5x = 24[/tex], will be our equation.

Solving the equation for x, we get

[tex]x + 5x = 24\\6x = 24\\x=\frac{24}{6} \\or x=4[/tex]

Therefore the number of bicycles at the Park Avenue station is 4.

And the number of bicycles at the Main Street station will be 5x i.e., [tex]5*4 = 20[/tex].

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