Mathematics College

The diagram shows two squares constructed on the sides of a rectangle. Write an expression for the area of Square C in terms of the areas of Square A and Rectangle B. Then simplify to find the area. (N RN.1.1-2 HELP PLSSS

Answers

Answer 1

Step-by-step explanation:

Since area of Square A = 7 ft²,

Side length of Square A = √7 ft.

Length of Rectangle B = √7 ft

Width of Rectangle B = 4/√7 ft

Hence Area of Square C

= (4)² / (√7)² ft² = 16/7 ft².

Answer 2

The area of Square C is the square of the height of the Rectangle B.

Correct responses:

[tex]\underline{Area \ of \ square \ C = \dfrac{\left(Area \ of \ Rectangle \ B \right)^2}{Area \ of \ Square \, A} }[/tex]

[tex]Area \ of \ square \ C = \underline{\dfrac{16}{7}} \, ft.^2[/tex]

Methods used for finding the area of Square C

The given area of square A = 7 ft.²

The given area of rectangle, B = 4 ft.²

Let s represent the side length of square C and let S represent the side length of square A, we have;

Area of rectangle B = S × s = S·s

Area of square A = S × S = S²

Area of square C = s × s = s²

[tex]\mathbf{\dfrac{(Area \ of \ rectangle \ B)^2}{Area \ of \ square \ A } } = \dfrac{\left(S \cdot s \right)^2}{S^2} = \dfrac{S^2 \cdot s^2}{S^2} = s^2 = Area \ of \ square \ C[/tex]

Therefore, the expression for the area of Square C in terms of the area

of Square A and Rectangle B is presented as follows;

[tex]\underline{Area \ of \ Square \ C = \dfrac{ \left (Area \ of \ rectangle \ B \right)^2}{\left(Area \ of \ square \ A\right)}}[/tex]

Which gives;

[tex]\underline{Area \ of \ square \ C = \dfrac{\left(4 \, ft.^2 \right)^2}{7 \, ft.^2}}[/tex]

By simplification, we have;

[tex]\mathbf{\dfrac{\left(4 \, ft.^2 \right)^2}{7 \, ft.^2}} = \dfrac{16}{4} \, ft.^2[/tex]

[tex]Area \ of \ square \ C = \underline{ \dfrac{16}{7}} \, ft.^2[/tex]

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Related Questions

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Answer:

option C

Step-by-step explanation:

(6+3)= 9

9 × 4= 36

36-2= 34

hope it helps! please make me brainliest..

Thank you! Have a good day ahead!

Answer:

(6+3)*4-2

Step-by-step explanation:

(6+3)*4-2

9*4-2

36-2

PEMDAS

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What is X 2(x+5)=3x+1

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Step-by-step explanation:

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Answer:

C. 65

Step-by-step explanation:

All the angles in a triangle add up to 180 degrees.

180-62-53 = 65

A marathon runner's time was 2% longer Tuesday than Monday. How much time did he log on Tuesday when compared to Monday.
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Step-by-step explanation:

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x equals 10

Step-by-step explanation:

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A set of data is summarized by the stem and leaf plot below.

Stem Leaf
1 0 0 2 2 4 5 5 5 6 7 8 8 9 9 9 9
2 0 0 0 3 3 4 5 8 8
3 0 0 1 1 3 4 5 5 5 6 6 6 6 7 7 8 8 8 9 9
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The value 52 appears _________time(s) in the data set. The value 47 _________appears time(s) in the data set.

Answers

Answer:

0 ; 1

Step-by-step explanation:

Given the dataset :

Stem _____ Leaf

1 _______ 0 0 2 2 4 5 5 5 6 7 8 8 9 9 9 9

2 _______0 0 0 3 3 4 5 8 8

3 _______0 0 1 1 3 4 5 5 5 6 6 6 6 7 7 8 8 8 9 9

4 _______ 1 2 2 3 3 3 5 5 6 6 7 8 8 9 9

The value 52 appears 0 times in the dataset

This is because the stem does not contain the digit 5.

The value 47 appears 1 time(s) in the data set ; stem of 4, leaf 7

what is the remainder and quotient of 11/3

Answers

Answer:

The remainder of 11 divided by 3 is 2. The quotient is 3.

Step-by-step explanation:

3 goes into 11 three times. 3 x 3 = 9. 11 - 9 = 2. 3 can't go into 2 so bring the two up and you get your answer of 3 r 2.

Lou buys 20 pounds of apples for $40. How many pounds can she buy for one dollar?

Answers

Answer:

She can buy 2 pounds per dollar.

Step-by-step explanation:

The sum of seven and the quotient of a number x and eight.

Answers

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Answer:

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Step-by-step explanation:

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Answer:

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for the linear function f, the graph of y=f(x) in the xy-plane passes through the points (0,2) and (9,9). what is the slope of y=f(x)?

Answers

Answer:

[tex]slope = \frac{(y _{2} - y _{1})}{(x _{2} - x _{1})} \\ = \frac{(9 - 2)}{(9 - 0)} \\ = \frac{7}{9} \\ hence \: slope \: is \: \frac{7}{9} [/tex]

Maximum value of a+b if ab=36 is

Answers

Answer:

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Step-by-step explanation:

Finding the factors of 36 and adding them together to get the greatest sum. 18(2)=36 18+2=20

Kelsea and Landon are playing in a park standing 100 feet away from each other. They both see a bird flying above them. The angles of elevation from each person to the bird are shown. How high is the bird from the ground? Round your answer to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

use an ASA triangle with law of sine

since we know that 180 = 20 +45 + C .. solve for C = 115°

now use law of sines c/ sin(C) = b/sin(B) .. and solve for b

Sin(20)*100/sin(115) = b

b = 37.73774 ft

that's the hypotenuse of the 45 triangle

SOH CAH TOA to remember how trig functions fit

use b*Cos(45) = adj

26.6846 = adj

The bird is 26.7 ft. from the ground

Which expression represents "8 times the difference of 52 and 9"?

Answers

Answer:

(52-9)*8

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Answer:

8(52-9)=

8x41=

328

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Henry went clothes shopping and bought 3 pairs of shorts for $22.99 each, 2
shirts for $32.99 each and one pair of shoes for $54.99. What is the most
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A. $135
B. $184
C. $190
D. $223

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Answer:

Step-by-step explanation:

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Answers

Answer:

0.66666666666

Step-by-step explanation:

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Sorry What do we need to look for here?

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Answer:

Step-by-step explanation:

24.395 times. Or 24 times if it’s to the nearest whole number.

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Answer:

Step-by-step explanation:

22 is 44% of 50. It's 50 because it's techincally half if you look at it. I don't know how to really explain that well. But the answer is 50, trust me.

50

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17 ft2

41 ft2

495 ft2

103 ft2

Answers

Answer:

103 ft.

Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

32. A volleyball team played 25 games. The ratio of games won to
games lost was 6:4. How many games did the team win?

Answers

Number of volleyball games team win is 15 games

Given that;

Number of volleyball games = 25 games

Won to lost ratio = 6:4

Find:

Number of volleyball games team win

Computation:

Number of volleyball games teams win = 25[6 / (6+4)]

Number of volleyball games teams win = 25[6 / 10]

Number of volleyball games team win = 15 games

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Answers

Answer:

Step-by-step explanation:kytiyfkutfdc

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $53,533. The variable costs will be $12.50 per book. The publisher will sell the finished product to bookstores at a price of $24.25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Answers

9514 1404 393

Answer:

4,556

Step-by-step explanation:

Revenue from the sale of n books is ...

R = 24.25n

Production cost for n books is ...

C = 53533 +12.50n

These are equal for ...

24.25n = 53533 +12.50n

11.75n = 53533

n = 53533/11.75 = 4556

The publisher must produce 4556 books so sales will equal production cost.

7. At an online retailer, the price of the camera is discounted 15% to $212.50. What was the
price of the camera before the discount?

Answers

Answer:

$250

Step-by-step explanation:

discounting 15 percent is the same as marking something for 85 percent. This is the same as multiplying by .85

set up equation and solve

.85x=212.50

x=250

Clare subscribes to an online music streaming service
for a yearly fee of $96. Starting next month, there will
be a 12% increase in the fee.
The ad for another music streaming service is shown
below. Should Clare switch? Explain.

Answers

Answer:

She should go with service 2 because it is, cheaper. Service 1 cost $107.52, but service 2 cost only $105.

Step-by-step explanation:

Cost now+increase$=new cost

(Part=percent*whole)

Increase=percent increase*cost now

i=12%*$96

i=0.12*96=$11.52

$96+11.52=107.52

Service two⬇️

8.72*12=$105

Yes Clare should switch to service 2 because; cheaper it costs only $105 which is lesser than $107.52

How to Calculate Yearly Fee?

To find the new cost, we will use the expression;

New Cost = Present Cost + increase

However,

Increase = percentage increase * present cost

Increase = 12% * $96

Increase = 0.12 * 96

Increase = $11.52

Thus;

New Cost = $96 + 11.52

New Cost = $107.52

For Service two;

We are told that digital streaming costs $8.75 per month. Thus;

Cost = 8.75 * 12

Cost = $105

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You have a square that has a side length of $1$ centimeter. Each minute, $2$ centimeters are added to the side length. After $10$ minutes, what will be the difference between the area of the last square and the area of the initial square in square centimeters (do not include the units in your answer)?

Answers

Answer:

Difference in area of the last square and the initial square = 440 cm²

Step-by-step explanation:

Length of the side of a square = 1 cm

Area of the square = (side)² = 1 cm²

Addition of side length every minute = 2 cm

After x minutes length of each side of the square = (1 + 2x) cm

If x = 10 minutes

Length of each side of the square = [1 + 2(10)]

= 21 cm

Area of the square after 10 minutes = (21)²

= 441 cm²

Therefore, difference in area of the last square and area of the initial square

= 441 - 1

= 440 cm²

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