Identify the domain and range of the function below.

Domain

Range

s = side length of square

4s = perimeter of square

L = length of rectangle

W = width of rectangle

P = 2L+2W = perimeter of rectangle

4s = 2L+2W .... since we want the perimeters the same

4s = 2(L+W)

s = 0.5(L+W)

s^2 = (0.5(L+W))^2 ... square both sides

s^2 = 0.25(L+W)^2

The last equation shows the area of the square, s^2, in terms of L and W. This way we can connect the square to the rectangle.

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The area of the rectangle is LW

Let's subtract this from the area of the square and see what we get

A = area of square = s^2

B = area of rectangle = LW

C = difference in area

C = A - B

C = s^2 - LW

C = 0.25(L+W)^2 - LW

C = 0.25(L^2+2LW+W^2) - LW

C = 0.25L^2+0.5LW+0.25W^2-LW

C = 0.25L^2-0.5LW+0.25W^2

C = 0.25(L^2-2LW+W^2)

C = 0.25(L-W)^2

Regardless of what we pick for L and W, the expression (L-W)^2 is always positive. Squaring a negative number leads to a positive result.

So C is always positive as long as [tex]L \ne W[/tex]

If C > 0, and C = A - B, then

C > 0

A-B > 0 .... replace C with A-B

A > B .... add B to both sides

This shows the square area is always larger than the rectangle.

Again this only works if L and W are different values. If L = W, then the argument falls apart because the rectangle becomes the square.

We make [tex]L \ne W[/tex] to have a nonsquare rectangle.

Answer:

Step-by-step explanation:

x2 + 2x - 7 + 11x2 - 5x - 1

Solving like terms

12x2 - 3x - 8

Answer:

60.5 pounds

Step-by-step explanation:

The total amount of pound is 181.5

And there are three pandas.

So 181.5 divide by 3 is 60.5

Answer:

20 containers

Step-by-step explanation:

Given:

D = 0.07N

Where,

D = Amount of deposits

N = Number of containers

If D = $1.40 find N

D = 0.07N

1.40 = 0.07N

Divide both sides by 0.07

N = 1.40 / 0.07

= 20

N = 20 containers

if you deposit $1.40, you will buy a total of 20 containers.

Answer:

1.23

Step-by-step explanation:

123

Answer:

The first one, there are no repeating x values

Step-by-step explanation:

Answer:

1.20 × 10^35

Step-by-step explanation:

There are 60 seconds in 1 min and there are 60 mins in 1 hour. So in an hour there are 60 × 60 = 3600 seconds. There are 24 hours in a day. In a day, there are 3600 × 24 = 86400 seconds. A year is 365 days. So in a year there are 86400 × 365 = 31536000 seconds.

[tex](3.8 \times {10}^{27}) \times 31536000 = 1.20 \times {10}^{35} [/tex]

Answer:

23

Step-by-step explanation:

7-5(1)+3(7)

7-5+21

2+21

23

Answer:

7-5+21 = 23

Step-by-step explanation:

7 - 5p+ 3q

7 - 5(1) + 3(7)

7 - 5 + 21

7 + 16

= 23 hope this helps :)

Answer:

x = undefined

Step-by-step explanation:

Expand brackets

4x - 1 = 4x + 4

Rearrange and make like terms next to each other

4x - 4x = 4 + 1

0x = 5

x = 5/0

when 0 is the denominator the answer is undefined

Answer: from what i calculated there is no solution

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

the diagnols are congruent meaning that the diagnol lines in the middle are the same length. So theoretically the left and right lengths are the same, and the top and bottom lengths are the same. The triagles named both have the same base and they're hieght is sbviouysly the same so they would be SSS each of the sides on one triangle coresspondes to the other.

Answer:

I believe it is

Step-by-step explanation:

None of the x and y values have the same number

Answer:

It is not the input 5 has 2 different output values, same as the input 3 it has more than one different output

Step-by-step explanation:

Hope this helps!

Answer:

  1.672 x 10 27

Step-by-step explanation:

Answer:

x would equal 23, so (x+92) would equal 115°, & (5x) would equal 115°.

Answer:

2744

Step-by-step explanation:

Let Al had x pennies initially.

Al agreed to give 3/7 of his pennies to Bev if she would give 3/7 of what she got from Al to Carl and if Carl in turn would give 3/7 of what he got from Bev to Dani.

So, as per the given condition,

The number of Pennies received by Ben from Al [tex]= \frac{3}{7} x[/tex]

The number of Pennies received by Carl from Bev

[tex]=\frac{3}{7} \times \frac{3}{7} x=\frac{9}{49}x[/tex]

The number of Pennies received by Dani from Carl

[tex]= \frac{3}{7}\times \frac{9}{49}x=\frac{27}{343} x[/tex]

Now, as Dani received 216 Pennies, so

[tex]\frac{27}{343} x =216[/tex]

[tex]\Rightarrow \frac{216\times 343}{27}=2744.[/tex]

Hence, initially, Al had 2744 Pennies.

Answer:

Option (A)

Step-by-step explanation:

Windmill is in the shape of a circle and each blade of the windmill is equally spaced.

There are 8 spaces in the windmill shown.

Therefore, angle between each blade = [tex]\frac{360}{n}[/tex]

Where n = number of blades

Angles between each blade = [tex]\frac{360}{8}[/tex]

                                               = 45°

To reach the position of blade U by blade P will cover 5 angles between the blades.

Therefore, angle of rotation covered by P to reach U = 5×45° = 225°

Option (A) will be the correct option.

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Explanation:

The domain is the set of all possible x values. The range is the set of all possible y values.

Since we don't have any repeated x values, we have a function. Any given input x leads to exactly one y output value. Visually plotting the points leads to the graph passing the vertical line test, which shows the relation is a function.

Answer:

x<6 should be the correct answer

Answer:

You have no apples then loose 11 more

Step-by-step explanation:

Trust

Answer: 19 weeks.

Step-by-step explanation: 600 - 125 = 475. This means he needs to save $475 more. 475 divided by 25 is 19. So the answer is he must wait 19 more weeks.

Answer:

19 weeks

Step-by-step explanation:

600=25x+125  

x=19

Answer:

First one, Third one, Fifth one, and the last one too.

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, make a ratio:

18 min/ 3mile = 6 min/mile

now multiply to finish the table:

1: 6

3: 18

5: 30

10: 60

25: 150

Shelly runs 2.5 miles every 18 mins. To find out how many minutes it takes her to run one mile, let's divide 18 by 2.5

18 mins / 2.5 miles = 7.2 mins / mile

Answer:

1/125

Step-by-step explanation:

=1/5*5*5

=1/5^3

=1/125

Using exponent rules, when a number is raised to a negative exponent, change the exponent to positive and make a fraction with 1 as the numerator and the number as the denominator:

5^-3 = 1/(5^3)

Answer:

[tex]y = - 4x - 3[/tex]

Step-by-step explanation:

[tex]y - 1 = - 4(x + 1) \\ y - 1 = - 4x - 4 \\ y = - 4x - 3[/tex]

Examine the operations above.

Answer:

x = 2

Step-by-step explanation:

10x - 7 = 7x - 1

10x = 7x + 6

3x = 6

x = 2

Answer:

x = 2

Step-by-step explanation:

Add seven to both sides to move it over to the right, then subtract 7x from both sides to move that over to the left.

You should be left with 10x - 7x = 7 - 1.

10x - 7x = 3x

7 - 1 = 6

3x = 6

Divide both sides by three to get your answer of x = 2.

Answer:6960

Step-by-step explanation:

(16•48)+(86•72)=6960

Answer:

ok

Step-by-step explanation:

Answer:

The midpoint of segment AB is (0, 2.5)

Step-by-step explanation:

Hope this helps!