Amusement Park Buildings Part 1 There are two buildings that you want to have in the amusement park, but the size hasn’t been determined yet. Although you don’t know the specific dimensions, you do know the relationships between the sides. The first is the rectangular gift shop. You know that the length will be 20x+24 feet and the width will be 36x-20 feet. 1. Write the expression that represents the area of the gift shop, in terms of x. 2. Write the expression that represents the perimeter of the gift shop, in terms of x. 3. If the perimeter is going to be 176 feet, what are the dimensions of the building? Part 2 The next building is the gazebo that will be in the shape of a regular hexagon. (What does regular mean?) Each side will be 5x + 21 4. Write the expression that represents the perimeter of the gazebo, in terms of x. 5. If the perimeter is going to be 36 feet, what are the dimensions of the building?

Answer:

1/5(p+2t) = r

Step-by-step explanation:

p = 5r – 2t

Add 2t to each side

p+2t = 5r – 22t

(p+2t) = 5r

Divide each side  by 5

1/5(p+2t) = r

Answer:

[tex] r = \frac{p + 2t}{5} \\ [/tex]

Step-by-step explanation:

[tex]p = 5r - 2t \\ p + 2t = 5r \\ \frac{ p + 2t}{5} = \frac{5r}{5} \\ r = \frac{p + 2t}{5} [/tex]

hope this helps

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good luck! have a nice day!

Answer:

x=35

Step-by-step explanation:

When a is parallel to b, the two angles will add to 180

x+ 3x+40=180

Combine like terms

4x+40 =180

Subtract 40 from each side

4x= 180-40

4x= 140

Divide by 4

4x/4 = 140/4

x=35

Answer: Her double time pay rate = $24.9 per hour.

Step-by-step explanation:

We have given that, Daja is paid $12.45 an hour.

In other words, her usual time pay rate = $12.45 per hour

Also, If Dahja worked overtime and gets paid double time.

Then, her double time pay rate = 2 x (usual time pay rate) [as double means 2 times]

= 2 x  $12.45 per hour

= $ 24.9 per hour

Hence, her double time pay rate = $24.9 per hour.

i.e. Daja is paid $24.9 an hour for overtime.

Answer:

is two quadrilaterals are congruent, ten there must be 4 pairs of corresponding sides.

Answer:

4 pairs of corresponding sides

Step-by-step explanation:

if two quadrilaterals are congruent, then they have the same sides and are identical

quadrilaterals have 4 sides

therefore, each of their 4 sides are identical to each other

making the answer 4 pairs of corresponding sides.

hope this helps!!!

(btw i just took the gradpoint test and the answer was right)

Answer:

64π

Step-by-step explanation:

Answer:

See below;

Step-by-step explanation:

1 . Consider the step below;

[tex]m< DCA = 90 degrees - Given ,\\m< ACB = 180 degrees - Straight < ,\\\\m< DCA + m< DCB = 180,\\m< DCB = 90 degrees,\\\\By Parts Whole Postulate - m< DCB = m< DCE + m< ECB,\\m< DCB = m< DCE + m< ECB,\\90 = 53 + g,\\Conclusion ; ( g = 37 degrees )[/tex]

Thus, Solution ; g = 37 degrees

2 . Knowing that these circle are " circumscribed " in this rectangle so that they are perfectly aligned, considering the length of this rectangle to be 20 inches, let us determine the radius;

[tex]Diameter Of 1 Circle - ( 20 inches ) / 4 = 5 inches,\\Radius of 1 Circle = ( 5 inches ) / 2 = 2.5 inches,\\\\Area of 1 Circle = \pi r^2 = \pi * ( 2.5 )^2 = 6.25\pi,\\Area of 4 Circles = 6.25\pi * 4 = 25\pi,\\Area of 4 Circles = Area of Shaded Region,\\\\Conclusion ; Area of Shaded Region = 25\pi[/tex]

Thus, Solution ; 25π

3. Let us first consider the given, then solve for the value of a, b, e;

[tex]Angles c + e - Vertical Angles,\\Angles a + c - Complementary,\\( a + c ) = 90,\\Angle c = 56 degrees,\\a + 56 = 90,\\Conclusion ; a = 34 degrees,\\\\[/tex]

[tex]m< e = m< c,\\Conclusion ; e = 56 degrees[/tex]

[tex]m< e + m< a + m< b = 180 - Straight Line,\\56 + 34 + m< b = 180,\\m< b = 180 - 56 - 34,\\Conclusion ; b = 90 degrees[/tex]

Solution; a = 34°, b = 90°, e = 56°

Answer:

The white paint is 1.5 times the red paint. 1.5 is the same as 1 1/2 or 3/2. x = 3/2 y

Step-by-step explanation: In the graph there is one point where both x and y is a whole number.  3,2  . 3 white paint is equal to 2 red paint. You divide 3 by 2 which is 1.5, or 1 1/2 or 3/2. The relationship is that x is 3/2 times y. x = 3/2y

Answer:   OA)  5:3

Step-by-step explanation:

5:3

5 to 3.  Or 5/3.      Are the 3 ways that you.can write a ratio.  

Answer:

OA, OB, OD

Step-by-step explanation:

It does depend on which side each number is on. If you are comparing the stawberries to whipped cream it would be 5:3 (OA).

But if you were to compare whipped cream to stawberries it would be 3:5 (OB) or 3/5 (OD)

Answer:

B

Step-by-step explanation:

P=(1/2)(1/2)=1/4

Answer:

The first one.

Step-by-step explanation:

For something to be considered to be a graph, every x value must have 1 y value. It does not matter if y values are the same, but you MUST make sure there is ONLY ONE of each value. So for example the second one wouldn't be a function because -5 appears twice for the x values, but with different y values. This would mean when graphed, it would fail the vertical line test (if you put a vertical line anywhere on the graph you will only get one point).

Answer:

The first one

Step-by-step explanation:

because it is the only one that actually applies to the function

Answer:

314.16ft²

Step-by-step explanation:

A = πr² = π · 10² ≈ 314.15927ft²

Answer:

100π ft²

Step-by-step explanation:

r= 10 ft

A= πr²= π*10²= 100π ft²

Answer: w = 125

Explanation: Since w is being divided by 5, to solve for w,

multiply both sides of the equation by 5.

On the left side, the 5's will cancel

and on the right side, 25(5) is 125.

So w = 125.

Please do not do this problem in your head.

Show the work that it takes to get w by itself.

Answer:

( -4920)

Step-by-step explanation:

we see that the first term is 3 and the common ratio between the succeeding terms is -3. so to  solve for the sum of the first 8 terms

 Sum = (a1)(1 – r^n) / (1 – r)

and substituting the known terms,we got  

  Sum = (3)(1 – (-3)^8)/(1 - (-3)) = -4920

Then the answer   = ( -4920)

Answer:

(x - 2)² + (y + 1)² = 9

Step-by-step explanation:

Circle equation: (x - h)² + (y - k)² = r²

Simply plug in your center (h, k) and your radius r and you have you final answer!

Answer: The next 5 numbers would be "33,37,41,45,49

Step-by-step explanation:

Answer:

4 is a coefficient

Step-by-step explanation:

4x - 10

x is the variable and 4 is the coefficient since it is next to the variable

-10 is the constant

4x is a term

4x-10 is a sum

Answer:

A) Coefficient.

Step-by-step explanation:

Answer:

Step-by-step explanation:

<6= 125 degrees

<3 = 125 degrees

x = 55 degrees

Answer:

Step-by-step explanation:

55° and ∠4 are corresponding angles made by parallel lines. Therefore, they're congruent.

∠4 = 55°

Lines s and t are parallel lines and ∠4 and x are the interior angles at the same side of the transversal l. Therefore, they're supplementary.

∠4 + x = 180°

55° + x = 180°

x = 180° − 55° = 125°

Answer:

42

Step-by-step explanation:

Average =

Sum of the terms/ number of terms

Terms here refers to the data or the values given

So,

The sum is 12+43+51+62= 168

The number of terms is 4

Therefore the average is,

168/4

= 42

Answer:

42

Step-by-step explanation:

Average =  

Sum

/Count

=  

168/4

=  42

MARK ME BRAINLIEST

Answer:

k=9

Step-by-step explanation:

m=–4=slope

slope formula= m = (y1–y2)÷(x1-x2)

In this case, we are missing the value of y1, so we just need to isolate it:

–4=(k–1)/(2-6)

simplify parentheses

–4=(k–1)/–2

multiply by –2 on both sides

8=k–1

add 1 to both sides

k=9

Thank You

Answer:

Area(PART)= 7.5 u^2

Step-by-step explanation:

RT=1 unit

PA=4 units

Distance between T (or R) and PA= 3 units

RT;PA = Bases

T (or R)--> PA= Altitude/Height

Area of trapezoid= Alt(B1+B2)/2

--> 3(1+4)/2

=> 3*5÷2

=15/2

=7.5

Thanks

Answer:

[tex]18m[/tex]

Step-by-step explanation:

[tex]P=4a=4*4.5=18m[/tex]

Answer:

Perimeter = 18m

Step-by-step explanation:

square = has four sides

P = perimeter

P = 4 · 4.5 = 18m

Perimeter = 18m

Answer:

x = 4, x = - 8

Step-by-step explanation:

(x+ 2)² = 36

√(x+2)² = + √36     √(x+2)² =  -√36  

x+2 = 6                     x+2 = -6

x= 4                          x = - 8

Given:

To find out:

Find the area of rectangle?

Formula used:

Area of rectangle = length × breadth

Solution:

We know that,

Area of rectangle = length × breadth

= ( x + 2 ) × 3

= 3x + 6

Answer: The area is  1 1/4. The perimeter is 6.

Step-by-step explanation: 2.45 is about 2.5.   5/8 is about 1/2.  To find the area we need to multiply length times width.  2.5 is  2 and 1/2 which is 5/2. 5/2 times 1/2 is 5/4. To simplify it divide 5 by 4 which is 1 with remainder 1. 5/4 is 1 1/4. Therefore the area is 1 1/4 meters squared. To find the perimeter we have to add length + length + width + width. . 2.5 is the same thing as 2 1/2.  5/8 is about 1/2 if we use benchmarks.     2 1/2 + 2 1/2 +  + 1/2 + 1/2 is 6. The perimeter is 6.

We began be finding the volume of each shape, the we subtracted the volume of the cone from the volume of the cube.

Volume of wood that remain = 436.6 cm^3

Given Data

Let us find the volume of the cone

Volume of cone = πr^2h/3

Volume of cone = 3.142*3^2*8/3

Volume of cone = 3.142*9*8/3

Volume of cone = 226.224/3

Volume of cone = 75.408cm^3

Let us find the volume of the cube

Volume of cube = L^3

Volume of cube = 8^3

Volume of cube = 512cm^3

Hence the volume of the wood that remains

= volume of cube - volume of cone

= 512 - 75.408

= 436.6 cm^3

Learn more about volume of solids here:

https://brainly.com/question/21036176

Answer:

[tex]y=\frac{5}{4} x + \frac{5}{4}[/tex]

Answer:

386 that lay eggs

Step-by-step explanation:

440-39= 401 hens

401hens- 15= 386

Answer:

386 that lay eggs

440-39= 401 hens

401 hens- 15= 386

:-)

Answer:

the answer is d

\can i get a brainliest pls

Answer:

the answer is 78

Step-by-step explanation:

3x6 is 18

4x3 is 12

4x3 is 12

6x6 is 36

added together it is 78