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3 years ago

The total area of the polygon is 176 square feet. Find the value of x.

Mathematics

2 answers:

My name is Ann [436]3 years ago

5 0

Answer:

x = 6 ft

Step-by-step explanation:

Total area of the given polygon = Area of triangle 1 + Area of rectangle 2 + Area of triangle 3

Area of triangle 1 = Area of triangle 3 = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(x)(8)$

= 4x square feet

Area of rectangle 2 = Length × Width

= 16 × 8

= 128 square feet

Total area of the given polygon = 4x + 128 + 4x

176 = 8x + 128

8x = 176 - 128

x = $\frac{48}{8}$

x = 6 ft

Serga [27]3 years ago

4 0

Answer:

The answer is six to one of the sides

Step-by-step explanation:

Total area of the given polygon = Area of triangle 1 + Area of rectangle 2 + Area of triangle 3

Area of triangle 1 = Area of triangle 3 =

= 4x square feet

Area of rectangle 2 = Length × Width

= 16 × 8

= 128 square feet

Total area of the given polygon = 4x + 128 + 4x

176 = 8x + 128

8x = 176 - 128

x =

x = 6 ft

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2. The path of a high diver is given by y = + (2x2 – 9x – 56), where y is the height of the diver

timofeeve [1]

Answer:

The diver will be 8 feet from the end of the board when he hits the water.

Step-by-step explanation:

The diver hits the water when y = 0.

To find the distance, we have to find the values of x when y = 0.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = (x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this problem, we have that:

$y = 2x^{2} - 9x - 56$

$2x^{2} - 9x - 56 = 0$

$a = 2, b = -9, c = -56$

Then

$\bigtriangleup = b^{2} - 4ac = (-9)^{2} - 4*2(-56) = 529$

$x_{1} = \frac{-(-9) + \sqrt{529}}{2*2} = 8$

$x_{2} = \frac{-(-9) - \sqrt{529}}{2*2} = -3.5$

It is a horizontal distance, so the answer is a positive value.

The diver will be 8 feet from the end of the board when he hits the water.

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3 years ago

There's 18 deer and 52 lions if 10 lions eat 17 deer how many deer are left

Mamont248 [21]

Answer:

1 deer

Step-by-step explanation:

18 deer minus 17 eaten leaves 1 deer

7 0

2 years ago

Read 2 more answers

Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign up for the trip, they must p

DanielleElmas [232]

Answer:

1. Let, Jamie needs "$ g" for the trip. Then, according to the question,

g = 600 -------------------(1)

2. Let, Stella needs "$ m" for the trip. Then, according to the question,

m = 600 -------------(2)

3. If Jamie washes x no. of cars and Stella makes y no. of pies, then,

25x ≥ 600 ≥ 15y -------------(3)

4. Yes, Stella can afford to sign up for the trip with the money she earns.

Step-by-step explanation:

Let, Jamie needs "$ g" for the trip. Then, according to the question,

g = 600 -------------------(1)

Let, Stella needs "$ m" for the trip. Then, according to the question,

m = 600 -------------(2)

if Jamie washes x no. of cars for $25 each and Stella makes y no. of pies

for $ 15 each, then, according to the question,

25x ≥ 600 ≥ 15y -------------(3)

Yes, Stella can afford to sign up for the trip with the money she earns. Because, she can make at most 40 pies for $15 each and

$ $40 \times 15$ = $ 600 = The amount of money Stella needs for the trip.

7 0

3 years ago

Football is selling boxes of candy as a fundraiser.Ms. South ordered three small boxes and two large box fora total of $36. Chri

JulsSmile [24]

Answer: The price of each small box is $4.8 and the price of each large box is $10.8.

Step-by-step explanation:

Let x = Price of each small box, y= price of each large box.

As per given,

3x+2y= 36 ...(i)

4x+y= 30 ...(ii)

Multiplying 2 to (ii), we get

8x+2y =60...(iii)

Subtract (i) from (iii), we get

5x= 24

x= 4.8

From (ii)

4(4.8)+y= 30

19.2+y=30

y= 10.8

Hence, the price of each small box is $4.8 and the price of each large box is $10.8.

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3 years ago

Solve by substitution x-y=12 x+y=18

slamgirl [31]

X = y + 12. You then substitute or plug in that from the first equation into the second equation. You get (y+12)+y=18, then you simplify to get your y value. In this case y = 3. The you can plug your y value into either equation. (x+3=18) or (x-3=12) or (x=3+12) either way you get x=15 and y=3.

3 0

3 years ago