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erma4kov [3.2K]
3 years ago
8

If x = 8 units, y = 3 units, and h = 10 units, find the area of the trapezoid shown above using decomposition.

Mathematics
2 answers:
kondaur [170]3 years ago
8 0
If by decomposition you mean breaking it ino parts then

break it itno 2 triangles and 1 rectangle

left to right

triangle with base y and height h
h=10
y=3
area of traignel=1/2bh
aera=1/2(10)(3)
area=5(3)
area=15

rectangel of legnth x and height h
area=legnth timwe width
x=8
h=10
area=8 times 10
aera=80


last triangle
should be same as other sinces same base (y) and same height (h)
15

add
15+80+15=120
goldfiish [28.3K]3 years ago
5 0
A = ¹/₂h(b₁ + b₂)
A = ¹/₂(10)(3 + 14)
A = 5(22)
A = 110 units²

The answer is A.
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Blizzard [7]
0 is in the hundredths place
1 is in the hundreds place
4 is in the ones place
3 is in the tenths place
6 is in the tens place
9 is in the hundred-thousands place
3 0
3 years ago
E
xz_007 [3.2K]

Answer:

1) n = 84

2) n = 78

3) n = 24

4) n = 16

5) n = 35

Step-by-step explanation:

To solve each proportion, we apply cross multiplication.

Question 1:

\frac{5}{12} = \frac{35}{n}

5n = 35*12

Simplifying both sides by 5

n = 7*12 = 84

Question 2:

\frac{n}{52} = \frac{180}{120}

120n = 52*180

Simplifying both sides by 20

6n = 52*9

Simplifying by 3

2n = 52*3

Simplifying by 2

n = 26*3 = 78

Question 3:

\frac{18}{n} = \frac{21}{28}

21n = 18*28

Simplifying both sides by 7

3n = 18*4

Simplifying both sides by 3

n = 6*4 = 24

Question 4:

\frac{n}{4} = \frac{24}{6}

\frac{n}{4} = 4

n = 16

Question 5:

\frac{10}{16} = \frac{n}{56}

16n = 56*10

Simplifying by 2, both sides

8n = 56*5

Simplifying by 8, both sides

n = 7*5 = 35

4 0
3 years ago
What is f(-2)?<br> 1 point<br> f(x)=x^2-3x-8
Inessa [10]
F(x) = x^2 - 3x - 8
f(-2) = (-2)^2 - 3 (-2) - 8
f(-2) = 4 - 3 (-2) - 8
f(-2) = 4 + 6 - 8
f(-2) = 10 - 8
f(-2) = 2 ✅
7 0
3 years ago
Identify the constant of proportionality from the table.
ivann1987 [24]

Answer:

The constant of proportionality is 3.

Step-by-step explanation:

6/2 is 3 and so on.

Correct me if I'm wrong

3 0
2 years ago
(From Textbook) A company makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce,
Doss [256]

Answer:

The company use 0 ounces of chicken and 100 ounces of grain in each bag of dog food in order to minimize cost.

Step-by-step explanation:

Let x be the number of ounces of chicken

let y be the number of ounces of grains

We are given that Chicken has 10 grams of protein and 5 grams of fat per ounce.

Chicken has protein in 1 ounce = 10

Chicken has protein in x ounces = 10x

Chicken has fat in 1 ounce = 5

Chicken has fat in x ounces = 5x

We are also given that grain has 2 grams of protein and 2 grams of fat per ounce

Grain has protein in 1 ounce = 2

Grain has protein in y ounces = 2y

Grain has fat in 1 ounce = 2

Grain has fat in y ounces =2y

Now we are given that . A bag of dog food must contain at least 200 grams of protein and at least 150 grams of fat.

So, equation becomes:

10x+2y\geq 200 ---A

5x+2y\geq 150  ---B

Since x and y represent the ounces .

So, x\geq 0 ---C and y\geq 0 ----D

Plot A ,B ,C and D on the graph

Refer the attached graph so , the corner points are (0,100),(10,50) and (30,0)

We are also given that chicken costs 10 cents per ounce and grain costs 1 cent per ounce

So, Cost function becomes : c=10x+y

At(0,100)

c=10x+y

c=10(0)+100

c=100

At(10,50)

c=10x+y

c=10(10)+50

c=150

At(30,0)

c=10x+y

c=10(30)+0

c=300

Minimum cost is 100 cents at (0,100)

So,  the company use 0 ounces of chicken and 100 ounces of grain in each bag of dog food in order to minimize cost.

3 0
3 years ago
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