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3 years ago

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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Place value of 0 1 4 3 6 9 in 987,164.302

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

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