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Nookie1986 [14]
3 years ago
10

the equation a=1/2(b1+b2)h can be used to determine the area, a, of a trapezoid with height, h, and base lengths, b1 and b2. whi

ch are equivalent equations? check all that apply.

Mathematics
2 answers:
zimovet [89]3 years ago
6 0

Answer:

(A) and (D)

Step-by-step explanation:

It is given that the given expression a=\frac{1}{2}(b_{1}+b_{2})hcan be used to determine the area, a, of a trapezoid with height, h, and base lengths b_{1} and b_{1}.

Thus, solving the given equation and finding the value of b_{1}, we get

a=\frac{1}{2}(b_{1}+b_{2})h

\frac{2a}{h}-b_{2}=b_{1}

And the expression for height is:

2a=(b_{1}+b_{2})h

h=\frac{2a}{(b_{1}+b_{2})}

(A) The given expression is:

\frac{2a}{h}-b_{2}=b_{1}

which is equivalent to the given expression, therefore this option is correct.

(B) The given expression is:

\frac{a}{2h}-b_{2}=b_{1}

which is not equivalent to the given expression, therefore this option is not correct.

(C) The given expression is:

\frac{2a-b_{2}}{h}=b_{1}

which is not equivalent to the given expression, therefore this option is not correct.

(D) The given expression is:

\frac{2a}{b_{1}+b_{2}}=h

which is equivalent to the given expression, therefore this option is correct.

(E) The given expression is:

\frac{a}{2(b_{1}+b_{2})}=h

which is not equivalent to the given expression, therefore this option is not correct.

galina1969 [7]3 years ago
5 0

Answer:

b₁ = (2a – b₂h)/h; b₁ = (2a)/h – b₂; h = (2a)/(b₁ + b₂)

Step-by-step explanation:

A. <em>Solve for b₁ </em>

          a = ½(b₁ + b₂)h        Multiply each side by 2

        2a = (b₁ + b₂)h           Remove parentheses

        2a = b₁h + b₂h           Subtract b₂h from each side

2a - b₂h = b₁h                    Divide each side by h

         b₁ = (2a – b₂h)/h     Remove parentheses

         b₁ = (2a)/h – b₂

B. <em>Solve for h </em>

2a = (b₁ + b₂)h     Divide each side by (b₁ + b₂)

 h = (2a)/(b₁ + b₂)

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A function assigns the values. The average rate of change for the given function g(x) is 1.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

The average rate of change of a function is given by the formula,

Average rate of change, = [f(b)-f(a)]/(b-a), [a,b]

Where a is the lower limit and b is the upper limit.

Given the upper limit for the function is 0, therefore, the value of a is 0, similarly, the value of b is -9. Thus,

a = 0

g(a) = 0²+10(0)+20 = 20

b = -9

g(b) = (-9)²+10(-9)+20 = 11

The average rate of change for the function g(x), can be written as,

\text{Average rate of change}= \dfrac{g(-9)-g(0)}{-9-0}=\dfrac{11-20}{-9} = 1

Hence, the average rate of change for the given function g(x) is 1.

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8 0
2 years ago
Work out the area of this shape. ? cm2<br><br> 4 cm<br> 9 cm<br> 6 cm<br> 12 cm<br><br> Help!!!
mars1129 [50]

Answer:

84 cm^2

Step-by-step explanation:

Area of triangle + area of rectangle

Area of triangle = 1/2*l*b

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Area of rectangle = l*b

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Answer:

answer is -35.84

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3 0
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The area of Sahara desert is 7 times the area of the Gobi Desert. If the sum of their areas is 4,000,000 square miles, find the
ryzh [129]
X=area of Sahara.
y=area of the Gobi Desert.
We suggest this system equations:
x+y=4000000
x=7y
solve by susbstitution method.
(7y)+y=4,000,000
8y=4,000,000
y=4,000,000 / 8=500,000

x=7y
x=7(500,000)=3,500,000

The area of Sahara=3,500,00 miles².
The area of the Gobi Desert=500,000 miles²

To check:
Te sum of their areas is : 3,500,000 miles²+500,000 miles²=4,000,000 miles²
Te area of sahara (3,500,000 miles²) is 7 times the area of the Gobi Desert (7*500,000 miles²=3,500,000 miles²).
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518 is the answer. **
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