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Oksanka [162]
3 years ago
15

The sum of the base and height of a triangle is 14 cm. Which of the following equations could be used to find the maximum area o

f the triangle?
A) A = 0.5x^2 - 15x

B) A = -0.5x^2 + 7x

C) A = -x^2 + 10x

D) A = x^2 - 10x
Mathematics
1 answer:
Montano1993 [528]3 years ago
8 0

Answer:

B

Step-by-step explanation:

Let the base of the triangle be <em>b</em> and the height be <em>h</em>.

The sum of the base and height is 14. Thus:

b+h=14

Recall that the area of a triangle is given by:

\displaystyle A=\frac{1}{2}bh

From the first equation, solve for either variable:

h=14-b

Substitute:

\displaystyle A=\frac{1}{2}b(14-b)

Distribute:

\displaystyle A=\frac{1}{2}(14b-b^2)

Distribute:

\displaystyle A=-0.5b^2+7b

Let <em>b</em> = <em>x</em>. Hence:

A=-0.5x^2+7x

Therefore, our answer is B.

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Jug A has 0.1 litres more than jug B. Jug C has 200 millilitres less than jug B. Jug D has ¼ of the amount that is in jug A. The
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Answer:

A = 0.8 litres

B = 0.7 litres

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D = 0.2 litres

Step-by-step explanation

Here's what we know:

1. Jug A = B + .1 litres

2. Jug C = B - 200 (or 0.2 litres)

3. Jug D = .25 x A

4. Jug A + Jug B = 1.5 litres

In problem 1, we learned that Jug A has .1 litres more than Jug B and in problem 4, the two of them added together are 1.5 litres. To solve this we can combine the problems.  

B + .1 litres + B = 1.5 litres

2B + .1 = 1.5

Subtract .01 from each side and you have 2B = 1.4

Divide each side by 2 and you have B = 0.7 litres

Plug this info into problem 1 and you can solve for A. (0.7 + 0.1 = 0.8)

Plug this info into problem 2 and you can solve for C. (0.7 - 0.2 = 0.5)

Since you have A, you can use that info to solve problem 3 (0.25 x 0.8 = 0.2)

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