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3 years ago

The height of a triangle is 5 less than its base. The area of the triangle is 42 square inches. Find the height and base

Mathematics

1 answer:

Bond [772]3 years ago

6 0

This can be solved using simple algebra.

Let's take the base as x

It's give that the height is the base - 5.

So, the height is (x - 5)

Now plug those in the formula for finding the area of the triangle and you get:

(x^2 - 5x)/2 = 42

x^2 - 5x = 84

x (x - 5) = 84

After solving the equation, you get x = 12 and x = -7. Since lengths can't be negative, we ignore the one with the negative value.

Since x was the base, the base = 12 and the height was x - 5 so 12 - 5 = 7

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3 years ago

The town recreation department ordered a total of 100 baseballs and bats for the summer.Baseballs cost $4.50 each and bats cost

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Answer:

The town recreation department ordered 66 baseballs and 24 bats.

Step-by-step explanation:

Let the number of baseball be 'x'.

Also Let the number of bats be 'y'.

Given:

Total items bought = 100

Now we can say that;

Total items bought is equal to sum of number of baseball and number of bats.

Framing in equation form we get;

$x+y =100 \ \ \ \ equation \ 1$

Also Given:

Cost of each baseball = $4.50

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framing in equation form we get;

$4.5x+20y =822 \ \ \ \ equation\ 2$

Multiplying equation 1 by 4.5 we get;

$4.5(x+y) =100\times4.5\\\\4.5x+4.5y = 450 \ \ \ \ equation \ 3$

Now Subtracting equation 3 from equation 2 we get;

$(4.5x+20y)-(4.5x+4.5y) = 822-450\\\\4.5x+20y-4.5x-4.5y =372\\\\15.5y = 372$

Dividing both side by 15.5 we get;

$\frac{15.5y}{15.5}= \frac{372}{15.5}\\ \\y =24$

Substituting the value of y in equation 1 we get;

$x+y =100\\\\x+24 =100\\\\x =100-24 =66$

Hence the town recreation department ordered 66 baseballs and 24 bats.

5 0

3 years ago