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3 years ago

7

There are 22 events at an indoor track and field meet. The ratio of track events to field events is 8:3. How many of the events

are track events? Explain how you found your answer.

1 answer:

MA_775_DIABLO [31]3 years ago

4 0

First, let's look at the ratio.
You also know that for every 8 indoor events, there is 3 field events.
Therefore, the amount of indoor events is 8 on 11 events total, as 8 + 3 = 11

Then, let's look at the actual number of events. If there is 22 events total, you need to solve this proportion :

$\frac{8}{11} = \frac{?}{22}$

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Answer:
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3 years ago

What two rational expressions sum to 2x+3/x^2-5x+4

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Answer:

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

Step-by-step explanation:

Given the rational expression: $\frac{2x + 3}{x^2 - 5x + 4}$ , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

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$x^2 - 4x - x + 4$

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Thus, we now have: $\frac{2x + 3}{(x- 1)(x - 4)}$

Step 2: Apply the concept of Partial Fraction

Let,

$\frac{2x + 3}{(x- 1)(x - 4)}$ = $\frac{A}{x- 1} + \frac{B}{x - 4}$

Multiply both sides by (x - 1)(x - 4)

$\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4)$ = $(\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)$

$2x + 3 = A(x - 4) + B(x - 1)$

Step 3:

Substituting x = 4 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(4) + 3 = A(4 - 4) + B(4 - 1)$

$8 + 3 = A(0) + B(3)$

$11 = 3B$

$\frac{11}{3} = B$

$B = \frac{11}{3}$

Substituting x = 1 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(1) + 3 = A(1 - 4) + B(1 - 1)$

$2 + 3 = A(-3) + B(0)$

$5 = -3A$

$\frac{5}{-3} = \frac{-3A}{-3}$

$A = -\frac{5}{3}$

Step 4: Plug in the values of A and B into the original equation in step 2

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}$

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

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Debora [2.8K]

Answer:

The width of the rectangle is 14'8", and the length is 33'4"

Step-by-step explanation:

We're given two pieces of information:

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The perimeter is 96 feet:

$p = 96$

We also need to apply one more piece of information that is not provided here, and that is the relationship between the perimeter of a rectangle, and it's length and width:

$p = 2l + 2w$

We can solve for w by plugging the other two values into the last:

$p = 2w + 2l\\96 = 2w + 2(2w + 4)\\96 = 2w + 4w + 8\\88 = 6w\\3w = 44\\w = \frac{44}{3}\\w = 14\frac{2}{3}$

Now we can find the length by plugging w into the first equation:

$l = 2w + 4\\l = 2(14\frac{2}{3}) + 4\\l = 29\frac{1}{3} + 4\\l = 33\frac{1}{3}$

One third of a foot is four inches, so the width is 14'8" and the length is 33'4"

To make sure our answer is correct, we should plug those numbers back into the area equation and see if we're right:

$p = 2l + 2w\\p = 2(33\frac{1}{3}) + 2(14\frac{2}{3})\\p = 66\frac{2}{3} + 29\frac{1}{3}\\p = 96$

So we know our answer's correct

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