Question

Multiple Choice

Answer 1

A) Answer: A. 22.5 cm, 30 cm, and 37.5 cm

Setting the unity measurement as x, the three sides will be 3·x, 4·x, and 5·x. The sum of the three sides will be (3 + 4 + 5)·x = 12·x; this corresponds to the perimeter, therefore:

12·x = 90 cm

We can solve for x:

x = 90 / 12 = 7.5 cm

Hence, the sides will be:

7.5 · 3 = 22.5 cm

7.5 · 4 = 30 cm

7.5 · 5 = 37.5 cm

This situation is represented in option A (which is also the only option whose sides add up to 90).

B) Answer: C. never true

We have:

6 + 8x - 9 = 11x + 14 - 3x

Bring all the terms with x on the left, by subtracting from both sides 11x and -3x, and all the numbers on the right by subtrcting from both sides 6 and -9:

6 + 8x - 9 - 11x - (-3x) - 6 - (-9) = 11x + 14 - 3x - 11x - (-3x) - 6 - (-9)

Cancel out the opposite terms from each side:

8x - 11x + 3x = 14 - 6 + 9

Combine likely terms:

0x = 17

Now you should ask yourself: what number multiplied by zero gives 17 as a result? The answer is none because a number multiplied by zero always equals zero.

Hence, the statement is never true.

C) Answer: $r \leq \frac{1}{5}$

We have:

5r + 4 ≤ 5

Subtract 4 from both sides:

5r + 4 - 4 ≤ 5 - 4

Combine likely terms:

5r ≤ 1

Divide both sides by 5:

$\frac{5r}{5} \leq \frac{1}{5}$

$r \leq \frac{1}{5}$

To graph the set of solutions, you need to set:

y₁ = 5x + 4 and

y₂ = +5

Plot these two lines:

y₂ is a horizontal line at a height of 5;

y₁ is a line passing through (0, 4) and (1, 9)

The set of solutions will be the part of the graph in which y₁ lies underneath y₂ (see picture attached), that happens for $x \leq \frac{1}{5}$.

Answer 2

1. A 
2. C
3. 5r + 4 ≤ 5 
(5r + 4) + (-5) ≤ + (-5)
5r + 4 - 5 ≤ 5 - 5 
r ≤ 1/5