Question 1

A rectangle has a perimeter of 560 meters. The length is 20 meters less than twice the width. Which equation correctly models the relationship between the length ($$l) $$and width ($$w) of $$the rectangle?

Accepted Answer

$$2l + 2w = 560$$ and $$l = 2w - 20$$

Question 2

Given the rectangle from the previous question, what is the width of the rectangle?

Accepted Answer

$$w = 80$$

Question 3

For the same rectangle, what is the length?

Accepted Answer

$$l = 180$$

Question 4

A projectile is launched from ground level with an initial velocity of $$96 ft/sec. $$Its height after $$t$$ seconds is given by $$s = -16t^2$ + 96t. At $$what time(s) will the projectile reach a height of $$80 ft$$?

Accepted Answer

$$t = 1$$ and $$t = 5$$

Question 5

Using the same projectile equation $$s = -16t^2$ + 96t$$, after how many seconds will the projectile return to the ground?

Accepted Answer

$$t = 6$$

Question 6

Dr. Tydings found that $$95\% of $$the babies he delivered weighed $$x$$ pounds, where $$|x - 8.2| \leq 1.5. $$What is the range of weights for these babies?

Accepted Answer

$$6.7 \leq x \leq 9.7$$

Question 7

Solve the equation $$x^2 - 4x = -6 + x$ by moving all terms to one side and factoring.

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 8

Which of the following is the correct quadratic equation to solve for $$t$$ when the projectile reaches $$80 ft$$, given $$s = -16t^2$ + 96t$$?

Accepted Answer

$$-16t^2 + 96t - 80 = 0$

Question 9

If you solve $$x^2 - 5x + 6 = 0$ by factoring, what are the solutions?

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 10

A rectangle has a length that is $$20$$ meters less than twice its width. If the width is $$80$$ meters, what is the length?

Accepted Answer

$$l = 180$$

Question 11

Given the equation $$|x - 8.2| \leq 1.5$$, which of the following is the correct way to write the compound inequality?

Accepted Answer

$$-1.5 \leq x - 8.2 \leq 1.5$$

Question 12

If a projectile is launched with an initial velocity of $$v_0 ft/sec $$from ground level, its height after $$t$$ seconds is $$s = -16t^2$ + v_0$ t. If$$ $$v_0 = 96$, what is the maximum height reached by the projectile?

Accepted Answer

$$144 ft$$

Question 13

Which method(s) can be used to solve the quadratic equation $$x^2 - 4x + 6 = 0$?

Accepted Answer

Completing the square or the quadratic formula

Question 14

If you solve $$x^2 - 4x + 6 = 0$ using the quadratic formula, what is the discriminant?

Accepted Answer

$$(-4)^2 - 4$$ \cdot 1 \cdot 6 = -8$$

Question 15

A student claims that the solution to $$|x - 8.2| \leq 1.5 is$$ $$x \leq 9.7. $$What is the error in this reasoning?

Accepted Answer

The student ignored the lower bound $$x \geq 6.7$$

Question 16

If the perimeter of a rectangle is $$560$$ meters and the width is $$80$$ meters, what is the length?

Accepted Answer

$$l = 180$$

Question 17

Given the equation $$x^2 - 4x + 6 = 0$, what is the nature of its solutions?

Accepted Answer

Two complex solutions

Question 18

A projectile is launched from the ground with an initial velocity of $$96 ft/sec. $$How long does it take to reach its maximum height?

Accepted Answer

$$t = 3$$ seconds

Question 19

If you solve $$x^2 - 4x + 6 = 0$ by completing the square, what is the resulting equation before taking the square root?

Accepted Answer

$$(x - 2)^2$ = -2$$

College Algebra Practice Test – Step-by-Step Guidance

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