Quiz about MAT 151-College Algebra Review for Finals

Question 1

A cartravels a total of 275 miles in 4 hours, traveling part of the time at 60 miles per hour and part of the time at 74 miles per hour. How long did the car travel at each speed?

Accepted Answer

1.5 hours at 60 mph and 2.5 hours at 74 mph

Answer

1 hour at 60 mph and 3 hours at 74 mph

Answer

2 hours at 60 mph and 2 hours at 74 mph

Answer

3 hours at 60 mph and 1 hour at 74 mph

Question 2

Solve the rational equation analytically: $$\frac{3}{x-1}+\frac{4}{x^2-1}=\frac{13}{x+1}$$

Accepted Answer

2

Answer

4

Answer

3

Answer

1

Question 3

Solve the equation analytically: $$\sqrt{2x+5}=x-5$$

Accepted Answer

10

Answer

5

Answer

15

Answer

0

Question 4

Solve the equation analytically: $$\sqrt{2x+5}\ge x-5$$

Accepted Answer

[-2.5, 10]

Answer

[1, 4]

Answer

[2.5, 10]

Answer

$$\left[10,\infty\right)$$

Question 5

Solve: $$\log_2x+\log_2(x-4)=5$$

Accepted Answer

8

Answer

2

Answer

16

Answer

4

Question 6

Solve the equation: $$\left(\frac{1}{3}\right)^{\left(2x+1\right)}=9^{\left(-4x-3\right)}$$

Accepted Answer

$$-\frac{5}{6}$$

Answer

$$\frac{5}{6}$$

Answer

-1

Answer

0

Question 7

Consider the rational function defined byf(x) $$f\left(x\right)=\frac{2x^2-3x-5}{x^2+x-2}$$ FInd the hole, the VA, & HA.

Accepted Answer

Hole: None, VA: x = -2, HA: y = 2

Answer

Hole: x = 3, VA: x = 1, HA: y = -1

Answer

Hole: x = -1, VA: x = 0, HA: y = 1

Answer

Hole: x = 1, VA: x = 2, HA: y = 0

Question 8

A sample of radioactive material has a half-life of 102 years. An initial sample weighs 22 grams.

(a) Find the formula for the decay function of this material.

(b) Find the amount left after 205 years.

(c) Find the time for the initial amount to decay to 6.2 grams.

Accepted Answer

The decay function is $$A(t)=22\left(\frac{1}{2}\right)^{\frac{t}{102}}$$

Accepted Answer

The amount left after 205 years is approximately 7.75 grams, and the time to decay to 6.2 grams is approximately 153.5 years.

Answer

The decay function is $$A(t)=22\left(\frac{1}{3}\right)^{\frac{t}{102}}$$

Answer

The amount left after 205 years is approximately 10 grams

The time to decay to 6.2 grams is approximately 200 years

Question 9

1. How much of a 70% orange juice drink must be mixed with 6 gallons of a 40% orange juice drink to obtain a mixture that is 50% orange juice?

Accepted Answer

3 gallons

Answer

8 gallons

Answer

2 gallons

Answer

5 gallons

Question 10

1. Write $$f(x)=x^2-2x-3$$ in vertex form by completing the square. Identify the vertex, x-intercepts, y-intercept and graph the parabola.

Accepted Answer

Vertex form: $$f\left(x\right)=\left(x-1\right)^2-4$$ Vertex: (1, -4); x-intercepts: (3, 0) and (-1, 0); y-intercept: (0, -3).

Answer

Vertex form: $$f\left(x\right)=\left(x-2\right)^2+1$$ Vertex: (-2, 1); x-intercepts: (0, 0) and (2, 0); y-intercept: (0, 1).

Answer

Vertex form: $$f\left(x\right)=\left(x+1\right)^2-2$$ ; Vertex: (-1, -2); x-intercepts: (0, 0) and (-2, 0); y-intercept: (0, -2).

Answer

Vertex form: $$f\left(x\right)=\left(x-3\right)^2+5$$ Vertex: (3, 5); x-intercepts: (4, 0) and (2, 0); y-intercept: (0, 5).

Question 11

Find a polynomial of least possible degree having the graph shown. You do not need to multiply it ou

Accepted Answer

$$f\left(x\right)=\frac{1}{2}\left(x+4\right)\left(x-5\right)\left(x-7\right)$$

Answer

$$f\left(x\right)=\frac{1}{2}\left(x-4\right)\left(x+5\right)\left(x+7\right)$$

Answer

$$f\left(x\right)=\left(x+4\right)\left(x-5\right)\left(x-7\right)$$

Answer

$$f\left(x\right)=2\left(x+4\right)\left(x-5\right)\left(x-7\right)$$

Question 12

1. A rectangular piece of cardboard measuring 12 in by 18 in is to be made into a box by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Answer the following questions. Justify your answers to parts c and d with a rough sketch of the volume function. Be sure to include units.

a. Give the restrictions on x.

b. Write the volume of the box as a function of x.

c. What value of x maximizes the volume?

d. What is the maximum value?

Accepted Answer

Restrictions on x: 0 < x < 6;

Accepted Answer

Value of x that maximizes volume: 3 inches; Maximum volume: 216 cubic inches.

Answer

Value of x that maximizes volume: 3 inches;

Maximum volume: 180 cubic inches

Answer

Restrictions on x: 0 < x < 12

Question 13

A person invested $7300 for 1 year, part at 5%, part at 9%, and the remainder at 15%. The total annual income from these investments was $827. The amount of money invested at 12% was $100 more than the amounts invested at 5% and 9% combined. Find the amount invested at each rate.

Accepted Answer

Amount invested at 5%: $2000, Amount invested at 9%: $3000, Amount invested at 15%: $2300

Answer

Amount invested at 5%: $3000, Amount invested at 9%: $3000, Amount invested at 15%: $1300

Answer

Amount invested at 5%: $2500, Amount invested at 9%: $2000, Amount invested at 15%: $2800

Answer

Amount invested at 5%: $1500, Amount invested at 9%: $3500, Amount invested at 15%: $2300

Question 14

Use a system of equations to find the parabola of the form $$y=ax^2+bx+c$$ that goes through the three given points: $$\left(4,71\right),\ \left(-2,11\right)\ and\ \left(3,41\right)$$

Accepted Answer

$$y=4x^2+2x-1$$

Answer

$$y=x^2+5x+10$$

Answer

$$y=3x^2+2x+4$$

Answer

$$y=2x^2+3x+1$$

Question 15

Graph

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Question 16

Graph

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 17

What is the correct graph of the function?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 18

What is the correct graph of the function?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 19

$$\ln\left(\frac{2x^2y}{z^4}\right)$$

Accepted Answer

ln2+2lnx+lny-4lnz

Answer

ln2+2lnx+lny+4lnz

Answer

2ln(2xy)-4lnz

Answer

2ln2x+lny-4lnz

Question 20

Solve the exponential function: 5^x + 7= 32

Accepted Answer

x = 2

Answer

x = 25

Answer

x = 6

Answer

x = 9

Question 21

Question 21.

Accepted Answer

log₅(x²z²y¹⁰)

Answer

log₅(z²y²x¹⁰)

Answer

log(zy²x¹⁰)

Answer

log₅(z² + y²+ x¹⁰)

Question 22

Expand:

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 23

Using the parent function $$y=\log_3x$$ what would the graph of $$y=\log_3\left(x+5\right)$$ look like?

Accepted Answer

Horizontal shift left 5 units

Answer

Horizontal shift right 5 units

Answer

Vertical shift up 5 units

Answer

Vertical shift down 5 units

Question 24

Using the parent function

$$y=\log_6x$$ what would the graph of $$y=\log_6x+9$$ look like?

Accepted Answer

Vertical shift 9 units up

Answer

Horizontal Shift to the right 9 units

Answer

Horizontal shift to the left 9 units

Answer

Vertical shift 9 units down

Question 25

Find the corresponding graph of
$$\log_3\left(x-1\right)+4$$

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 26

Match the given graph to its appropriate equation.

Accepted Answer

$$c\left(x\right)=\frac{x+5}{\left(x+4\right)\left(x-3\right)}$$

Answer

$$a\left(x\right)=\frac{\left(x+4\right)\left(x-3\right)}{x+5}$$

Answer

$$b\left(x\right)=\frac{\left(x+5\right)\left(x-4\right)}{x-3}$$

Answer

$$d\left(x\right)=\frac{x}{\left(x-4\right)\left(x+3\right)}$$

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