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### Write a verbal expression for the algebraic expression 5(x² +2)

Five times the quantity x squared plus two

### Evaluate and name the property used in each step 2 + 6(9− 3²) − 2

2 + 6 (9 − 9) − 2 (sub) . . . . . . . . . . . . . . . . . . . . 2 + 6(0) − 2 (sub) . . . . . . . . . . . . . . . . . . . . . . . . 2 + 0 − 2 (Mult prop of zero). . . . . .. . .. . . . .. . 2-2 (add iden). . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 (sub) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

### Find the value of n and name the property used: 3 · 1/3 = n

n = 1 Multiplicative inverse or reciprocal

### Find the solution set if the replacement set is x = {0. 1/2, 1, 3/2, 2} for the equation 120 − 28x = 78

3/2

### List the domain and the range for the following relation {(−2,−1), (3, 3), (4,3)}

Domain = {−2, 3, 4} Range = {−1, 3}

### Identify the hypothesis and conclusion for the following relation: If it is Sunday, then mail is not delivered

Hypothesis: It is Sunday Conclusion: mail is not delivered

### Explain the difference between an algebraic expression and a verbal expression.

Algebraic expression consists of numbers, variables, and arithmetic operations. Verbal expression consists of words.

### Determine whether each pair of ratios is an equivalent ratio. 5/9, 7/11

No because when you cross multiply, 55 is not equal to 63

### State whether the percent of change is a percent of increase or percent of decrease. Find the percent of change to the nearest whole percent. Original $25, New $10

Decrease of 60%

### Two trains leave Chicago, one traveling east at 30 miles per hour and one traveling west at 40 miles per hour. When will the trains be 210 miles apart?

3 hours

### Write an equation and solve. X plus 10 is equal to 3 times x.

x + 10 = 3x When the equation is solved, x = 5

### Write an equation and solve. Twenty decreased by three times a number equals −10.

20 − 3x = −10 When the equation is solved, x = 10

### Choc chip cookies sell for $6.95 and white choc cookies sell for $5.95 per lb. How many pounds of choc chip cookies must be mixed with 4 lbs of white choc cookies to obtain a mixture that sells for $6.75 per pound

16 pounds

### Translate the equation in to a sentence 2x + 10 = 26

Two times x plus ten equals twenty-six or the product of two and x increased by ten is twenty-six.

### Determine whether the equation is linear or not. If yes, write the equation in standard form xy = 6

No, because variables are multiplied together

### Determine whether the equation is linear or not. If yes, write the equation in standard form y = 2 − 3x

Yes. 3x + y = 2

### Determine whether the equation is linear or not. If yes, write the equation in standard form y = 3x² + 1

No, because the x is raised to a power greater than one

### Look at problem 11 on page 183. Name the constant of variation. What is the slope?

Constant of variation is −5 The slope is −5

### Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve. If y = −4 when x = 2, find y when x = −6.

The equation is y = −2x. The value for y is 12

### Suppose y varies directly as x. Write a direct variation equation that relates x and y. Solve. If y = 7.5 when x = .5, find y when x = −0.3.

The equation is y = 15x. The value for y is −4.5

### Find the value of r so the line that passes through each pair of points has the given slope. (r, 3), (5, 9), m = 2

r = 2

### Find the value of r so the line that passes through each pair of points has the given slope. (−4, 3)), (r, 5), m= 1/4

r = 4

### Graph 2x + 4y = 16 using x an y intercepts

x intercept is 8, and the y intercept is 4. See page 155 and 156 to check the work and graph

### Graph y = 1/3 x + 2 using a table

Some points on the line are (0, 2),(3, 3), (6, 4). Check page 156 to see the graph.

### Graph y = −6x

Some points on the line are (0, 0), (1, −6),(−1, 6) See page 181 for a picture of the graph

### Write an equation for the nth term of the arithmetic sequence 7, 13, 19, 25 ...

The nth term = 6n + 1

### Write an equation for the nth term of the arithmetic sequence 30, 26, 22, 18 ....

The nth term = −4n + 34

### Look at the graph for problem #7 on page 198. Write an equation for the graph in function notation

f(x) = 3x − 2

### Look at the graph for problem #3 on page 198. Write an equation for the graph in function notation

f(x) = −x + 3

### Which of the following equations is a direct variation equation? y = x + 2 or y = 3x

y = 3x because it is of the form y = kx

### Solve the equation 15x −30 = 5x − 50 by graphing and algebraically

Graph f(x) = 10x + 20 and it crosses the x-axis at − 2. Solve 10x + 20 and x = −2

### Graph y − x = 4 using a table

Solve the equation for y. y = x + 4. Some points on the line are (0, 4), (1, 5), (−1, 3)

### Look at the graph for problem #12 on page 218. What is the equation in slope intercept form?

y = −1/5 x + 1

### Look at the graph for problem #14 on page 218. What is the equation in slope intercept form?

y = −2 x + 3

### Look at the graph for problem #34 on page 219. What is the equation in slope intercept form?

y = −4/7 x − 2

### Look at the graph for problem #40 on page 235. Write the equation in point slope form

y − 3 = 4(x − 1)

### Look at the graph for problem #42 on page 235. Write the equation in point slope form

y − 7 = −4/3(x + 3)

### Determine whether the lines are parallel, perpendicular, or neither: . . . . . . . . . . . . . . . . . y = −2x and 2x + y = 3

Parallel

### Determine whether the lines are parallel, perpendicular, or neither: . . . . . . . . . . . . . . . . . 3x + 5y = 10 and 5x − 3y = −6

Perpendicular

### Determine whether the lines are parallel, perpendicular, or neither: . . . . . . . . . . . . . . . . . 2x + 5y = 15 and 3x + 5y = 15

Neither

### What form should you put lines in to determine if they are parallel, perpendicular, or neither?

Slope intercept form

### What is true about the slopes of perpendicular lines?

The product of slopes of perpendicular lines is −1. (Slopes of perpendicular lines are opposite reciprocals)

### Write the equations for two lines that are parallel.

There are many answers. An example would by y = 2x and y = 2x + 7.

### Write the equations for two lines that are perpendicular.

There are many answers. An example would by y = 2x and y = −1/2 x + 6. The product of the two slopes has to be −1

### Write an equation in slope intercept form for the line that passes through (−2, 2) and is perpendicular to y = −1/3 x + 9.

y = 3x + 8

### Write an equation in slope intercept form for the line that passes through (3, 2) and is parallel r to y = x + 5.

y = x − 1

### Write an equation in slope intercept form for the line that passes through (10, 5) and is perpendicular to 5x + 4y = 8.

y = 4/5x − 3

### Write an equation in slope intercept form for the line that passes through (−1, −2) and is parallel to 3x − y = 5.

y = 3x + 1

### Describe how you would graph y = 1/3 x + 2 using the slope and the y interept.

Put a dot on the y-axis on the number 2. Count a slope of 1/3 by going up 1 and right 3 or down 1 and left 3. Count the slope two or three times and then draw the line.

### Graph 3x − y < 2

Solve the equation for y (slope intercept form) Graph the line with a dotted line. Check a point to see what side to shade. See a graph for this inequality on page 315

### Graph x + 5y ≤ 10

Solve the equation for y (slope intercept form) Graph the line with a solid line. Check a point to see what side to shade. See a graph for this inequality on page 316

### Solve x + 11 > 16 Graph the inequality.

{x|x > 5} The graph of the number line is an open circle on five and shading to the right.

### Solve 3x + 17 < 4x Graph the inequality

{x|x > 17} The graph is a number line with an open circle on 17 and shading to the right.

### Solve the compound inequality x − 5 < − 4 or x − 5 ≥ 1 Graph the compound inequality.

{x | x < 1 or x ≥ 6 The graph is an open circle on 1 and shading to the left and a closed circle on 6 and shading to the right.

### Solve the inequality −2x + 4 > −6 Graph the inequality.

{x | x < 5} The graph is a number line with an open circle on 5 and shading to the left.

### Solve the compound inequality 4 < x + 6 and x + 6 < 5 Graph the inequality

{x | −2 < x < −1 The graph is a number line with an open circle on negative two and an open circle on negative one and shading between

### Write a compound inequality and solve: A number minus one is at most nine, or two times the number is at least twenty-four

x − 1 ≤ 9 or 2x ≥ 24 {x |x ≤ 10 or x ≥12}

### Solve and graph the inequality x + 12 ≥ 8

{x |x ≥ − 4} The graph is a number line with a closed circle on negative four and shading to the right.

### Solve and graph the inequality x − (−5) > −2

{x | x > − 7} The graph is a number line with an open circle on negative seven and shading to the right.

### Wriite and solve in inequality: Twice a number minus 4 is less than three times the nunmber.

2x − 4 < 3x {x | x > − 4}

### Graph x > 3 or x ≤ 0

Open circle on three and shading to the right. Closed circle on zero and shading to the left.

### Solve and graph |x − 4|< 4

{x | 0 < x < 8} The number line has an open circle on zero and an open circle on eight with shading between

### Use an augmented matrix to solve the system of equations: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2x − y = 7 and −x + 3y = −11

(2, −3)

### State the dimensions of the matrix and identify the circled element for problem #12 on page 372

2 X 5 The circled three is in the second row and first column

### Subtract the two matrices for problem #18 on page 373. If the matrix does not exist write impossible

Impossible

### Perform the indicated matrix operations for problem #28 on page 374. If the matrix does not exist, write impossible.

First row of matrix −9 4 second row of matrix −3 67 This is a 2 X 2 matrix

### Evaluate. Express in scientific and standard form (4.9 X 10−³)/(4.0 X 10−⁵)

Scientific 1.96 X 10−⁷and standar 0.000000196

### Evaluate. Express in scientific and standard form (4.8 X 10⁴)(6 X 10⁶)

Scientific 2.88 X 10¹¹ and standard 288,000,000,000

### Write 4 − x + 3x³ − 2x² in standard form and identify the leading coefficient

3x³ − 2x² −x + 4 The leading coefficient is 3

### Write the equation of the function that would translate the graph of x² over the x-axis, stretch it vertically by a factor of 2 and translate it down 3

y = −2x² − 3

### Describe how the graph of the function is related to the graph of f(x) = x² g(x) = x² + 9

Translates up 9

### Solve x² − 2x − 8 by graphing. What are the domain and range?

The axis of symmetry is 1. The vertex is (1, −9). Some points in the table may be (1, −9), (0, −8), (2, −8), (4, 0), (−2, 0) The solutions are 4 and −2. See the graph on page 537.Domain reals and range y ≥ −9

### Solve the equation by using the quadratic formula. Round to the nearest tenth if necessary x² + 8x + 7 = 0

−7 and −1

### What is a geometric sequence?

A geometric sequence has a first term that is not zero and each term after the first is found by multiplying the previous term by a nonero constant

### What is an arithmetic sequence?

An arithmetic sequence is a numerical pattern that increases or decreases at a constant rate called the common difference. The next term is found by adding the same positive or negative number to the preceding term.

### Write an equation to find the nth term of the sequence −2, 10, −50... and then use the equation to find the eleventh term

a₁₁ = −2 ∙ (−5)ⁿ⁻¹ The eleventh term is −19,531,250

### Solve x² + 6x + 8 = 0 by graphing and what are the domain and range.

The axis of symmetry is −3. The vertex is (−3,−1). Some points in the table may be (−3, −1), (−2, 0), (−4, 0), (−1, 3), (−5, 3) The solutions are − 4 and −2. Domain reals, Range y ≥ −1

### The value of a new television depreciates by about 7% per year. You purchase a $3,000 TV. What is its value after 4 years. Write and solve an expontential equation to solve.

y = 3000(.93)⁴ In four years, the value of the TV is about $2244.16

### $20,000 is invested at an interest rate of 5.2%. The interest is compounded quarterly. Write and evaluate an equation to determine how much money will be in the account in 10 years.

y = (20000)(1.013)⁴⁰ The amount would be $33528.01

### Sketch a graph that has a minimum at the point (4, −2) and has roots (or solutions) at 2 and 6

Put a point on the minimum of (4, −2) Put points on the x-axis on 2 and 6 and connect the parabola

### Describe how the graph of the function is related to the graph of f(x) = x² g(x) = −2x²

Reflected over the x-axis and stretched vertically

### Sketch a quadratic equation that has one root (solution).

The parabola touches the x-axis at one point. See page 537

### Sketch a quadratic equation that has two roots (solutions).

The parabola touches the x-axis at two points. See page 537