Algebra Chapter 1-9 Review

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Write a verbal expression for 6x + 7

Six times x plus seven

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

Five times the quantity x squared plus two

Write an algebraic expression for the product of ten and x

10x

Write an algebraic expression for the sum of eight and the square of a number x

8 + x²

Evaluate the expression 5 raised to the fourth

625

Evaluate 162 ÷ [6(7 − 4)²]

3

Evaluate 6²+ 3 ∙ 7 − 9

48

Evaluate 30 − 5 ∙ 4 + 2

12

Evaluate if a = 12, b = 9, c = 4 a² + b − c²

137

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 for n and name the property 5 · n · 2 = 0

n = 0 multiplication property of zero

Find the value for n and name the property used: 11· n = 11

n = 1 Multiplicative identity

Find the value for n and name the property used: 7 + n = 7

n = 0 Additive identity

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

n = 1 Multiplicative inverse or reciprocal

Evaluate if x = 2, y = 3, z = 4 2xyz + 5

53

Simplify the expression. If not possible, write simplified 3x + 6x

9x

Simplify the expression. If not possible, write simplified 5x + 4 + 3x² − 3x

3x² + 2x + 4

Simplify the expression. If not possible write simplified 3x + 2(4y + 5x)

13x + 8y

Simplify the expression. If not possible write simplified 7(2x + 5)

14x + 35

Find the solution set if the replacement set is x = {4, 5, 6, 7, 8} for the equation 5x − 9 = 26

7

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

Solve the equation that follows 2(x + 2) =20

8

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.

f(x) = 2x − 4 Find the value of f(−5)

−14

f(x) = 2x − 4 Find f(k + 1)

2k − 2

f(x) = x² + 3 Find f(b) + 4

b² + 7

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

Solve 2/3 n + 8 = 1/3 n + 2

−18

Solve the equation. Show work. |5y − 2| = 7

−1, 9/5

Solve the equation. Show work. x/5 + 6 = 2

− 20

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

Evaluate if x = −1, y = 3, and z = −4. . . . . . . . |−3y + z| − x

14

Solve the equation for the variable a listed . . . 7a − b = 15a for a

a = −b/8

Solve −2m = 16

m = −8

Solve h/3 = −2

h = − 6

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

Dress $69 and tax is 5 %. Find the total price

$72.45

Backpack $56.25. Discount 20%. Find the discounted price

$45.00

Find three consecutive integers whose sum is 36

11, 12, 13

Find two consecutive even integers whose sum is 126.

62, 64

Find three consecutive odd integers whose sum is 117

37, 39, 41

Solve 18 − 4x = 42

x = −6

Solve −x/3 − 4 = 13

−51

Solve the equation for the variable indicated. 7x + 3y = m, for y

y = (m − 7x)/3

Solve the proportion. . . . . . . . . 9/(y + 1) = 18/54

26

Solve 5(x + 3)+9= 3(x − 2) + 6

x = −12

Solve 3(x + 1) − 5 = 3x −2

All numbers

Solve 3(x − 6) = 3x

No solution

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.

Solve |x + 1| = 5

−6 and 4

Solve (4x + 7)/15 = (6x +2)/10

0.8

Solve 3.2x − 4.3 = 12.6x + 14.5

x = −2

Translate the sentence in to an equation. Three times the sum of g and h is 12.

3(g + h) = 12

Translate the sentence in to an equation. Twice a increased by the cube of a equals b

2a + a³ = b

Look at problem 17 on page 176. You will see a graph. What is the slope of the graph?

1/2

Look at problem 16 on page 176. You will see a graph. What is the slope of the graph?

−4/3

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

y = 2x The constant of variation is _________

2

y = 2x The slope is ____________

2

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

Solve the equation 4x − 1 = 0

x = 1/4

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

Find the next three terms of the arithmetic sequence 22, 20, 18, 16 ...

14, 12, 10

Find the next three terms of the arithmetic sequence 3.1, 4.1, 5.1, 6.1 ...

7.1, 8.1, 9.1

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

What point does every direct variation equation go through?

(0, 0)

What is the general equation for a direct variation equation?

y = kx

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

Find the slope of the line that passes through (6, 1) and (−6, 1)

0

Find the slope of the line that passes through (5, 2) and (5, −2)

Undefined

Find the slope of the line that passes through (10, 0) and (−2, 4)

−1/3

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

Solve the equation 0 = 4 − 2x

x = 2

Graph 2x + y = −2 using the x and y intercepts

x intercept is −1 and the y intercept is −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)

Define slope

(y2 − y1)/(x2 − x1) Other definitions are rise/run and change in y/change in x

Is the following an arithmetic sequence 1, 4, 9, 16...

No. There is not a common difference.

In the equation, y = mx + b, the m stands for _____________

Slope

In the equation, y = mx + b, the b stands for _____________

y-intercept

In the equation y = 3x + 7, the slope is _______________

3

In the equation y = 3x + 7, the y intercept is _______________

7

In the equation y = −2x − 6, the slope is ________________

−2

In the equation, y = −2x − 6, the y intercept is _____________

−6

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

Given the point (1, 9) and the slope 4, write the equation in slope intercept form

y = 4x + 5

Given the point (1, 3) and (−3, −5), write the equation in slope intercept form

y = 2x + 1

Write the equation in slope intercept form: 2x + 4y = 12

y = −1/2x + 3

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)

Given the point (2, 2) and m = −3, write the equation in point slope form

y − 2 = −3(x − 2)

Given the point (−8, 5) and m = −2/5, write the equation in point slope form

y − 5 = −2/5(x + 8)

The point slope form of a linear equation is ________

y - y1 = m(x − x1)

The slope intercept form of a linear equation is ____

y = mx + b

Write the equation in standard form: y − 11 = 3(x − 2)

3x − y = −5

Write the equation in standard form: y − 10 = −(x − 2)

x + y = 12

Write the equation in slope intercept form:. . . y + 2 = 4(x + 2)

y = 4x + 6

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 parallel lines?

The slopes of parallel lines are the same

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

What is true about any horizontal line and a vertical line?

They are perpendicular

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}

Solve x/6 ≤ 2

{x | x ≤ 12}

Solve −8x < −64

{x | x > 8}

Solve 6x + 12 < 8 + 8x

{x | x> 2}

Solve −8x − 3 < 18 − x

{x | x > − 3}

Solve 2(x + 3) ≥ 16

{x |x ≥ 5}

Solve −5 − x/6 ≥ −9

{x |x ≤ 24 }

Graph x > 3 or x ≤ 0

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

Graph x ≤ 3 and ≥ −2

Closed circle on 3 and closed circle on negative two with shading between

Solve and graph |x|< 3

{x |−3 < x < 3} Open circle on three and negative three with shading between

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

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