chapter 3, 4, & 5 review
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CHAPTER 3, 4, & 5 REVIEW. January 10, 2012. 1. Solve + 5 = 11 . 11. + 5 = . + 5 – 5 = . 11 – 5. x. x. x. x. x. 6. = . 2. 2. 2. 2. 2. x =. 12. 2 =. 2 6. ANSWER. The solution is 12 . Check by substituting 12 for x in the original equation. - PowerPoint PPT PresentationTRANSCRIPT
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CHAPTER 3, 4, & 5 REVIEW
January 10, 2012
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1. Solve + 5 = 11.x2
Write original equation.+ 5 = x2 11
+ 5 – 5 = x2 11 – 5 Subtract 5 from each side.
= x2 6 Simplify.
2 =x2 2 6 Multiply each side by 2.
x = 12 Simplify.
ANSWER
The solution is 12. Check by substituting 12 for x in the original equation.
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8x – 3x – 10 = 20
8x – 3x – 10 = 20 Write original equation.
5x – 10 = 20 Combine like terms.
5x – 10 + 10 = 20 + 10 Add 10 to each side.
5x = 30 Simplify.
Divide each side by 5.
x = 6 Simplify.
= 305
5x5
Solve
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Write original equation.
7d + 4 = 32 Combine like terms.
7d + 4 – 4 = 32 – 4 Subtract 4 from each side.
7d = 28 Simplify
Divide each side by 7.
d = 4 Simplify.
= 287
7d7
9d – 2d + 4 = 32
9d – 2d + 4 = 32
2. Solve the equation. Check your solution.
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3. Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds.How much food should the seal be fed per day ?SOLUTION
STEP 1
x280=
8 amount of food100 weight of seal
Write a proportion involving two ratios that compare the amount of food with the weight of the seal.
Seals
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STEP 2Solve the proportion. 8100
x280= Write proportion.
8 280 = 100 x Cross products property
2240 = 100x Simplify.
22.4 = x Divide each side by 100.
ANSWER
A 280 pound seal should be fed 22.4 pounds of food perday.
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b. lasagnaa. macaroni and cheese
Type of Pasta Students
Spaghetti 83
Lasagna 40Macaroni and cheese
33
Fettucine alfredo
22
Baked ziti 16
Pasta primavera
15
Other 11
4. A survey asked 220 students to name their favorite pasta dish. Find the percent of students who chose the given pasta dish.
Survey
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Solve for x.x = 15%
Use cross products.
Substitute 33 for is and 220 for of.
Write percent equation.
SOLUTION
3300 = 220x
The survey results show that 33 of the 220 students chose macaroni and cheese.
a.
is = %of = 10033 = x
220 =100
ANSWER
15% of the students chose macaroni and cheese as their favorite dish.
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b. The survey results show that 40 of the 220 students chose lasagna.
Solve for x.x = 18%
Use cross products.
Substitute 40 for is and 220 for of.
Write percent equation.
4000 = 220x
is = %of = 10040 = x
220 =100
About 18% of the students chose lasagna as their favorite dish.
ANSWER
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‾ b = ‾ 8/5y + 16
8/5y = b + 16
(8/5) y = (8/5) (5/8b + 10)
SOLUTION
5. Solve y = 5/8 b + 10 for b.
‾ 1 (‾ b) = ‾ 1 (‾ 8/5y + 16)
b = 8/5y - 16
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Solve the equation for y.
SOLUTION
6. Graph the equation – 2x + y = – 3.
– 2x + y = – 3y = 2x – 3
STEP 1
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Substitute 0 for y.
Write original equation.
To find the x-intercept, substitute 0 for y and solve for x.
SOLUTION
7. Find the x-intercept and the y-intercept of the graph of 2x + 7y = 28.
Solve for x.
2x + 7(0) = 28
x = = 14282
2x + 7y = 28
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2(0) + 7y = 28
To find the y-intercept, substitute 0 for x and solve for y.
Write original equation.
Substitute 0 for x.
Solve for y.
ANSWER
The x-intercept is 14. The y-intercept is 4.
2x +7y = 28
y = 287 = 4
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Let (x1, y1) = (–2, 3) = (x2, y2) = (4, 6).
m =y2 – y1
x2 – x1
(6) – 34 – (–2)=
Simplify.
Substitute.
Write formula for slope.
8. Find the slope of the line with these two points (–2, 3) and (4, 6)
= 3 6
= 1 2
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9. Find the slope of the line shown.
m =y2 – y1
x2 – x1
Let (x1, y1) = (3, 5) and (x2, y2) = (6, –1).
–1 – 56 – 3=
– 63= = –2
Write formula for slope.
Substitute.
Simplify.
*** Or, if given the graph, count your rise over run!
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Identify the slope and y-intercept of the line with the given equation.
y = 3x + 410.
3x + y = 211.
The equation is in the form y= m x + b.So, the slopeof the line is 3, and the y-intercept is 4.
Rewrite the equation in slope-intercept form by solving for y.
3x + y = 2 Write original equation.
y= – 3x + 2 Subtract 3x from each side.
The line has a slope of – 3 and a y-intercept of 2.
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12. Graph y + 2x = 4
ANSWER
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13. Find the x-intercept and the y-intercept of the graph of 3x – y = 3
x-int: 1, y-int: – 3 ANSWER
14. Find the slope of the line that passes through the points
(12, – 1) and (– 3, – 1)
ANSWER 0
(–2, 6) and (4, –3)
ANSWER 32–
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15.
Identify the slope and y-intercept of the line 2x + 4y = –16.
16. y = + 123
x
ANSWER
12
–Slope: ,y-intercept: –4ANSWER
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17. Which equation represents the line shown?
The line crosses the y-axis at (0, 3). So, the y-intercept is 3.
y = mx + b Write slope-intercept form.
2y = – x + 352Substitute – for m and 3 for b.5
= = –The slope of the line is riserun
–2 5
25 .
A y = – x + 325 B y = – x + 35
2
C y = – x + 125 D y = 3x + 25
The correct answer is A. B DCA
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18. Write an equation of the line that passes through the point (6, 3) and has a slope of 2.
SOLUTION
y = m x + b Write slope-intercept form.
Substitute 3 for y, 2 for m and 6 for x.
3 = 2(6) + b
Identify the slope. The slope is 2.STEP 1
Find the y-intercept. Substitute the slope and the coordinates of the given point in y = m x + b. Solve for b.
STEP 2
– 9 = b Solve for b.
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y = m x + b Write slope-intercept form.
Substitute 2 for m and – 9 for b.y = 2x – 9
Write an equation of the line.STEP 3
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19. Write an equation of the line that passes through (1, –2) and (–5, 4).
SOLUTION
Calculate the slope.
m = y2 – y1x2 – x1
= 4 –(– 2) –5 – 1 = 6
–6= – 1
Find the y-intercept. Use the slope and the point (1, –2).
y = m x + b Write slope-intercept form.
STEP 1
STEP 2
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– 1 = b Solve for b.
y = m x + b Write slope-intercept form.
Substitute – 1 for m and – 1 for b.y = – x – 1
Write an equation of the line.STEP 3
–2 = –1(1) + b Substitute – 2 for y and – 1 for m.
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20. Write an equation in point-slope form of the line that passes through the point (4, –3) and has a slope of 2.
y – y1 = m (x – x1) Write point-slope form.y + 3 = 2 (x – 4) Substitute 2 for m, 4 for x1, and –3 for y1.
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y – y1 = m (x – x1) Write point-slope form.
y – 4 = –2 (x +1) Substitute – 2 for m, 4 for y, and –1 for x.
Write an equation in point-slope form of the line that passes through the point (– 1, 4) and has a slope of – 2 .
21.
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SOLUTION
22. Write an equation of the line that passes through (–3,–5) and is parallel to the line y = 3x – 1.
STEP 1Identify the slope. The graph of the given equation has a slope of 3. So, the parallel line through (– 3, – 5) has a slope of 3.
STEP 2Find the y-intercept. Use the slope and the given point.
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y = mx + b
– 5 = 3(– 3) + b
4 = b
Write slope-intercept form.
Substitute 3 for m, -3 for x, and -5 for y.
Solve for b.
STEP 3Write an equation. Use y = mx + b.
y = 3x + 4 Substitute 3 for m and 4 for b.
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SOLUTION
STEP 1Identify the slope. The graph of the given equation has a slope of – 1.So, the parallel line through (– 2, 11) has a slope of – 1.
STEP 2Find the y-intercept. Use the slope and the given point.
23. Write an equation of the line that passes through(–2, 11) and is parallel to the line y = – x + 5.
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y = mx + b
11 = (–1 )(– 2) + b
9 = b
Write slope-intercept form.
Substitute 11 for y, – 1 for m, and – 2 for x.
Solve for b.
STEP 3Write an equation. Use y = m x + b.
y = – x + 9 Substitute – 1 for m and 9 for b.
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24. Solve the equation.
3x + 17 – 5x = 12 – (6x + 3)
A. x = ‾ ½B. x = ‾ 1C. x = ‾ 2D. x = ‾ 4/7
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25. Solve the proportion.
3 = 5 x – 4 x
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26. Write an expression.
Three times the difference of a number x and 5.
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27. Simplify.
30 – 18x 6
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28. Find the MPG.
The red vette traveled 368 miles on 16 gallons of gas. What is the mpg of the vette?
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29. What’s my checking account balance?
Monday…wrote a check to Starbuck…$ 35Tuesday…got a refund from Macy’s…$125Wednesday…wrote a check to Sam’s…$ 45Thursday…wrote a check for car…$ 895Friday…wrote a check for dinner…$ 48
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30. For which value of x is the relationship not a function?
{(1,2), (x,1), (4,6), (3,7)}
A. 2 B. 4 C. 5 D. 6*** Use MAP DIAGRAM!!!
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