Download Substitute 280 – s for c, Now substitute 200 for s in the first equation

1) 𝑠𝑜𝑦𝑏𝑒𝑎𝑛 + 𝑐𝑜𝑟𝑛𝑚𝑒𝑎𝑙 = 280𝑙𝑏𝑠; 𝑠𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 1 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 => 𝑐 = 280 − 𝑠
.14𝑠 + .07𝑐 = .12(280)
Substitute 280 – s for c,
.14𝑠 + .07(280 − 𝑠) = .12(280)
.14𝑠 + .07(280 − 𝑠) = .12(280)
.14𝑠 + 19.6 − .07𝑠 = 33.6
.07𝑠 = 14
𝑠𝑜𝑦𝑏𝑒𝑎𝑛 = 200
Now substitute 200 for s in the first equation:
200 + 𝑐𝑜𝑟𝑛𝑚𝑒𝑎𝑙 = 280𝑙𝑏𝑠
𝑐𝑜𝑟𝑛𝑚𝑒𝑎𝑙 = 80𝑙𝑏𝑠
2) The domain of an equation is all possible values of x. As we know, fractions are
undefined when x = 0. So in this case, the domain would be all values of x, except for
those which make the denominator equal to 0.
2 − 5𝑥 = 0
2 = 5𝑥
2
=𝑥
5
So, the correct answer here is B. X cannot equal 2/5.
3) 8𝑥 = −56, divide both sides of the equation by 8 and you get:
𝑥 = −7
4) E(t), where t represents the # of years from 1995. The values for t lie on the x-axis. The
values for E will lie on the y-axis. Find the slope of the function using the 2 points given:
a. (67.3-64.4)/(6-0) = .5
1995 = year 0. The corresponding life expectancy is 64.4. Plug those values into the
y=mx+b equation to find the value for b.
b. 𝑦 = 𝑚𝑥 + 𝑏
64.4 = (. 5)(0) + 𝑏
𝑏 = 64.4
The answer is: E(t) = .5t + 64.4
Now, for the 2nd part of the problem, substitute 12 for t: .5(12)+64.4 = 70.4
5) slope = change in y values/change in x values
slope = [4-(-4)]/[6-(-1)] = 8/7
To graph the line, plot the 2 points and draw a line to connect them.
To plot (6,4), go to 6 on the x-axis and up to 4 on the y-axis
To plot (-1,-4) go to -1 on the x-axis and down to -4 on the y-axis
6) Solve by elimination. You need to eliminate 1 of the variables. To do this, multiply both
sides of the first equation by 3 and the both sides of the 2nd equation by 4.
3(3𝑟 − 4𝑠) = (−11)(3), 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 9𝑟 − 12𝑠 = −33
4(4𝑟 + 3𝑠) = (52)(4), 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 16𝑟 + 12𝑠 = 208
Now add the 2 equations together:
25𝑟 = 175
𝑟=7
Now substitute 7 for r in one of the equations:
3(7) − 4𝑠 = −11
−4𝑠 = −32
𝑠=8
The ordered pair would be (r,s) or (7,8)
7) Solve for y to put the equation into slope-intercept form:
1
𝑦=2− 𝑥
2
The y-intercept is where x=0. Sub in 0 for x, and you get y = 2. Plot a point at (0,2)
To find the x-intercept, sub in 0 for y, and solve for x. You get x=4. Plot a point at (4,0).
Draw a line connecting the 2 points.
8) 2L + 2W > 82
2(10) + 2W > 82
2W > 62
W > 31
9) Plot a point at (6,-4). Extend the vertical line only in the upward direction since y is
greater than -4, and the horizontal line only gets extended to the right since x is greater
than 6.
10) A, consistent, dependent
11) D
12) 9(𝑤 − 2) = 18
9𝑤 − 18 = 18
9𝑤 = 36
𝑤=4
13) Count how many units up and to the right the 2 points are apart:
Slope = rise/run = 3/2
14) 8𝑥 − 5𝑥 − 6 = 18
3𝑥 = 24
𝑥=8
15) Substitute 39 for x in the given equation and you get 178.73
16) Start in the middle at (0,0) and go up to 8 on the y-axis and draw a horizontal line
extending to the right and left.
17) C
18) Graph the points (0,2) and (3,0). Draw a downward sloping line, and shade the area on to
the right of the line.
19) Start in the center at (0,0) and go up to 4 and plot the point.
1
20) −7(15)𝑥 > 15 (15)
−105𝑥 > 1
1
𝑥<−
105
21) B
22) Convert to slope-intercept form. Since the slopes are negative reciprocals, the lines are
perpendicular. Answer is B
23)
24) (3,-3)
25) 26
26) ≥ 11.25
27) 2005 = 18,268
2008 = 12,937
2010
2
28) − 9
29) Plot a point at (0,2). Plot your next point up 5 units and 4 to the right at (4,7). Connect
the 2 points.
21
30) 20
31) Plug in the numbers to see if the given ordered pair is a solution.
Since 2(-3) – 3(-1) is not equal to 20, (-3,-1) is NOT a solution.
Answer is: NO
13
32) − 3 𝑎𝑛𝑑
33) C
34) B
35) B, A
36) f(0) = 0
f(-1) = 6
f(2) = 0
1
3
37) 50
38) D
17
39) − 2
40) Y-intercept (0,-8)
For the graph, plot the y-intercept (0.-8), and (8,-16) and connect the 2 points
41) >
42) 0.27y
43) d/6
44) B
45) 1
46) X< 2
47) 90
48) No
49) (-8,5)
50) 91.58
51) 152
52) Plot the points (0,2) and (10,0). Draw a line to connect the 2 points and extend the line in
both directions.
53) 3 months service = $100, C, Graph D
54) 6
55) Slope = -4
y-intercept = -8
56) 9r – 5s