10.4
2.5
Solve for x:
10x=100
x = 2
Find the line that has slope 3 and goes through (0,1)
y = 3x+1
Express the area (A) of a square in terms of its perimeter (P).
A = (P/4)2
You’re mixing 5L of a 20% bleach solution with 10L of a 10% bleach solution. How many liters of bleach are in the result?
2L
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.2(5)+.1(10)=1+1=2
log(2)
.3
Solve for x:
2x=82
x = 6
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2x=(23)2=26
Find the line with slope -2 that goes through (3,5)
y = -2x+11
Express the perimeter (P) of the circle (fig. 1) in terms of the side length (s) of the square.
P = πs
You mix 3L of a 10% salt solution with 1L of a 18% salt solution. What's the percentage of salt in the mixture?
12% salt
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amount of salt in mix = .1(3)+.18(1) = .48
amount of mixture = 3+1 = 4
percentage of salt = (.48/4)x100% = 12%
log(700)
2.85
Solve for x:
2(3x)=4
x = log(2)/log(3)
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3x=2
xlog(3)=log(2)
Find the line that passes through (2,2) and (4,6)
y = 2x-2
Find the area (A) of the region outside of the circle (fig. 1) in terms of the radius (r) of the circle.
A=(4-π)r2
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Area of square = (side)2=(2r)2=4r2
Area of circle = πr2
Shaded area = (area of square)-(area of circle) = 4r2-πr2
You have 3L a mixture of 20% salt. How much water should you add to get a mixture of 10% salt?
3L
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x = amount of water
.2(3)+0(x)=.1(3+x)
.6=.1(3+x)
x = 3
10-1.4
.04
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10-1.4=10-2x10.6=.01x4=.04
Solve for x:
3x=9x+1
x = -2
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3x = (32)x+1=32(x+1)
x = 2x+2
Find the intersection of y = 3x+1 and y = 2x+1
(0,1)
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3x+1=2x+1
x=0
Figure 2 shows a field. The fencing for it costs $10/m. How much does the fence cost?
(only the solid lines represent fences, not the dashed line)
Cost = $(15π+150)
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Outside perimeter of half-circle = π(diameter)/2 = 1.5π
Perimeter = 2(6)+3+1.5π = 15+1.5π
Cost = ($10)x(perimeter) = ($10)x(15+1.5π) =$(150+15π)
You need 1 gallon of 30% alcohol solution, you have a 25% solution and a 40% solution. How much of the 25% solution should you use?
2/3 gallon
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x = gallons of 25%
.25x+.4(1-x)=.3(1)
-.15x=-.1
x=.1/.15=2/3
log(5003)
8.1
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log(5003)=3log(500)=3[log(100)+log(5)]= 3[2+.7]=6+2.1=8.1
Solve for x:
4x=2(5x-1)
x=log(2/5)/log(4/5)=[log(2)-log(5)]/[log(4)-log(5)]
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4x=(5x)(2/5)
xlog(4)=xlog(5)+log(2/5)
x[log(4)-log(5)]=log(2/5)
x = log(2/5)/[log(4)-log(5)]= log(2/5)/log(4/5)
Find the intersection of y = 2x+3 and the line with slope 1 that passes through (3,4).
(-2,-1)
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y = x+1
2x+3 = x+1
x = -2
You have a box with a square base and no top with volume 400 cm3. The material for the base costs $3/cm2 and the material for the sides costs $2/cm2. Express the cost of the box in terms of its height, h.
Cost = $1200/h+160h1/2
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V = 400 cm3 = (area of base) x (height)
400/h = area of base = side2, so side = 20/h1/2
Area of box side = (height) x (side) = 20h1/2
($3)x(area of base)+4x($2)x(area of box side)= $ (1200/h+160h1/2)
You have x mL of a solution that is 40% acid. You add a solution that is 10% acid until the result is only 30% acid. How much of the mixture do you end up with?
1.5x mL
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y = amount of mixture
.4x+.1(y-x) = .3y
.3x = .2y
y = .3x/.2 = 1.5x