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If m varies directly as n, then m=k*n, where k is some number. If m also varies inversely as p, then m=k*n/p. So plug in the values to solve for k and get a general formula.
m=k*n/p (Note that (k*n)/p is the same as k*(n/p).)
2=k*16/16
2=k*1
2=k
So the formula is m=2*n/p. Now plug in the other values.
m=2*n/p
16=2*25/p
16=50/p
16*p=50 (I cross-multiplied.)
p=50/16
p=3.125

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You are correct in using a volume formula and plugging in given values. The problem is you used the wrong volume formula and therefore had to plug in your values for the wrong variables. The formula you used, V=s^2*h, is for a rectangular prism with a square base. This coal bin has a rectangular base- it has 3 different dimensions instead of having 2 that are equal. So you need the formula Volume=length*width*height, or in this case, Volume=length*width*depth. Now let's plug in our values.
V=l*w*d
60=5*4*d
60=20*d
60/20=d
3=d
The bin must be filled to a depth of 3 meters.

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If the measures are x and y degrees, and they are supplementary, then their sum is 180 degrees. So you can write and solve a system of equations.
x + y = 180
x - y = 20
Now you can use any method to solve. Let's use the elimination method by adding the equations together.
x + x + y - y = 180 + 20
2x = 200
x = 100
Now solve for y.
100 + y = 180
y = 80
So the angles measure 100 and 80 degrees.

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You can just plug in 60 for x and see which answer gives you 2, since you know it should be 2 inches in 60 minutes.
The answer is B since 60/30 = 2.

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To use the elimination method, make either the x terms or the y terms cancel out when you add or subtract the equations.
You can start by multiplying both equations by 10 to get rid of the decimals.
3x - 2y = 40
5x + 3y = -70/17
Multiply the first equation by 3 and the second equation by 2 so you can add -6y and 6y to get 0.
9x - 6y = 120
10x + 6y = -140/17
[I got -140/17 by multiplying -70/17 by 2. Anything you do to one side of the equation you have to do to the other in order for the equation to still work. So we multiplied each term on each side by 2.]
Now add the equations.
19x = 120 - 140/17
19x = (2040 - 140)/17
19x = 1900/17
x = 1900/(17*19)
x = 1900/323
Now plug this x into either equation to solve for y.
3x - 2y = 40
3(1900/323) - 2y = 40
5700/323 - 2y = 40
2y = 5700/323 - 40
2y = (5700 - 12920)/323
2y = -7220/323
y = -7220/646
The approximate solution is (5.88, -11.18).

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6-3x must be greater than or equal to 0.
-3x must be greater than or equal to -6.
x must be less than or equal to 2.
In interval notation: x is in (-infinity, 2]

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Since the triangle is isosceles, the sides are the same length, x. The base is then x + 40.
So x + x + x + 40 = 370
3x + 40 = 370
3x = 330
x = 110
The lengths of the sides are 110 mm, 110 mm, and 150 mm.

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The area of a parallelogram is base times height.
The height is one-fourth times the base, or 28.4/4 = 7.1 cm.
So the area is (28.4)(7.1) = 201.64 cm^2.

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Substitution method means make one of the equations "x=_" or "y=_", and then substitute that into the other equation.
Since the first equation has a y with no coefficient, solve for y in that equation.
5x + y = 13 --> y = 13 - 5x
Now substitute "13 - 5x" for y in the second equation.
2x = -3y --> 2x = -3(13 - 5x)
Solve for x.
2x = -39 + 15x
39 = 15x - 2x
39 = 13x
x = 3
Now solve for y using the equation y = 13 - 5x
y = 13 - 5x
y = 13 - 5(3)
y = 13 - 15
y = -2
The solution is x=3, y=-2.

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If these vectors are parallel, the slope of the line through (0,0) and (3,6) must be equal to the slope of the line through (0,0) and (-2,k).
The slope of the line through (0,0) and (3,6) is (6-0)/(3-0), or 2.
So the slope through (0,0) and (-2,k) must be 2.
(k-0)/(-2-0)=2
k/-2=2
k=-4

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There are 8 vertices- 4 are part of the rectangle that is at height 0 like the origin. This is the bottom face of the rectangular solid. The other 4 are part of the rectangle that is at height 2 like the given point R. This is the top face of the rectangular solid.
The bottom rectangle has vertices (0, 0, 0), (0, 3, 0), (-1, 3, 0), and (-1, 0, 0). The top rectangle has vertices (-1, 3, 2), (-1, 0, 2), (0, 0, 2), and (0, 3, 2).

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Distribute sqrt(15) to both terms.
sqrt(15)(2sqrt(3) - 4sqrt(5))
= 2sqrt(15)sqrt(3) - 4sqrt(15)sqrt(5)
= 2sqrt(5)sqrt(3)sqrt(3) - 4sqrt(5)sqrt(3)sqrt(5)
= 2sqrt(5)*3 - 4sqrt(3)*5
= 6sqrt(5) - 20sqrt(3)

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Use x for the number of yellow blocks. Then there are x + 4 red blocks. So there are x + x + 4, or 2x + 4 blocks in all.
P(red) = (x + 4)/(2x + 4)
P(yellow after red) = x/(2x + 3)
So the probability is the product, x(x + 4)/(2x + 4)(2x + 3).

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If the rectangle's area is 36 square centimeters, and its length is 9 cm, then its width must be 36/9 = 4 cm.
perimeter = 2l + 2w
= 2*9 + 2*4
= 18 + 8
= 26 cm

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The expected value is the sum of each probability times its value.
P(penny) = 9/60
P(nickel) = 8/60
P(dime) = 12/60
P(quarter) = 16/60
P(half-dollar) = 11/60
P(dollar) = 4/60
Expected value = 1*9/60 + 5*8/60 + 10*12/60 + 25*16/60 + 50*11/60 + 100*4/60
= (9 + 40 + 120 + 400 + 550 + 400)/60
= 1519/60
= approx. $25.32

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A' contains the elements that are in U but not A.
A' = {10, 11, 13, 15, 17, 19}
B' contains the elements that are in U but not B.
B' = {10, 12, 16, 17}
Their intersection contains the elements in both.
A′ ∩ B′ = {10, 17}

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Find the average of the x values and the average of the y values.
x: (-3 + -1)/2 = -4/2 = -2
y: (4 + -6)/2 = -2/2 = -1
The midpoint is (-2, -1).

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A rational expression is undefined when the denominator is 0. So in this case, solve the equation x + 7 = 0. It will be undefined when x = -7.

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The first gummy bear you pick can be any color, so it can be any one of the 25. The probability of that is 25/25, or 1. The second then has to be one of the 4 others of that color. The probability of that is 4/24, or 1/6. So the probability is 1 * 1/6, or 1/6.

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There are 4 terms that keep repeating. So any number divisible by 4 (4, 8, 12, 16, 20,...) will be 9. Which number near 5017 will that be? #5016. That means the 5017th number is the one right after, which will be 3.

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^3sqrt5x+8 +6=1
Subtract 6 from each side.
^3sqrt5x+8 = 1 - 6
^3sqrt5x+8 = -5
Cube each side.
5x + 8 = (-5)^3
5x + 8 = -125
Subtract 8 from each side.
5x = -133
x = -133/5, or -26.6

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There will be 10 pounds of Virginia peanuts and x pounds of Spanish peanuts. The total cost will be 3.5(10) + 3(x). The total amount of pounds will be 10 + x. You want the cost per pound to be $3.40, so the (total cost)/(total pounds) should be 3.4, so solve the equation:
(35 + 3x)/(10 + x) = 3.4
35 + 3x = 3.4(10 + x)
35 + 3x = 34 + 3.4x
1 = 0.4x
x = 1/(4/10)
x = 10/4
x = 2.5
She should use 2.5 pounds of Spanish peanuts.
Then the total cost will be 35 + 7.5, or $42.50.
The total weight will be 10 + 2.5, or 12.5 pounds.
The total cost per pound will be 42.5/12.5 = $3.40/pound.

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If it's length and width are x and y, then its area is xy and its perimeter is 2x + 2y. So you can write 2 equations and solve the system.
xy = 70
2x + 2y = 34
Substitute 70/y for x (from the first equation) into the second equation.
2(70/y) + 2y = 34
140/y + 2y = 34
Multiply everything by y.
140 + 2y^2 = 34y
2y^2 - 34y + 140 = 0
Divide everything by 2.
y^2 - 17y + 70 = 0
(y - 10)(y - 7) = 0
y = 7 or 10
So the dimensions are 7 cm by 10 cm.

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Say the length of the longer leg is x. Then the hypotenuse measures x + 60. So, using the Pythagorean Theorem, x^2 + 180^2 = (x + 60)^2.
x^2 + 32400 = x^2 + 120x + 3600
32400 = 120x + 3600
120x = 28800
x = 240
The longer leg measures 240 m.

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Shifting the parabola to the left 9 units means that to get a certain y-value, you now need to add 9 to the x-value to compensate for the shift. So you plug in "x + 9" for x. So the equation is y=(x+9)^2.

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1. I think you are correct.
2. I think your first choice is correct.
These seem to just want you to know the meaning of "plus or minus".
3. You are correct, 4 is the answer.
4. Look at what you did for #3. You took the coefficient of m and divided it by 2, and then squared it. (-4/2 = -2, and (-2)^2 = 4.) This comes from the fact that (a + b)^2 = a^2 + 2ab + b^2. So in this case, for #4, divide 12 by 2 (and get 6), and then square that (and get 36). So the answer is 36. The factored expression would be (a + 6)(a + 6).

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Write an equation to represent the situation. Call the width x. Then the length is x + 3. So the area is length times width, or x*(x + 3).
x(x + 3) = 700
x^2 + 3x = 700
x^2 + 3x - 700 = 0
Use the Quadratic formula:




x = 25
So the length is x + 3, or 28. The rectangle is 25 yards wide by 28 yards long. (You also could have factored x^2 + 3x - 700 into (x - 25)(x + 28) to get this answer.

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Depends what the spinner looks like. Assuming is has 6 sections, all the same size, with numbers 1, 2, 3, 4, 5, and 6, the probability of getting a number greater than 1 is 5/6, since 5 numbers (2, 3, 4, 5, and 6) of the 6 possibilities will qualify.

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For the line represented by the equation y = mx + b, m is the slope and b is the y-intercept. So plug in 3/4 for m and -2 for b. The equation is y = 3/4 * x + (-2), or y = 3/4 * x - 2.

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It looks like you are trying to figure out why 2 numbers can both be substituted in for x in a quadratic equation. The reason is a quadratic equation has 2 values of x that make it true. An equation can have even more than 2 solutions- the equation x + 3 = x + 5 - 2 is true for any value of x.
You can think of it graphically, too. The graph of a linear equation is a line. When you solve the equation x + 5 = 10, you get the solution x = 5. That means that when you graph the equation y = x + 5, the value of y is 10 when x = 5.
The graph of a quadratic equation is a parabola- it looks like a U. So sometimes more than one x-value will give the same y-value. x^2 - 2 = 14 when x is 4 and -4. When you look at the graph of y = x^2 - 2, the value of y is 14 when x is 4 and -4.