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Simplify:
Since there is a common denominator, you can subtract the numerators:
Now factor the denominator.
Cancel the indicated common factors.

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Set up the equation for the cost of the rental.
where d = number of days rented and m = number of miles driven.
Substitute C = $200.00 and d = 2 days.
Simplify.
Subtract 59.90 from both sides.
Divide both sides by 0.29

You can drive for 483 miles.

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Simplify:

To divide fractions, you invert the second fraction and multiply.
Now factor each of the trinomials.
Cancel the common factors as indicated. You now have:
Substitute
Cancel the indicated common factors to leave you with:
or

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You can set up the proportion as follows:
(7 PCs infected)/(12 PCs connected) = (x PCs infected)/(216 PCs connected) or...
Multiply both sides by 216.
Evaluate.
This is the estimated number of infected PCs.

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FInd the lateral surface area, the total surface area, and the volume of a cylinder whose radius (r) is 3 cm. and whose height (h) is 10 cm.
a) Lateral surface area is:
(Area = Circumference times the height) Substitute r = 3 and h = 10.

This is the exact answer. For an approximation, substitute to get:

sq.cm.
--------------------------------------------
b) The total surface area of the cylinder is the sum of the lateral surface area (see a) above) and the areas of the top & bottom of the cylinder.
These areas (top & bottom) are the same so you need compute only one and then double it to get both.
Area of the top:
Substitute r = 3.

now double this to include the bottom:

For an approximation, substitute

sq.cm.
Now add this to the lateral surface area () to get:

Exact answer, or approximately:
sq.cm.
-----------------------------------------------
c) The volume of a cylinder is given by:
Substitute r = 3 and h = 10.

or approximately:

cu.cm.

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Given:

Find a and c.
First, you are told that the maximum (vertex) of the parabola is at (1, 8).
The value of the x-coordinate of the vertex is given by:
Substitute b = 4 and x = 1 (from (1, 8)) to get:
Multiply both sides by a.
Simplify.
so we have...
Now to find the value of c, just substitute the x- and y-coordinates of any of the points given in the problem. (1, 8) or (-1, 0) or (0, 6) or (3, 0).
The reason you can do this is because every one of these points lies on the curve (parabola) and thus satisfies the given equation.
Let's choose the point (0, 6).
Simplify.

The equation is:

Let's see what the curve looks like!

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Solve by graphing:
1) x-y = 3
2) x+y = 5
First solve the equations for y.
1) x-y = 3 Subtract x from both sides.
-y = -x+3 Now multiply both sides by -1 to make the y positive.
y = x-3
2) x+y = 5 Subtract x from both sides.
y = -x+5
Now the graph.

From the graph, you can see that the two lines intersect at the point (4, 1) and this is the solution to the system of equations.

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Since we are talking about linear equations, we need only two points to define the line and we can write the equation of the line if we know its slope and its y-intercept.
We can write the equations in the slope-intercept form: y = mx+b where m = slope and b = y-intercept.
For line M, pick any two of the given five points to find the slope (m) of the line:
Let's pick the first two points from the list (1, 3) and (2, 5) and substitute their x- and y-cordinates into the slope formula:


so, we have, so far...
To find b, the y-intercept, you can use the x- and y-coordinates of either one of the two points (or any of the other given points for that matter, as long as they lie on the line). Let's use the first point in the list (1, 3):
Subtract 2 from both sides of the equation.
so the final equation for line M is:

Similarly, for line N:
Pick points (1, -1) and (2, -3), substitute their x- and y-coordinates:


so...
use the second point (2, -3) to find b, substitute:

Add 4 to both sides.
so the final equation for line N is:

-------------------------------------
The point of intersection of the two lines is found by solving the system of linear equations just developed. This is esily done by setting the two equations equal and solving for x.
Add 2x to both sides.
Subtract 1 from both sides.
so...
now substitute this into either one of the two equations and solve for y:


The point of intersection of the two lines is (0, 1)
--------------------------------------------
The line intersect the x-axis at y = 0, so, set y = 0 in each equation and solve for x.
For line M:
Substitute y = o.
Subtract 1 from both sides.
Divide both sides by 2.
or
For line N:
Substitute y = 0.
Subtract 1 from both sides.
Divide both sides by -2.
or
---------------------------------------
Remember that the intersection of the lines with the y-axis is called the y-intercept or b in the equation of the lines.
Foe line M: b = 1.
For line N: b = 1.
----------------------------------

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You first need to find the length of the digonal path.
The length of the diagonal path can be found by use of the Pythagorean theorem: where c represents the diagonal path.


Take the square of both sides.
meters.
Now multiply 30 meters by $12 per linear meter.
The cost is $360.00

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Let M = Mother's age.
A = Alex's age.
S = Sister's age.
A = S-8
M = 2S+6
M = 42, so...
2S+6 = 42 Subtract 6 from both sides.
2S = 36 Divide both sides by 2.
S = 18
A = 18-8 = 10
Alex is 10 years old and his sister is 18 years old.

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1) Solve by eliminating the decmals:
Multiply through by 100.
Subtract 8t from both sides.
Add 950 to both sides.
Finally, divide both sides by 42.

---------------------
2) Start with 2x+1 as the first odd number. (You can see that no matter what value x takes on, 2x+1 will give you an odd number), then the next consecutive odd numbers will be:
(2x+1)+(2x+3)+(2x+5)+(2x+7) = 120 Simplify and solve for x.
8x+16 = 120 Subtract 16 from both sides.
8x = 104 Divide both sides by 8.
x = 13.
The first odd integer is 2x+1 = 2(13)+1 = 27.
The second consecutive odd integer is 2x+3 = 2(13)+3 = 29.
The third consecutive odd integer is 2x+5 = 2(13)+5 = 31
The fourth consecutive odd integer is 2x+7 = 2(13)+7 = 33

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Simplify:
Rearrange a bit.

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Solve for x by completing the square:
First add 1 to both sides.
Now complete the square in x by adding the square of half the x-coefficient ( to both sides.
Factor the left side and simplify the right side.
Take the square root of both sides.
(+ or -) in front of the sq.rt. Now add to both sides.
or

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Let x = the orignal price.
The sales price is x (the original price) less the discount 0.2x ( 20% of the original price), so...
x-0.2x = $12,590.00
x(1-0.2) = $12,590.00
x(0.8) = $12,590.00 Divide both sides by 0.8
x = $15,737.50

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Let a = the smaller number and b = the larger number, then...
1) a+b = 88 "The sum of two numbers is 88"
2) 3a = 2b+29 "Three times the smaller equals twice the larger plus 29"
Rewrite equation 1) as a = 88-b and substitute into equation 2).
3(88-b) = 2b+29 Simplify and solve for b.
264-3b = 2b+29 Add 3b to both sides.
264 = 5b+29 Subtract 29 from both sides.
235 =5b FInally, divide both sides by 5.
47 = b and a = 88-47 = 41
The two numbers are: 41 and 47

k^2+3k-10      3
_________ x ________
    36       k^2-4

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It would help if you were to use paretheses to clarify the problem, eg:
((k^2+3k-10)/(36))*(3/(k^2-4)) I hope I've got this right!
Factor the first numerator and denominator and factor the second denominator.
Cancel the common factors as shown to leave you with:
or

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Find the GFC of:
, , and
The answer is: These three expressions have no common factors!

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Factor the trinomials in the numerators and the denominators.
Now cancel the common factors as shown to leave you with:

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Let's do the first problem to, hopefully, clear up your confusion!
Use the quadratic formula:
to solve:
Here, , , and
Making these substitutions into the formula, we get:




or and this can be further simplified to:
or
These are the solutions in simplest radical form.
When the intructions are to "leave the roots in simplest radical form"
it simply means that you do not try to evaluate the square root but do simplify the fraction as much as you can.
I hope this helps you solve the second problem, but if you are still having difficulties, please re-post.

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You need to add the following integers: (Gain = +) (Loss = -)
9+(-26)+28 = 9+2 = 11
11 yards is the total net gain.

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Multiply:
You multiply the each term in the second group by the first term in the first group.
Then multiply each term in the second group by the second term in the first group.
Finally, multiply each term in the second group by the last term in the first group.
Then you simplify the result.

Now we simplify this by combining like-terms.

This is the answer.

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Let I = the measure of an interior angle and E = the measure of the corresponding exterior angle.
Recall that the interior angle and the exterior angle are supplementary so: I+E = 180 degrees.
You are told in the problem that:
I = 8E "The measure of each interior angle of a regular polygon is 8 times that of an exterior angle."
Substitute I = 8E into the first equation and solve for E.
8E+E = 180
9E = 180
E = 20 Degrees. This is the measure of an exterior angle.
The interior angle is:
I = 8E
I = 8(20)
I = 160 degrees.
Now the measure of an interior angle of a regular polygon of n sides is given by:
But we just found the measure of an interior angle: I = 160, so we substitute and solve for n.
Multiply both sides by n.
Subtract 160n from both sides.
Add 360 to both sides.
Finally, divide both sides by 20.

The regular polygon has 18 sides.

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1. Let a be the length of the shorter piece and b = the length of the longer piece.
a+b = 33
b = 2a-3 Substitute this into the first equation.
a+(2a-3) = 33 Solve for a.
3a-3 = 33 Add 3 to both sides.
3a = 36 Divide both sides by 3.
a = 12
The shorter piece is 12 inches long.
-----------------------------------
Let n be the missing number, then:
Multiply through by 3.
Subtract n from both sides.
Add 24 to both sides.
Divide both sides by 5.

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1.
-------------------
2. =
-------------------
3. =
-------------------
4. =

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Let BL = the number of black shoes and BR = the number of brown shoes.
From the problem statement:
1) BL = 2*BR "the shoe store has twice as many black shoes as it does brown shoes."
2) BL+BR = 66 "the total number of shoes is 66."
Rewrite equation 2) as:
BL = 66-BR and substitute this into equation 1).
(66-BR) = 2*BR Add BR to both sides of the equation.
66 = 3*BR Divide both sides by 3.
22 = BR
There are 22 brown shoes.

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Given:

a) Rewrite by factoring the GCF (that's P).

b) Find A if P = $8300, r = 15% (that's 0.15 in decimal) and t = 3 years.
Evaluate.


A = $12,035.00

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Problem 1. )d = distance, r = rate(speed), and t = time of travel)
For the first cyclist:

For the second cyclist:

The question is at what time, t, will ?
The first cyclist travels 3 hours longer than the second cyclist, so...
, so rewriting the first two equations, we get:
and
but, when the cyclists meet, , so...
Solve for .
Subtract from both sides.
Divide both sides by 4.
hours.
The second cyclist will catch up with first cyclist after 4.5 hours.
The first cyclist however will have traveled for (4.5+3) = 7.5 hours.
So if you start counting when the first cyclist begins, then the answer is 7.5 hours.
If you start counting when the second cyclist begins, then the answer is 4.5 hours.
The problem is not clear as to when you should start the clock!
Problem 2.
It's best to work out the rate (per minute) at which each of the three individuals work.
If Jim can fill the pool in 30 minutes, then he can fill 1/30 of the pool in 1 minute.
If Sue can fill the pool in 45 minutes, then she can fill 1/45 of the pool in 1 minute.
If Tony can fill the pool in 1 1/2 hours (that's 90 minutes), then he can fill 1/90 of the pool in 1 minute.
Working together, the three of them can fill (1/30 + 1/45 + 1/90 = 1/15) of the pool in 1 minute.
This means that they can fill the entire pool in 15 minutes working together.

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Rewrite as an exponential equation:

The definition is:
"The logarithm of a number (it's 3 here) is the power (this is the 0.4771) to which the base (that's 10) must be raised to equal that number"

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Well, you've got the right idea!
Simplify:
=

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Solve for x:
Rewrite this in exponential form:

Add 7 to both sides.
Divide both sides by 2.

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System of equations:
1)
2)
Multiply equation 1) by 6 to get:
1a)
As you can see, the two given equations are identical, so...
The system is a consistent system since there is at least one solution and the equations are said to be dependent equations.