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Solve by completing the square:
Subtract 13 from both sides of the equation.
Complete the square in the x-terms by adding the square of half the x-coefficient to both sides.
Factor the left side.
Take the square root of both sides.
= +or- Finally, subtract 4 from both sides.
or

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Solve:
Take the square root of both sides.
= +or-9 Subtract 8 from both sides.
x = -8+9 or x = -8-9
x = 1 or x = -17

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Well, if and , then and so

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Here's one way to tackle problems like this:
x/100 = is#/of#
Explanation:
The x is the percentage you are trying to find.
The is# is taken from the problem, which in your case, it says" ...19.8 is what..." So 19.8 is the is#
The of# is also taken from the problem, which in your case, it says "...what percent of 36." So 36 is the of#.
So we have:
Now multiply both sides of this equation by 100.



The answer is:
19.8 is 55% 0f 36

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The two isosceles triangles are "similar" so their sides are "proportional"
Find the scale factor by dividing the known length of one side of the larger triangle by the known length of a "corresponding" side of the smaller triangle.
Scale factor is: 8"/2" = 4
Multiply the length of the base of the smaller triangle by the scale factor of 4 to find the unknown length of the base of the larger triangle.
Base of smaller triangle = 3"
Base of larger triangle = 4 X 3" = 12"

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1) Solve:
Subtract from both sides of the equation.
Now square both sides.
Divide both sides by x

2) Here's the graph: The red line is y=x. The green line is
The points of intersection are: (0,0) and (4, 4)

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Cost of desk: $125
Selling price: $350 Subtract cost of repairs ($75)
Profit is selling price less cost of repairs less cost of desk.
Profit: ($350 - $75) - $125 = $275 - $125 = $150
Percent profit = (Profit/cost) X 100
Percent profit = ($150/$125)X100 = 120%

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Solve: Try factoring.
The factors will have the form: where:
a + b = 1 and a*b = -72
Try: a = -8 and b = 9
-8+9 = 1
(-8)(9) = -72
So,
Factor.
Apply the zero products principle.
and/or
If then
If then
The roots (solutions) are:
x = -8
x = 9

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Factorise:
Look for common factors in each term. 3w is a common factor.
Factor the 3w.

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To solve this problem, you will need to find "weighted average" speed.
While it does seem that the average speed for Jackie's round trip ought to be , Jackie did not drive at the given speeds for equal amounts of time, so you must find the weighted average speed for the trip.
Using the formula: where: d = distance traveled, r = rate of travel (speed), and t = the time taken to travel the distance, d, you can find the weighted average speed by dividing the sum of the distances for each leg by the sum of the times taken for each leg.

The distance for each leg is given as x, so the sum for the trip is 2x.
The times for each leg are not given so they must be calculated. Using or



----------------



Now we can find the weighted average speed (M) for the round-trip.


Cancel the x's


The aveage speed for the trip is 44.4 mph

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Factor:
This is a sum of two cubes and can be factored thus:

=
=

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The percentage of rented apartments is found by: %

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Solve:
Take the square root of both sides of the equation.
(x-3) = +or- 4 Add 3 to both sides.
x = 3+4 or 3-4
The two roots are:
x = 7
x = -1

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Factor:

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Think about this! A vertical line has the same x-coordinate wherever you are on the line.
So the equation of a vertical line that passes through the point (6, 5) is just: x = 6

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Anything (except zero) to the zero power is equal to 1.
So,

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1) If the car goes from standstill to 54 mph in 5 seconds, you can find the acceleration, assuming it's uniform of course, by dividing the speed (54 mph) by the time (5 secs).
But you must work in similar units, so convert the speed of 54 mph to mps (miles per second) before you divide by the 5 seconds.
54 miles/hour divided by 3600 seconds/hour = 0.015 miles per second.
Now divide 0.015 miles/sec by 5 secs = 0.003 miles/second squared.
This means that the car is increasing its speed at the rate of 0.003 miles for each second of travel.
2) The speed of light,
Distance to sun,
Time of travel, t = distance/speed.


seconds. Divide this by 60 to get minutes.
t = 8.28 minutes.

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Let x = the required number of pounds of 16%-protein soybean meal
15-x = the required number of pounds of 10%-protein corn meal.
You want x lbs of 16%-protein (0.16x) plus (15-x) lbs of 0.10%-protein (0.10(15-x)) to equal 15 lbs of 12% (0.12)(15) of mixture.
Change the percents to their eqivalent decimals and write the equation.
Simplify and solve for x.
Combine the x-terms.
Subtract 1.5 from both sides of the equation.
Divide both sides by 0.06

You will need 5 lbs of 16%-protein soybean meal and 10 lbs of 10%-protein corn meal to make a 15-lb mixture that is 12% protein.

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Well, the way you have spelled it (pie), it means a delicious baked item, usually circular in shape, whose contents can be any of a variety of delectable fruits.
But seriously...
Pi is a greek letter that used in mathematics to represent the ratio of the circumference of a circle to its diameter. This ratio is a constant for any circle . The value of is an irrational number (a non-repeating, non-terminating decimal) and is commonly approximated by 3.14 or .

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Let x = the amount originally invested. After one year, Sharon will have $x (the original amount) plus 6% of $x (the interest earned on the original amount in one year) and this will equal $6996.00: Change the 6% to its decimal eqivalent.(6% = 0.06) and write the equation.
Combine the x-terms.
Divide both sides of the equation by 1.06

Sharon originally invested $6600.00

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You can let x = the length of the short side. Then the length of next largest side would be x+2 and the length of the largest side would be x+4. These sides add up to 195 mm. You can set up the equation to find x, the length of the short side.
Simplify and solve for x.
Subtract 6 from both sides of the equation.
Divide both sides by 3.

The length of the short side is 63 mm
The length of the middle side is x+2 = 63+2 = 65 mm
The length of the long side is x+4 = 63 + 4 = 67 mm
Check: 63+65+67 = 195 mm

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To graph these, first get the equations into the slope-intercept form: y = mx + b
1) is
2) is
Now you can graph them:

It's a little hard to read from the graph, but the point of intersection (solution) is: (5, 7)

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First look for common factors in each term. 2a is a common factor, so factor out 2a.
Now factor the parentheses.

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Factor:
The factors will have the form:
(x + m)(x + n) where (m)(n) = -60 and (m) + (n) = -11
Try m = 4 and n = -15
(m)(n) = -60 and (m)+(n) = 4+(-15) = -11
The factors are:
(x+4)(x-15)

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By definition:
A line segment has a beginning and an end.
A ray has a beginning but no end.
A line has neither beginning nor end.

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Find the cube root of 500. The cube root of 500 can be expressed with exponents:
=
==
The answer:
The cube root of 500 =

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To find the area inside the square not covered by the circle, you need to find the area of the square then subtract from it the area of the circle.
It is assumed, although you don't say, that the sides of the square are tangent to the circumference of the circle.
The area of the square is found by: whers S is the length of one side of the square, or 9 inches.

Square inches.
The area of the circle is found by and the radius, r, of the circle is equal to half the length of one side of the square, or 4.5 inches. Using 3.14 as an approximation for


square inches.
Now you will subtract the area of the circle (63.585 square inches) from the area of the square (81 square inches)
81 - 63.585 = 17.415 Rounded to the nearest tenth this is 17.4 square inches.
Answer: 17.4 square inches.

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Solve by completing the square:
First, subtract 5x from both sides of the equation.
Complete the square in the x-terms by adding the square of half the x-coefficient (that's to both sides of the equation.
Simplify.
Now take the square root of both sides.
...and , of course, the right side has a + or - in front. Now add 5/2 to both sides.
+or-

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1) Factor:
You should recognise this as the difference of two squares: and
The difference of two squares can be factored:
Appplying this to your problem:
=
2) Factor:
If you rearrange this expression, you will see that it is really the difference of two squares.
Factor the parentheses.
Now it's in the form of: which will factor nicely.
=
You can verify these answers by multiplying the factors to see that you get back the original expressions.
I'll leave this as an exercise for the student!

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To find the toatal change in xyz's stock price, you will need to add (-2 1/8) and (-1 3/4).
-2 1/8 + (-1 3/4) = -2 1/8 + (-1 6/8) = -3 7/8
The stock price dropped a total of 3 7/8 points.

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Let the two numbers be a and b.
You can write two equations from the problem description.
Solve this one for a and substitute into the second equation.

Simplify and solve for b.
Subtract 105 from both sides of the equation.
Multiply through by -1.
Factor out a 3.
Apply the zero products principle.
Factor this quadratic equation.
Apply the zero products principle again.
and/or
If then
If then
The two numbers are: 5 and 7