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Factor:
This is a difference of squares, and and...

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100mg = 4cc. Multiply both sides by 0.4 because mg.

so...
1.6cc are contained in 40mg. (cc. = cubic centimeters)

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Let the angle be A, then its complement is (90-A), so...
Simplify. Multiply by 2.
Add A to both sides.
Divide by 3.
degrees.

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Two consecutive numbers can be expressed as:
x and x+1, so...
x+(x+1) = 117 Simplify.
2x+1 = 117 Subtract 1.
2x = 116 Divide by 2.
x = 58.
So the two numbers are:
58 and 59.

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It looks like you did everything right and you got the correct answer.
Let's check:
Now substitute your answer of
Evaluate.



You did good!

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You can use the compound interest formula to get your answers:

A = The present amount (your answer).
P = the principal amount invested (P = $40,000).
i = the rate of interest, expressed as a decimal (i = 0.09).
q = The number of compounding periods per year (q = 1 for annually, 4 for quarterly, and 12 for monthly).
n = number of years (n = 16).
Compounded annually:
Substitute P = 40000, i = 0.09, q = 1 (once per year), and n = 16:
Use your calculator.

A = $158,812.24
Compounded quarterly:
Substitute P = 40000, i = 0.09, q = 4 (4 times per year), and n = 16.
Use your calculator.

A = $166,154.56
You should now be able to do the last one yourself using the same formula and the same numbers except that q = 12 (for 12 times per year).

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Isn't that the truth! This is not an uncommon phenomenon.
Do you have a specific problem that you'd like help with?

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You can work this out yourself when you realise that:
1 cubic entimeter = 0.999972 milliliters.
For all practical purposes:
1 cc. = 1 ml.

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Solve:
Apply the "power rule" to the right side.
Now if then so...
Rearrange as:
Solve by factoring:
Apply the "zero product" rule:
or so that...
or
Now you must check the results for "extraneous" or "invalid" values:
Try
Substitute


This is not valid!
Try
Substitute


This is valid.
Solution is

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Let D = Dad's present age and S = Son's present age.
1) D-10 = 4(S-10) "Ten years ago the age of a father (D-10) was four times the age of his son (4(S-10))."
2) D+10 = 2(S+10) "Ten years hence, the age of the father (D+10) will be twice that of his son ((2(S+10))."
So now you have two equations with two unknowns (D & S). Simplify the two equations:
1a) D-10 = 4S-40
2a) D+10 = 2S+20 Subtract equation 2a) from equation 1a) to get:
3) -20 = 2S-60 Now add 60 to both sides.
3a) 40 = 2S Divide both sides by 2.
3b) 20 = S or S = 20 Now substitute this value of S into 1a) or 2a) and solve for D.
2a) D+10 = 2S+20 Substitute S = 20
2b) D+10 = 2(20)+20 Simplify.
3c) D+10 = 60 Subtract 10 from both sides.
3d) D = 50
The father is 50 years old and the son is 20 years old.

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The area of the square with sides of (x+1) is:


The area of the rectangle with sides (x+2) and (x) is:


Subtract the area of the rectangle from the area of the square:

-()
-----------
The area of the square is larger by 1 square unit.

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Let x = the required number of liters of the 25% acid solution, then (10-x) is the required number of liters of the 50% acid solution. These are mixed to obtain 10 liters (x+(10-x)) of 40% acid solution. Let's write the equation to solve for x after changing the percentages to their decimal equivalents.
0.25x+0.5(10-x) = 0.4(10) Simplify.
0.25x+5-0.5x = 4 Combine the x-terms.
-0.25x+5 = 4 Subtract 5 from both sides.
-0.25x = -1 Finally, divide both sides by -0.25
x = 4 and 10-x = 6, so...
The chemist will need to mix 4 liters of the 25% acid solution with 6 liters of the 50% acid solution to obtain 10 liters of 40% acid solution.

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Let the scores of the first three tests be a, b, and c. Then:
To find the sum of the first three test scores, multiply both sides by 3.
Now let the fourth test score be x, so...
Substitute
Multiply both sides by 4.
Subtract 261.

Takia must score at least 99 points on the fourth test to achieve an overall average of 90.

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Simpl;ify:
Evaluate this:
or

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Factor by grouping:
Group as shown:
Factor as shown:
Now factor the
You can check the answer by multiplying the two factors.

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Factor:
24) Rearrange as:
=
74) Factor out a 6.
Factor the difference of squares.

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Let R = Rosa's present age, then...
Solve for R. Subtract R from both sides.
so...
Rosa's present age is less than 5 years.

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First, apply the "power rule" for logarithms:

Substitute and
Now apply the "product rule" for logarithms:

Now apply the "quotient rule" for logarithms:


and if then so...

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3x+4x Factor out the x.
(3+4)x = 7x

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Let x = the required number of gallons of the 40% glycol solution. This is to be added to (24-x) gallons of the 10% glycol solution to obtain 24 gallons of 30% glycol solution. The equation to solve for x is:
0.4x+0.1(24-x) = 0.3(24)
0.4x+2.4-0.1x = 7.2 Simplify.
0.3x+2.4 = 7.2
0.3x = 4.8
x = 16 gallons and (24-x) = 8 gallons.
The mechanic will need to mix 16 gallons of the 40% glycol solution with 8 gallons of the 10% glycol solution to obtain 24 gallons of 30% glycol solution.

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Simplify(?):
Factor the numerator and the denominator:
=

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If the two numbers are a and b, then a+b = 56 which can be written as a = 56-b.
Now a*b must be a maximum (call it y)so we can write a*b as:
Simplify.
This is a quadratic equation and the graph will be a parabola opening downward.
So all you need to do to find the maximum is find the value of b at the point of the parabola's vertex which is given by:


So the two numbers are: a = 28 and b = 28.

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Reading from right-to-left (like arabic), the binary number 1001 can be read as:
+++= in decimal.
The octal (base 8)equivalent is and this is deciphered as follows:
Group the digits of the binary number in groups of three starting from the right sides thus:
which is 11
In octal (base 8) the binary-to octal conversion looks like:

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In a regular polygon of n sides, the measure of an internal angle is given by:

An internal angle and the corresponding external angle are complementary so that if the external angle is 20 degrees then the corresponding internal angle is 180-20 = 160 degrees.
Solve for n.

Subtract 160n from both sides.
Add 360 to both sides.
Divide by 20.

The regular polygon has 18 sides.

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Let x = the number of customers who ordered decaffeinated coffee, then x+126 cutomers ordered regular coffee, so we can right a proportion:
Solve for x. Cross-multiply.
Subtract x from both sides.
Divide both sides by 3.

42 customers ordered decaffeinated coffee and 168 (42+126) customers ordered regular coffee.
Check:

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Start with:
for the area of a triangle. A is given as 338.
now you can write the equation.
Substitute
Simplify the left side.
Divide both sides by 2.
Take the square root of both sides.
and...



The base is 13 and the height is 52.

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Simplify by using the "distributive property".
Subtract 2x from both sides.
Subtract 15 from both sides.
Finally, divide both sides by -5.

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Let Ja be Jack's present age and Ji be Jill's present age.
1) Ja + Ji = 78 "...the sum of their ages is 78."
2) Ja = 5Ji+6 "Jack is six years more than five times as old as Jill." Rewrite equation 1) as:
1a) Ja = 78-Ji and substitute for Ja in equation 2) to get:
2a) 78-Ji =5Ji+6 Solve for Ji. Add Ji to both sides
2b) 78 = 6Ji+6 Now subtract 6 from both sides.
2c) 72 = 6Ji Finally, divide both sides by 6.
2d) 12 = Ji Jill is 12 years old.
1b) Ja = 78=Ji
1c) Ja = 78-12
1d) Ja = 66 Jack is 66 years old.

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Remove the absolute-value bars from the left side and you get two equations thus:
1) or 2) Now solve each of these equations for x.
1) Rewrite as a quadratic equation in standard form:
Factor this quadratic equation.
Apply the "zero product" rule:
or so that...
or
2) Simplify the right side.
Rewrite as a quadratic equation in standard form:
Factor this quadratic equation.
Apply the "zero product" rule:
or so that...
or

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Let K = Kay's age and M = Max's age.
"...the sum of their ages (is) 25."
"Kay is two years less than twice the age of Max." Substutute this into the first equation.
Simplify and solve for M.
Add 2 to both sides.
Divide both sides by 3.

Max is 9 years old.

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Do you want to factor this expression?
First factor a y from each term.
Now factor the trinomial.
...and that's the best you can do!