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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!

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Solve for x:
Add the fractions by finding the LCDs.
Simplify.
Multiply both sides by .
Subtact 2x from both sides.
Subtract 6 from both sides.
Divide both sides by 5.

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You can solve this by factoring.
Apply the "zero product" rule.
or then...
so or
so
The roots are:
and

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Let n = the number, so...
7n = 1596 Divide both sides by 7.
n = 228
Seven times 228 is 1596.

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First find the volume of the fish tank:
W = 80cm., d = 35cm., and h = 50cm., so...

cc.
Now you would apply the conversion factor of:
One litre = 1,000 cu.cm. Divide 140,000cc by 1,000cc/litre to find the number if litres in the fish tank.
litres.

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A linear equation of the form: is called the "slope-intercept" form in the U.S.
The "slope", m, would be equivalent to the "gradient".
Compare this with the "slope-intercept" form:
and you can see that the slope (or gradient), m = 5.
Does this make sense?

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Let a = Doug's count of ducks, b = Dave's count, and c = Don's count.
a = 2b "Doug counts twice as many as Dave."
b = 2c "Dave counts twice as many as Don."
a+b+c = 42 ""Together they spotted a total of 42 ducks."
Rewrite the first equation:
a = 2b Replace b = 2c to get:
a = 2(2c)
a = 4c Now rewrite the second equation:
a+b+c = 42 Substitute a = 4c and b = 2c.
4c+2c+c = 42 Simplify.
7c = 42 Divide by 7.
c = 6 and...
b = 2(6)
b = 12 and...
a = 4c
a = 4(6)
a = 24.
Doug spotted 24 ducks.
Dave spotted 12 ducks.
Don spotted 6 ducks.

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OK, Emily, your first step was correct and you should have got 2 meters = 2,000 mm.
Now each earring requires 25mm of gold so each pair of earrings would need 50mm of gold.
So you should have divided the 2,000mm of gold wire by 50 to find the number of pairs of earrings.

The jeweler can make 40 pairs of earrings.

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No, it isn't!
When you subtracted 3 from both sides of:
3x+3 = 33 you should have got:
3x = 30 not 3x = 33, so...
3x = 30 Divide by 3 to get:
x = 10
The three consecutive numbers ar:
10, 11, and 12 whose sum is 33.

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Let x = the required number of milliliters of 6% alcohol solution.
Let's find out how much alcohol we have.
The number of milliliters of alcohol in the x ml. of the 6% solution is:
x(0.06) and in the 12 ml. of the 31% solution we have 12(0.31) ml. of alcohol.
When added together, these are to equal (12+x)(0.16)ml. of alcohol, so we can write the equation to find x.
0.06x+0.31(12) = 0.16(12+x) Simplify and solve for x.
0.06x+3.72 = 1.92+0.16x Subtract 0.06x from both sides.
3.72 = 1.92+0.1x Subtract 1.92 from both sides.
1.8 = 0.1x Divide by 0.1
x = 18
You will need to add 18ml. of 6% alcohol solution to the 12ml. of the 31% alcohol solution to obtain (12+x = 30)ml. of 16% alcohol solution.

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With fractional exponents, such as the number in the denominator indicates the root.
Example:
means the cube root of 3.
means the fifth root of 256 squared.

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Let A be the angle, then its complement is 90-A, so...
Multiply both sides by 4.
Add A to both sides.
Finally, divide both sides by 5.
degrees.

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hours
hours andminutes.

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Let n = the number, then:
2n+5 = 23 Subtract 5.
2n = 18 Divide by 2.
n = 9

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After removing the corner squares of side x, the remainder of the sides of the original rectangular cardboard will measure (40-2x) and (30-2x) and the height of the finished box will be x.
The volume of this box can be expressed as:
If you multiply these factors, you'll get:

Clearly, this is a "cubic" function.
From a practical standpoint, x cannot equal or exceed half the length of the smaller side of the original rectangle, otherwise, you could not make a box.
So x can take on values:

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Er...not quite!
Try:
Simplify and solve for x.

Multiply both sides by 90.
Divide both sides by 5.
minutes.

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Presumably you are required to solve for the variable a.
Simplify.
Subtract 6 from both sides.
Divide both sides by
Rationalise the denominator.
Simplify.
Cancel the 3's.

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Try this!
Let x = the number of pounds of the 50% corn. Then the number of pounds of the 90% corn required to make 30 pounds of 80% corn will be (30-x) and, when added together (x+(30-x) = 30) you will get 30 pounds of corn. So we can write an equation to solve for x:
0.5x+0.9(30-x) = 0.8(30) Simplify and solve for x.
0.5x+27-0.9x = 24
-0.4x+27 = 24
-0.4x = -3
x = 7.5
The farmer will need to mix 7.5 pounds of the 50% corn with (30-7.5 = 22.5)pounds of the 90% corn to obtain 30 pounds of 80% corn.

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Find the LCM of 120 and 135.
First, find the prime factors of each of the two numbers using exponents for repeated factors:
120: 2*2*2*3*3*3*5 =
135: 3*3*3*5 =
Now, from the two lists of prime factors, take the product of the highest power of each factor.

The LCD of 120 and 135 is 1080.

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Treat this as a quadratic equation in thus:
Now factor this.
Apply the "zero product" rule:
or
Now since the original equation is a 6th order equation, we can expect 6 roots.
Here's how we get them:
This is the sum of cubes which can be factored thus:
so...
Apply the "zero product" rule:
so
Apply the quadratic formula to get:
and
For the other three roots, we have:
This is the difference of cubes which factors as:
Apply the "zero product" rule:
so
Apply the quadratic formula to get:
and

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First, let's find the sum of the first three test grades, which we'll call a, b, and c.
this is the average of the first three grades. Multiply both sides by 3.
Now let's call the fourth test grade x, so...
This is the desired average of the four test grades. But so substitute:
Multiply both sides by 4.
Subtract 234 from both sides.

You will need to make a grade of 86 on the fourth test to obtain a final average of 80.

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Solve for n:
Cross-multiply:
Perform the indicated multiplication.
Subtract from both sides.
Add n to both sides.
Subtract 1 from both sides.
Finally, divide both sides by 3.

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You can find the area of any triangle by:
Where b = the length of the base and h = the height of the triangle.
It doesn't matter which leg you call the base, so we'll say and , so...

square miles.
To find the perimeter, you'll need to know the length of the hypotenuse of the right triangle. Use the Pythagorean theorem: where: , , and is the length of the hypotenuse.
Evaluate.

Take the square root of both sides.
So the length of the hypotenuse = 41 miles.
Now you can add the three sides to get the perimeter P.
=miles.

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Try this!
Let x = the required number pounds of the nuts worth $4.20 per pound.
We can express the cost of these x pounds of nuts as:
$4.20(x). Now we want to add this to 12 pounds of nuts worth $3.00 per pound the cost of which can be expressed as: $3.00(12).
Now if we add these together, we get:
$4.20(x)+$3.00(12) and this sum is to equal (12+x) pounds of nut mixture to cost $3.90 per pound. Now we can write the equation to solve for x.
4.20(x)+3.00(12) = (12+x)(3.90) Simplify.
4.2x+36 = 46.8+3.9x Subtract 3.9x from both sides.
0.3x+36 = 46.8 Now subtract 36 from both sides.
0.3x = 10.8 Finally, divide both sides by 0.3
x = 36
You will need to mix 36 pounds of nuts worth $4.20 per pound with 12 pounds of nuts worth $3.00 per pound to obtain 48 (12 + 36) pounds of nuts worth $3.90 per pound.

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If n is the number, then means one half of the number.

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You must have been given more information about the right triangle.
Look!
In this case, so . Now we have:
This equation has an infinite number of solutions unless you place some restrictions on a and b.
Let's assume the the numbers a and b must be integers (not an unreasonable assumption), then a and b can only take on the values of and , so you'd get:
or

This implies that the triangle is an isosceles right triangle.
No other integers for a and b would work.

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Let the length of the side of the square be s.
The area of the square is given by:
Increase the area by 9 means: and we'll show the increase in the length of the side by: , so...
but so we substitute...
Simplify and solve for s.
Divide both sides by
Take the square root.

So the sides of the square (s) would increase by 3 times.

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You need to discover how many times can you get feet of wrapping paper out of a ft. roll.
So you need to divide by .
=
So Kim will be able to fully wrap only 4 of the 5 packages and she will have 2 feet of wrapping paper remaining.

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Solve by factoring:
Can't really solve this "expression" until you set it equal to something, thus making it an "equation", but we can factor it.
so we have the sum of cubes and there is a factored form for this:
so...
...and that's the best we can do!

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Apply the "product rule" for logarithms: and the "power rule":
but...If then so...

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Here's the formula:
Where: is the first number (That's number 1), is the nth number (that's 1000), and is the number of numbers (that's 1000).
So...
=500,500