How to evaluate algebraic expressions - SAT Math

The "is" in the question means "equal," so whatever comes before "is" must be equal to whatever comes after. We will find an expression for the information before "is" and an expression for the information after "is," and then we will set these two expressions equal.

Twenty percent of a number can be represented as 0.2n, because 20% expressed as a decimal is 0.2, and because twenty percent "of" a number means the product of that number and twenty percent.

Four greater than the product of a number and six means that we must first find the product of that number and six, and then increase this value by 4.

The product of a number and six means that we must multiply this number by six, which can be represented by 6n. Increasing 6n by 4 can be modeled by the expression 6n + 4, or 4 + 6n (because of the commutative property of addition).

Setting the two expressions equal gives us 0.2n = 4 + 6n .

There are B+G total students in the elementary school class, so G out of B+G are girls.

There are a few ways to do this problem, but we will focus on the total number of votes method as follows. First, let Clinton = C, Gore = G, Paul = P, and Johnson = J. We know C + G + P + J = 150 million. We also know that C = 3J. Paul received 30% of the vote which is 150,000,000 * .3 = 45 million votes. Gore received 30 million votes. We can now create an equation with individual totals and substitute 3J for Clinton's vote total:

3J + 30 million + 45 million + J = 150 million

4J = 75 million

J = 18.75 million

Then C = 3J = 56.25 million. So Clinton received 56.25 million votes, Paul received 45 million votes, Gore received 30 million votes, and Johnson received 18.75 million votes. The correct answer is Hillary Clinton.

The operation x || y is evaluated as: 3x – 14y

What is the value of 5 || (6 || 2)?

Do this in parts. Start with 6 || 2:

6 || 2 = 3 * 6 – 14 * 2 = 18 – 28 = –10

This leaves us with:

5 || –10 = 3 * 5 – (14 * –10) = 15 – (–140) = 15 + 140 = 155

Taking 23 terms * 8 = 184; adding the original term of 15 yields 199.

The easiest way to solve this problem is to guess-and-check the answer choices. The equation that can be used to match the table will be correct.

We can see that the values in the table match the equation for each given value. Thus, this must be our answer.

We can also determine certain characteristics from the table itself. For example, as x increases, y(x) decreases. This tells us that there is likely a negative coefficient, which can help narrow down the answer options.

Find how many free throws Justin made: 84 x 0.619 = 51.99. Since the problem talks free throws, we round to 52 shots went in. To calculate shots missed:

84 – 52 = 32.

Combine like terms by subtracting 6 from both sides so: 5x + 24 = –7x. Then subtract 5x from both sides: 24 = –12x. Divide both sides by –12 and x = –2.

ab - bc + d = d2 - c2

We need to substitute values in for b, c, and d, and then solve the equation for a.

a(2) - 2(-1) + 0 = 02 - (-1)2

2a +2 + 0 = 0 - (1)

2a + 2 = -1

2a = -3

a = -3/2

The answer is -3/2.

First solve for x. The first equation would simplify as:

16 = 8x

x = 2

If we plug x = 2 into the second expression:

2(2) – 4 = 0

0 is the correct answer.

To evaluate an expression we make substitutions into the expression

2(x – 3) + 5y2 becomes 2(2 – 3) + 5 * 32 = –2 + 45 = 43

Use the first equation to solve for x, then plug into the 2nd equation to find a value.

5x3 = 40

x3 = 8

x = 2

12(2) – (2/2) = 24 – 1 = 23

Upstream: p – w = (10/2) or p – w = 5 miles/hour

Downstream: p + w = (27/3) or p + w = 9 miles/hour

Then we add the two equations together to cancel out the w's. After adding we see

2p = 14

p = 7 miles/hour where p is the rate of the paddling. We plug p into the equation to find

w = 2 miles/hour where w is the rate of the stream's water.

The answer is 23.

Since Rachel and Claire are twins they are the same age. We will use the variable r to represent both Rachel and Claire's ages.

From the question we can form two equations. They are:

t = r + 2 and 65 = t + 2r

lets plug the first equation into the second to solve for r.

65 = (r + 2) + 2r

65 = 3r +2

63 = 3r

r = 21 This means Rachel and Claire are 21 years old. Plug this into the equation so

t = 23 Tim is 23 years old.

Note that x must be greater than y and that y must be greater than 0. This means that x and y are different, positive integers. In addition, the sum, _x_2 + _y_2 must equal to 100. If we list squares beginning from the square of the first integer greater than 0 (12) up to the square of the greatest integer less than 100 (92) we will get:

1, 4, 9, 16, 25, 36, 49, 64, 81

We must observe that the only two numbers that will add up to 100 are 36 and 64.

Remember that x > y > 0 and that _x_2 + _y_2 =100.

This means that x must be and y must be

When we solve for x and y we get:

x = 8

and y = 6.

Therefore, x + y can only be 14.

Each term equals the previous term multiplied by .

The fifth term in the sequence is .

The sixth term in the sequence is thus .

Plug in numbers for each alternative. If both sides of the inequality are multiplied by 2, the result is the original inequality, . The other options fail (if confused, try plugging in as a positive, as a negative).

Begin by rearranging the equation to solve for z:

This means that , which can be rewritten as .

Assume the first section equals inches, then the second(or the middle section) must be equal to and the third piece must be equal to .

and now you solve for which equals 10. Hence the middle piece must be equal to 20 inches and the third piece is only 6 inches long.