How to evaluate algebraic expressions - SAT Math

If we use order of operations (PEMDAS), the answer is 36.

Use the second equation to find x in terms of a. Plug it back in the second equation, that will give you 1 = y.

You set up the equation to solve for a.

75 = 3000/(2(15) + a)

a = 10

You then set up the formula again for each movie costing $20, s(20)= 3000/(2(20) + 10), and solve for x, the number sold, giving you 60.

Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.

We are told that x&y = (x – y)xy .

–1&2 = (–1 – 2)(–1)(2) = (–3)–2

To simplify this, we can make use of the property of exponents which states that a– b = 1/(ab ).

(–3)–2 = 1/(–3)2 = 1/9

The answer is 1/9.

We need to rewrite this problem in mathematic terms.

8 less than 32 can be written as 32 – 8

so we will get the equation

18 – w = 32 – 8.

Now, we need to solve for w.

–w = 32 – 8 – 18

–w = 6

w = –6

Find the value of the given expression, , by plugging in –6 for w.

To convert into , we will do the following conversions

It's easiest if we convert all percentages to actual oz of water for each step here. As such, 35% of the 80 oz of drink B would have 0.35(80) = 28 oz of water in it.

We can set up an equation that similarly converts each "percentage of a fixed weight of liquid" to ensure that our final weight is equivalent to 30% to the sum of drink A and B. On the left side, the fixed values are the percentages of each drink individually, and on the right side is what the question requires as a fixed percentage of the final weight:

0.2(A) + 0.35(80) = 0.3(A + 80)

0.2A + 28 = 0.3A + 24

A = 40

Solving for A, we get 40 oz of A that must be poured into B. You may plug this back into the equation to check it.

First, we need to evaluate 5&3.

Since x&y = xy – x + y, we can find 5&3 as follows:

5&3 = 5(3) – 5 + 3

= 15 – 5 + 3

= 13

Now, we need to go through each of the choices and determine which one equals 13.

Let's start with 2&(8&1). Remember that we must first evaluate inside the parantheses.

2&(8&1) = 2&(8(1) – 8 + 1)

= 2&(8 – 8 + 1)

= 2&(1)

= 2(1) – 2 + 1 = 1, which doesn't equal 13.

Next, let's evaluate 4&(3&4).

4&(3&4) = 4&(3(4) – 3 + 4)

= 4&(13) = 4(13) – 4 + 13 = 61.

Next, we can evaulate 8&(2&0).

8&(2&0) = 8&(2(0) – 2 + 0)

= 8&(–2) = 8(–2) – 8 + 2 = –22.

Next, let's find 3&(5&2).

3&(5&2) = 3&(5(2) – 5 + 2)

= 3&(7) = 3(7) – 3 + 7 = 25.

Finally, lets evaluate 11&(0&2).

11&(0&2) = 11&(0(2) – 0 + 2)

= 11&(2) = 11(2) – 11 + 2 = 13.

The answer is 11&(0&2).

Just take this step by step. First write out each equation:

x = 0.75y

y = 8(1.5z)

First, simplify the second equation:

y = 12z

Then, substitute y from this equation into the first:

x = 0.75(12z) = 9z

The key to solving this question is noticing that we can factor out a two:

2x + 6y = 44 is the same as 2(x + 3y) = 44

Therefore, x + 3y = 22

In this case, x + 3y + 33 is the same as 22 + 33 or 55

Let's make 3 equations based on our data:

J = 4S + 4

P = 3J

S = 20

All we have to do is sequentially replace values.

Substitute 20 for S in the J equation:

J = 4 * 20 + 4 = 84

Now, we can calculate P: P = 3 * 84 = 252

Rewrite our question as a set of equations:

R + G + B = 42

R = 42/2 = 21

Therefore, we already know:

G + B = 21

Also, we know that B = 5 + G

Replace that value into the B + G equation:

G + 5 + G = 21 → 2G + 5 = 21 → 2G = 16; G = 8

Therefore, we know that there are 5 + 8 or 13 blue marbles.

The total is therefore 21 Red, 13 Blue, 8 Green

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.