Algebra - SAT Math

Explanation: The values of each answer are A)3 B) 2, C) 1, D)4, E)5.

1. Add 7 to both sides

3(z + 4)3 – 7 + 7= 17 + 7

3(z + 4)3 = 24

2. Divide both sides by 3

(z + 4)3 = 8

3. Take the cube root of both sides

z + 4 = 2

4. Subtract 4 from both sides

z = –2

First, solve for x:

11 + 3_x_ = 29

29 – 11 = 3_x_

18 = 3_x_

x = 6

Then, solve for 2_x_:

2_x_ = 2 * 6 = 12

Create 3 separate equations to solve for each variable separately.

1. 2_x_ = 48

2. 3_y_ = 48

3. 6_z_ = 48

x = 24

y = 16

z = 8

x * y * z = 3072

There are two values where _x_2 = x, namely x = 0 and x = 1. All values between 0 and 1 get smaller after squaring. All values greater than 1 get larger after squaring.

Start by combining like terms.

4_x_ + 5 = 13_x_ + 4 – x – 9

4_x_ + 5 = 12_x_ – 5

–8_x_ = –10

x = 5/4

First we solve for x.

Subtracting 3 from both sides gives us –3_x_ < 17.

Dividing by –3 gives us x > –17/3.

–6 is less than –17/3.

(20+a2) / 2a is the answer. Find a common denominator to add the 2 fractions after plugging in the values. So we get 10/a + a/2 after plugging in the values. The lowest common denominator would be 2a. Mutiply 10/a by 2/2, and multiply a/2 by a/a. The new equation appears as 20/2a + a2/2a. Add them together to get (20 + a2)/2a.

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.

There are only x * 10 liters of water on the island. n * m equals how many liters are consumed per day. Divide x * 10 liters by n * m. Note the units (days) are correct in the answer.

This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4_xs and ks are both equal to v, which means that 4_xs_ and ks must be equal to each other--that is, 4_xs_ = ks. Dividing both sides by s gives 4_x_ = k, which is our solution.

1. Substitute y in the equation for 4.
2. You now have 6 * 4 = 10z + 4
3. Simplify the equation: 24 = 10z + 4
4. Subtract 4 from both sides: 24 – 4 = 10z + 4 – 4
5. You now have 20 = 10z
6. Divde both sides by 10 to solve for z.
7. z = 2.

This goes up at a constant number between values, making it an arthmetic sequence. The first number is 2, with a difference of 3. Plugging this into the arithmetic equation you get An = 2 + 3 (n – 1). Plugging in 20 for n, you get a value of 59.

Looking at the sequence you can see that it doubles each term, making it a geometric sequence. Since it doubles r = 2 and the first term is 5. Plugging this into the geometric equation you get An = 5(2)n–1. Setting n = 6, you get 160 as the 6th term.

The zeroes of the equation are where f(x) = 0 (aka x-intercepts). Setting the equation equal to zero you get x2 = 9. Since a square makes a negative number positive, x can be equal to 3 or –3.

In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.