Question

Rationalize the denominator: 5^7/2^2

^10/4
^35/2
35/2
5^14/4

Answer 1

Which equation represents a line with a slope of -5/7 and a y-intercept of 3?

5x + 7y = 21
7y - 5x = 21
5x - 7y = 21
7y - 5x = -21

Answer 2

What are the prime factors of 15?

Answer 3

Simplify: 8^-4/3

Answer 4

Multiply 30 x 2 14/15

Answer 5

Let f (x) = x^3 - 6x^2 + 12x and g (x) = 3x. Evaluate f (x) / g (x).

Answer 6

35/2

Answer 7

7y - 5x = 21

Answer 8

The prime factors of 15 are 3 and 5.

15 = 3 * 5

Answer 9

To simplify 8^-4/3, we first need to rewrite 8 as a power of 2 because it will be easier to work with in this form.

8 = 2^3

So, 8^-4/3 can be rewritten as (2^3)^-4/3. When raising a power to a power, we multiply the exponents.

(2^3)^-4/3 = 2^(3 * -4/3)

= 2^-4

Now, to simplify 2^-4, remember that a negative exponent indicates taking the reciprocal of the base raised to the positive exponent.

2^-4 = 1 / 2^4

= 1 / (2 * 2 * 2 * 2)

= 1 / 16

Therefore, 8^-4/3 simplifies to 1/16.

Answer 10

To multiply 30 by 2 14/15, we first convert the mixed number 2 14/15 to an improper fraction.

2 14/15 = (2 * 15 + 14)/15 = (30 + 14)/15 = 44/15

Now, we multiply:

30 * 2 14/15 = 30 * 44/15

To multiply fractions, we multiply the numerators and the denominators.

30 * 44 / 15 = (30 * 44) / 15 = 1320 / 15

Now, we simplify this fraction by dividing the numerator and the denominator by their greatest common factor, which is 5.

1320 / 15 = 264 / 3

Finally, we divide 264 by 3 to get the simplified fraction:

264 ÷ 3 = 88

Therefore, 30 x 2 14/15 equals 88.

Answer 11

To evaluate f(x) / g(x), we first find the expressions for f(x) and g(x).

Given:
f(x) = x^3 - 6x^2 + 12x
g(x) = 3x

Now, we substitute these into the expression f(x) / g(x):

f(x) / g(x) = (x^3 - 6x^2 + 12x) / 3x

Now, we simplify this expression by dividing each term in the numerator by the denominator:

= (x^3 / 3x) - (6x^2 / 3x) + (12x / 3x)

= x^2 - 2x + 4

Therefore, f(x) / g(x) simplifies to x^2 - 2x + 4.