Question

Give the reduced form of 20x^2y^3.

a) 5x
b) 5y
c) 5x^2y
d) 5xy^2
What are the common factors in the numerators and denominators of 6ab^5 and abc?
a) abc
b) abc
c) abc
d) a^2b^2c
Find the product of (3 - a)/(6 - 2a) and 2.
a) 0
b) 1
c) 2
d) 3
Write as one fraction and simplify 2(2x + 2)/(x^2 + x).
a) 3
b) 4
c) 6
d) 8
Find the common factors of the numerator and denominator of x^2 - 16/(x^2 - 8x + 16).
a) x - 3
b) x - 4
c) (x - 3)(x - 4)
d) (x - 4)(x - 4)
What is the product of (x - 3)(x^2 - 8x + 16) divided by (x^2 + x - 20)/(2x - 8)?
a) x - 4
b) x - 4
c) x + 4
d) x + 4
What is the quotient of 6/(3 - 1)/(2 - 1)?
a) 4
b) 2
c) 3
d) 2/3
From 5 = 472, what is the divisor?
a) x - 5
b) x - 3
c) x - 5
d) x - 3

Answer 1

To find the reduced form of 20x^2y^3, we need to find the common factors. The common factors of the numerators and denominators of 6ab^5 and abc are abc. To find the product of (3 - a)/(6 - 2a) and 2, we multiply the numerators and denominators together and simplify. The expression 2(2x + 2)/(x^2 + x) can be simplified to 4/x. The common factors of the numerator and denominator of x^2 - 16/(x^2 - 8x + 16) are (x - 4)(x - 4). To find the product of (x - 3)(x^2 - 8x + 16) divided by (x^2 + x - 20)/(2x - 8), we multiply the numerators and denominators together. The quotient of 6/(3 - 1)/(2 - 1) is 3. From the equation 5 = 472, the divisor is x - 3.

Step-by-step explanation:

To find the reduced form of 20x^2y^3, we need to find the common factors of 20, x^2, and y^3. The largest common factor is 5, so the reduced form is 5x^2y^3, which corresponds to option c.

The common factors of the numerators and denominators of 6ab^5 and abc are abc. Therefore, the reduced form is abc, which corresponds to option b.

To find the product of (3 - a)/(6 - 2a) and 2, we multiply the numerators and denominators together and simplify. The product is 2(3 - a) / (6 - 2a) = (6 - 2a) / (6 - 2a). Simplifying further, we get 1, which corresponds to option b.

The expression 2(2x + 2)/(x^2 + x) can be written as 4(x + 1)/(x(x + 1)). Simplifying further, we get 4/x, which corresponds to option b.

The common factors of the numerator and denominator of x^2 - 16/(x^2 - 8x + 16) are (x - 4)(x - 4). Therefore, the reduced form is (x - 4)(x - 4), which corresponds to option d.

To find the product of (x - 3)(x^2 - 8x + 16) divided by (x^2 + x - 20)/(2x - 8), we multiply the numerators and denominators together and simplify. The product is (x - 3)(x^2 - 8x + 16) / (x^2 + x - 20)/(2x - 8) = (x - 3)(x - 4), which corresponds to option a.

The quotient of 6/(3 - 1)/(2 - 1) is calculated by performing the division from left to right. So, 6/(3 - 1)/(2 - 1) = (6/2)/(2 - 1) = 3/(2 - 1) = 3/1 = 3, which corresponds to option d.

From the equation 5 = 472, the divisor can be found by subtracting 5 from both sides. So, the divisor is x - 3, which corresponds to option b.