the expanded form of (3x + 4)(2x − 5) is 6x² - 7x - 20. The third option is the correct option.
The simplified form of (3x + 2y) - (x + 2y) is 2x. The correct option is the third option.
3x + 4y equals 36. The third option is the correct option.
To evaluate f(x) = 4x + 3x² - 5, f(x) evaluates to -1. The last option is the correct option.
The Breakdown
To expand the expression (3x + 4)(2x − 5), you can use the distributive property:
(3x + 4)(2x − 5) = 3x(2x) + 3x(-5) + 4(2x) + 4(-5)
Now, simplify each term:
= 6x² - 15x + 8x - 20
Combine like terms:
= 6x² - 7x - 20
So, the expanded form is 6x² - 7x - 20.
To simplify the expression (3x + 2y) - (x + 2y), we can remove the parentheses and combine like terms:
(3x + 2y) - (x + 2y) = 3x + 2y - x - 2y
The terms "2y" and "-2y" cancel each other out:
= 3x - x
Simplifying further:
= 2x
Therefore, the simplified form of (3x + 2y) - (x + 2y) is 2x.
To find the value of 3x + 4y, we need to solve the given equation and then substitute the values into the expression.
Given: 1/2x + 2/3y = 6
To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of the denominators, which is 6:
6 × (1/2x + 2/3y) = 6 × 6
This simplifies to:
3x + 4y = 36
Therefore, 3x + 4y equals 36.
To evaluate f(x) = 4x + 3x² - 5 when x = -2, we substitute -2 for x in the expression:
f(-2) = 4(-2) + 3(-2)² - 5
Simplifying:
f(-2) = -8 + 3(4) - 5
f(-2) = -8 + 12 - 5
f(-2) = -1
Therefore, when x = -2, f(x) evaluates to -1.