Answer:
C) translated 1 unit to the left and then rotated 180° counterclockwise about the origin
Step-by-step explanation:
by inspection, shape A has been translated 1 unit to the left and then rotated 180° counterclockwise about the origin
Answer:
(x + 1)² = 7
Step-by-step explanation:
Given:
-2x = x² - 6
We'll start by rearranging it to solve for zero:
x² + 2x - 6 = 0
The first term is already a perfect square so that's fine. Normally, if that term had a non-square coefficient, you would need to multiply all terms a value that would change that constant to a perfect square.
Because it's already square (1), we can simply move to the next step, separating the -6 into a value that can be doubled to give us the 2, the coefficient of the second term. That value will of course be 1, giving us:
x² + 2x + 1 - 1 - 6 = 0
Now can group our perfect square on the left and our constants on the right:
x² + 2x + 1 - 7= 0
x² + 2x + 1 = 7
(x + 1)² = 7
To check our answer, we can solve for x:
x + 1 = ± √7
x = -1 ± √7
x ≈ 1.65, -3.65
Let's try one of those in the original equation:
-2x = x² - 6
-2(1.65) = 1.65² - 6
- 3.3 = 2.72 - 6
-3.3 = -3.28
Good. Given our rounding that difference of 2/100 is acceptable, so the answer is correct.
Answer:
first one is A and the second one is B.
Step-by-step explanation:
The expression for the cost of Taxi B is 0.40<em>x</em> + 2.<em> </em>The expression for the cost of Taxi A is 0.20<em>x</em> + 4. The inequality asks for when the cost of Taxi B will be greater than Taxi A, so you write it as 0.40<em>x </em>+ 2 > 0.20<em>x</em> + 4, or 0.20<em>x</em> + 4 < 0.40<em>x </em>+ 2.
The answer is B) 0.20<em>x</em> + 4 < 0.40<em>x </em>+ 2.
