Complete the square:
F(x) = -3x² - 6x - 5
F(x) = -3 (x² + 2x) - 5
F(x) = -3 (x² + 2x + 1 - 1) - 5
F(x) = -3 ((x + 1)² - 1) - 5
F(x) = -3 (x + 1)² + 3 - 5
F(x) = -3 (x + 1)² - 2
The y-intercept has x-coordinate equal to 0, so it corresponds to the value of F(0) :
F(0) = -3 (0 + 1)² - 2 = -3 - 2 = -5
The axis of symmetry is the vertical line running through the vertex of this parabola, so we'll come back to this.
The vertex of the parabola is (-1, -2). This represents the maximum value of F(x), which follows from
(x + 1)² ≥ 0 ⇒ -3 (x + 1)² ≤ 0 ⇒ -3 (x + 1)² - 2 ≤ -2
This is to say, every point on the parabola has a y-coordinate no greater than -2.
As mentioned earlier, the axis of symmetry is the vertical line through the vertex, and its equation is determined by the x-coordinate of the vertex. Hence the AoS is the line x = -1.
Answer:
Step-by-step explanation:
These triangles are similar triangles, so there is a number that you can multiply the sides of TUV to find the side lengths of QRS. looking at the triangle, the similar sides are RS being similar to UV and RQ being similar to UT.
If RS~UV, then there is a ratio between them. 54/36=1.5. The ratio is 1.5.
RQ~UT, and by a factor of 1.5, so divide RQ by the scale factor. 24/1.5=16. UT=16=x+5.
x+5=16, subtract 5 from both sides.
x=11
Answer:
a = 6
Explanation:
7a − 17 = 4a + 1
Subtract 4a from both sides
7a − 17 − 4a = 4a + 1 − 4a
3a − 17 = 1
Add 17 to both sides
3a − 17 + 17 = 1 + 17
3a = 18
Divide both sides by 3
3a / 3 = 18 / 3
a = 6
She had bread for the hungry, clothes for the naked, and comfort for every mourner, that came within her reach. Slavery soon proved its ability to divest of her heavenly qualities. Under its influence the tender heart became stone, and the lamb-like disposition gave way to one of the tiger-like fierceness. From the excerpt above, which statement best describes the changes in his mistress’s character? She was always loyal only to the laws and to her husband. He felt sorry for her since she was oppressed, too. The change in her character was inexcusable. She was unwilling to face the conflict of betraying her culture for her personal beliefs.
