Answer:
(b) t-4 and t not equal 8
Step-by-step explanation:
The equation of parabola is y = -8(x -3)² - 9.
<h3>Define parabola.</h3>
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Given Data
Focus = (3, -9)
Directrix: y = -5
The focus-passing line has an equation of x = -5 that is perpendicular to the directrix. The symmetry line of a parabola is seen here.
The parameter of the parabola is the separation between the focus and the directrix, so
p = -9 - 3
p = -12
p = 12
The distance between the focus and the directrix is divided into two equal portions by the parabola's vertex, which is located on the line of symmetry. Its coordinates are as follows: (3,-9).
Since a parabola moves in the opposite direction of y, its equation is
y -(-9) = -2(4(x -3)²)
y + 9 = -8(x-3)²
y = -8(x -3)² - 9
The equation of parabola is y = -8(x -3)² - 9.
To learn more about parabola, visit:
brainly.com/question/13804934
#SPJ13
Answers: 13) b 14) c 15) c 16) c
<u>Step-by-step explanation:</u>
13)
The possible options are: BBB, BBG, BGB, GBB = 4 : 8
Simplified (divide by 2) is 1 : 2
14)
Odd: 1, 3, 5, 7, 9 = 5:10
Prime: 2, 3, 5, 7 = 4:10
≤ 5: 0, 1, 2, 3, 4, 5 = 6:10 This has the highest probability!
÷ 3: 3, 6, 9 = 3:10
15)
There are 8 - 3 sections that are not red and 8 total sections
(8 - 3) : 8 = 5:8
16)
Reese has 15 votes and there are 15 + 13 + 12 total votes
15 : (15 + 13 + 12) = 15 : 40
Simplified (divide by 5) is 3 : 8
Answer:
x = -5
Step-by-step explanation:
Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.
This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).
So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.
On the right side we are given 9 for AD, and 18 for DC.
9/18 = 0.5
This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:
If AD/DC = 0.5, then BE/EC will also = 0.5
BE = x+23
EC = x+41
Therefore:
Now we can solve by multiplying both sides by x+41 to eliminate the fraction:
Now we multiply out the brackets and move the terms to different sides:
And if we substitute the -5 into the equations:
-5+23 = 18
-5 + 41 = 36
We will see that -5 does indeed give us the same ratio between the lengths:
18/36 = 0.5
Hope this helped!
