Answer:
z = 7/3 is extraneous.
Step-by-step explanation:
√(z^2+8) = 1 - 2z
z^2 + 8 = (1 - 2z)^2
z^2 + 8 = 1 -4z + 4z^2
3z^2 - 4z - 7 = 0
3z^2 + 3z - 7z - 7 = 0
3z(z + 1) - 7(z + 1) = 0
(3z - 7)(z + 1) = 0
3z = 7, z = -1
z = 7/3, -1.
One of these might be extraneous.
Checking:
√(z^2+8) = 1 - 2z, if z = -1:
√(1 + 8) = 3, -3
1 - 2(-1) = 3. So its not z = -1
if z = 7/3
√((7/3)^2 + 8) = 13.44
1 - 2(7/3) = -3.66
So its z = 7/3
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Answer:
A and D should be checked.
Step-by-step explanation:
The first one.
It's center is (-12, - 9) and it has a radius of sqrt(9) = 3 The 12 on the x axis will guarantee that the most in either direction in the x direction is (-15,-9) going left from the center and (-9,-9) going right of the center point.
The two points for up and down are (-12, -12) and (-12,-6)
A graph is included below. The red circle is shown as being entirely in quad 3. It is red in color. It should be checked.
B is Blue and it is shown to be 1/2 in quad 3
C is in green. It is 3/4 in quad 3, but not all of it is there.
D is dark blue and it is quad 3 so it should be checked.
<span>There were 12 peaches on the tree originally.
Let's make an equation to describe the problem and then solve it.
"Bill picked 1/4 of the peaches on his grandmothers tree."
Which means that 3/4ths of the original number of peaches remain. So:
(3/4)x
"After Bill finished Sally picked 1/3 of the peaches that were left on the tree."
Which means that she left behind 2/3rds of the peaches that Bill left behind. So:
(2/3)((3/4)x)
"After Sally finished there were 6 peaches left on the tree." So:
(2/3)((3/4)x) = 6
Now we just need to solve for x.
(2/3)((3/4)x) = 6
(3/2) * (2/3)((3/4)x) = 6 * (3/2)
(3/4)x = 9
(4/3)(3/4)x = 9*(4/3)
x = 12
There were 12 peaches on the tree originally.</span>
The value of x is 5, if a, b, and c are collinear points.
According to the given question.
a, b, and c are collinear points.
Which means points a, b, and c both lie in a same line.
b is between a nd c .
Also, ab = 12
bc = 5x - 2
and ac = 3x + 20
Since, b lies in between a and c
Therefore,
ab + bc = ac
12 + 5x - 2 = 3x + 20
⇒ 10 + 5x = 3x + 20
⇒ 5x - 3x = 20 - 10
⇒ 2x = 10
⇒ x = 10/ 2
⇒ x = 5
Therefore, the value of x is 5.
Find out more information about collinear points here:
brainly.com/question/5191807
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