Answer:
x = -1 and x = 5
Step-by-step explanation:
<em>What are the solutions of the equation (x – 3)² + 2(x – 3) -8 = 0? Use u substitution to solve.</em>
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(x – 3)² + 2(x – 3) -8 = 0 -------------------------------------------------------(1)
To solve this problem, we will follow the steps below;
let u = x-3
we will replace x-3 by u in the given equation:
(x – 3)² + 2(x – 3) -8 = 0
u² + 2u -8 = 0 ----------------------------------------------------------- --------------(2)
We will now solve the above quadratic equation
find two numbers such that its product gives -8 and its sum gives 2
The two numbers are 4 and -2
That is; 4×-2 = -8 and 4+(-2) = 2
we will replace 2u by (4u -2u) in equation (2)
u² + 2u -8 = 0
u² + 4u - 2u -8 = 0
u(u+4) -2(u+4) = 0
(u+4)(u-2) = 0
Either u + 4 = 0
u = -4
or
u-2 = 0
u = 2
Either u = -4 or u = 2
But u = x-3
x = u +3
when u = -4
x = u + 3
x = -4 + 3
x=-1
when u = 2
x = u + 3
x = 2 + 3
x=5
Therefore, x = -1 and x =5
x
We have a fraction with the unknown in the denominator, review how to treat unknowns in the denominator as a refresher for this exercise:
<span>(2/3) - (1/x + 6) = 2
</span>(2/3) - (1 + 6x)/x = <span>2
</span>(2/3) - 2 = (1 + 6x)/x
2/3 - 6/3 = (1 + <span>6x)/x
-4/3 = </span>(1 + <span>6x)/x
-4x = 3</span>(1 + <span>6x)
</span><span>-4x = 3 + 18x
</span>22x = -3
x = -3/22
Answer:
57.885
Step-by-step explanation:
For such calculations a probability calculator is very helpful. The one in the attachment shows the 87th percentile to be 57.885.
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A table of the standard normal distribution will tell you the 87th percentile corresponds to a z-value of 1.12639. Then the X value is ...
X = Zσ +μ = 1.12639(7) +50 = 57.885
Answer and Step-by-step explanation:
<u>You should pick Spinner A.</u> There is a high chance of getting red since there are three pieces of the spinner that has red on it, while Spinner B only has 2 instances of red.
<em><u>#teamtrees #PAW (Plant And Water)</u></em>
SAS because they tell you that two sides anre congruent and also one angle is
