The difference of 32 · x² / (x² + 8 · x + 15) - 14 · x² / (x² - 9) is equal to [18 · x³ - 166 · x²] / [(x + 3) · (x + 5) · (x - 3)]. (Correct choice: B)
<h3>What is the result of the subtraction between two algebraic rational functions?</h3>
In this question we have a subtraction between two <em>rational</em> functions, which have to be simplified by <em>algebra</em> properties. The complete procedure is presented below:
32 · x² / (x² + 8 · x + 15) - 14 · x² / (x² - 9) Given
32 · x² / [(x + 3) · (x + 5)] - 14 · x² / [(x + 3) · (x - 3)] Factorization
[x² / (x + 3)] · [32 / (x + 5) - 14 / (x - 3)] Distributive and associative properties
[x² / (x + 3)] · [32 · (x - 3) - 14 · (x + 5)] / [(x + 5) · (x - 3)] Subtraction of rational numbers with distinct denominators
[x² / (x + 3)] · [32 · x - 96 - 14 · x - 70] / [(x + 5) · (x - 3)] Distributive property / (- 1) · a = - a
[x² / (x + 3)] · (18 · x - 166) / [(x + 5) · (x - 3)] Distributive property / Definitions of addition and subtraction
[18 · x³ - 166 · x²] / [(x + 3) · (x + 5) · (x - 3)] Mutiplication between rational numbers / Multiplication between powers / Distributive property
The difference of 32 · x² / (x² + 8 · x + 15) - 14 · x² / (x² - 9) is equal to [18 · x³ - 166 · x²] / [(x + 3) · (x + 5) · (x - 3)]. (Correct choice: B)
To learn more on rational functions: brainly.com/question/27914791
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Answer:
0.50
Step-by-step explanation:
Let A represent the probability that it will be cloudy
Let B represent the probability that it will be rainy
P(A) = 0.40
P(B) = 0.30
P(A and B) = 0.20
For non mutually exclusive events the probability of event A or B is
P(A or B) = P(A) + P(B) - P(A and B)
= 0.40 + 0.30 - 0.20
= 0.50
There is a 50% probability that the picnic will be postponed. Therefore the probability that the picnic will not be postponed is equals 1 - P(A and B)
= 1 - 0.50
= 0.50 or 50%
Answer:
Step-by-step explanation:
Part A:
-mk-120 > 95
-mk > 215
Divide both sides by -k
Since we are dividing by a negative, the inequality sign flips
m < 215/-k
Part B:
2c-9fb = 45
Subtract 2c from both sides
-9fb = 45-2c
Divide both sides by -9b
f = (45-2c) / -9b
Please let me know if this helps :)!
Answer:
x = -3
There is a base f 5 on the left side, so write the denominator on the right as a base of
5 as well.
5
x
=
1
125
5
x
=
1
5
3
Move the base to the numerator.
5
x
=
5
−
3
If the bases are equal, the indices are equal:
x
=
−
3
