Answer:
30(x+1)/(x+7)
Step-by-step explanation:
This is not a rational expression because denominator has a domain of which it can be undefined.
To rationalize multiply by the reciprocal of the denominator (1/6+1/x+1)
___<u>5___ </u>*(6)(x+1) --> _____<u>30(x+1)_____</u> --><u> 30x+1</u>_ --> <u>30x+1</u>
1/6+1/x+1 *(6)(x+1)--> 6(x+1)/6 + 6(x+1)/(x+1) --> (x+1)+6 --> x+7
Final Answer: 30(x+1)/(x+7)
Answer:
3/2 / 2/5 = 3/2 x 5/2 = 15/4
Step-by-step explanation:
Answer:
40m Since it is the shortest side
Step-by-step explanation:
Answer:
129
Step-by-step explanation:
Considering the survey to be representative, you can simply multiply the share of students <em>p</em> preferring “Track & Field” with the whole school population at the same time to estimate the number of such students in the whole school.
First we need to find the relative share <em>p</em> of such answers in the study by dividing it by the sum of answers, assuming that the table is complete for that random sample:
<em>p</em> = 4/(8 + 5 + 4) = 4/17
Then for the whole school we get 550 <em>p</em> ≈ 129.4
<u>Step-by-step explanation:</u>
transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis
(???, 0): 0 = - ln (x - 4)

0 = ln (x - 4)

1 = x - 4
<u> +4 </u> <u> +4 </u>
5 = x
(5, 0)
(???, 1): 1 = - ln (x - 4)

1 = ln (x - 4)

e = x - 4
<u> +4 </u> <u> +4 </u>
e + 4 = x
6.72 = x
(6.72, 1)
Domain: x - 4 > 0
<u> +4 </u> <u>+4 </u>
x > 4
(4, ∞)
Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that
No vertical asymptotes
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transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis
Domain: there is no restriction on x so domain is all real number
(-∞, ∞)
Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.
(-∞, 0)
Y-intercept is when x = 0:
f(x) = - 3ˣ⁺⁵
= - 3⁰⁺⁵
= - 3⁵
= -243
Horizontal Asymptote: y = 0 <em>(explanation above)</em>