4. What is the solution of 5^3x = 900? Round your answer to the nearest hundreth

Question

1.24
1.41
4.23
0.69

5. Let f(x) = x^2 + 6 and g(x) = x+8/x Find (g F) (-7)
-55/7
384/7
295/49
63/55

7. Is the relationship between the variables in the table a direct variation, an inverse variation, both, or neither? If it is a direct or inverse variation, write a function to model it.
x 2 5 12 20
y 20 12 5 3
A. direct variation y=15x
B. inverse variation y = 60/x
C. Direct variation y=2x+2
D. Neither

8. A dramam club is planning a us trip to New York City to see a broadway play. The cost per person for the bus rental varies ibversely as the number of people on the trip. It will cost $30 per person if 44 people fo on the trip. How much will it cost per person if 55 people go on the trip Round Your answer to the nearest cent if necessary.
48. 00
12. 50
24.00
33.00

9. write an equation for the translation of y=6/x that has the asympotes x-4 and y = 5
y = 6/x+4 + 5
y = 6/x-4 + 5
y= 6/ x+5 + 4
y= 6/x-5 + 5

Answer 1

4. Solution: 0.69

5. (g F) (-7) = g(f(-7)) = g((-7)^2+6) = g(55) = 384/7

7. The relationship is an inverse variation, and the function to model it is y = k/x, where k is a constant. Using the given values, k = xy, so k = 20*2 = 40. Therefore, the function is y = 40/x.

8. Cost per person = k/number of people. Using the given values, we have k = 44*30 = 1320. Therefore, cost per person if 55 people go on the trip = 1320/55 = 24.00 (rounded to the nearest cent).

9. The translation of y=6/x that has the asymptotes x-4 and y=5 is given by y = a/(x-4) + 5, where a is a constant. To find a, we use the fact that the original function y=6/x has a horizontal asymptote of y=0, which means that the translated function must have a horizontal asymptote of y=5. Therefore, we need to add 5 to the function y=6/x to get the translated function. This gives y = 6/x + 5. To get the asymptote x=4, we need to shift the graph 4 units to the right, which means replacing x with x-4, giving us y = 6/(x-4) + 5.

Answer 2

11. What are the points of discontinuity y=(x-8)/(x^(2)+6x-7)
A X = 1, x=-7
B x= -1, x=7
C x=8
D x=1, x=7

12. What is the quotient 4-x/x^2+ 5x-6 ÷ x^2-11x+28/x^2 + 7x +6 in simplified form.
-(x+1)/(x-1) (x-7) x ≠ 1 x≠ 7
-1/(x-7) x≠7
-1/(x-7) x≠1, X≠ -6, x ≠4
-(x+1)/(x-1)(x-7) X ≠ 1, X≠-6, X≠4, X≠7

13. simplify the complex fraction (x)/((x+4)/((1)/(x)+(1)/(x+4)))
x^2/2x
x^2/x+4
x^2+2x+4/2x+4
x^2/2x+4

Answer 3

11. Points of discontinuity: x=1, x=-7, x=1 are the roots of the denominator, x=8 is not a point of discontinuity since the function is defined at that point.

Answer: A x=1, x=-7.

12. To simplify the quotient, we need to factor the denominators, find the reciprocal of the second fraction, and multiply the numerators and denominators.

(x)/((x+4)/((1)/(x)+(1)/(x+4)))

= x * (x^2-6x-16) / (4-x) * (x+7)

= x * (x-8) * (x+2) / (x-4) * (x+7) * (x+2)

= x * (x-8) / (x-4) * (x+7)

Answer: A -(x+1)/(x-1) (x-7) x ≠ 1 x≠ 7

13. To simplify the complex fraction, we need to simplify the expression inside the second fraction first:

(1)/(x)+(1)/(x+4) = (x+4+x) / x(x+4) = 2(x+2) / x(x+4)

Now we can substitute this expression into the original fraction:

x / ((x+4) / (2(x+2) / x(x+4)))

= x * (2(x+2) / x(x+4)) / (x+4)

= 2(x+2) / (x+4)

= 2(x+2) / (x+4)

Answer: C x^2+2x+4/2x+4

Answer 4

4. Not clear
5^3x = 900
if you mean
5^3 * x = 900
then
x = 900 / 75 = 12
if you mean 5^(3x) = 900
3 x log 5 = log 900 = 2.95424
3 x * .69897 = 2.95424
x = 1.41 (which is one of your choices)

Answer 5

Thank you for your clarification! Yes, the correct interpretation is 5^(3x)=900, and the solution you provided is correct as well.