4. What is the solution of 5^3x = 900? Round your answer to the nearest hundreth
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
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.
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
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
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)
Thank you for your clarification! Yes, the correct interpretation is 5^(3x)=900, and the solution you provided is correct as well.
4. To solve the equation 5^(3x) = 900, we need to take the logarithm of both sides using the base 5 because the exponent is 3x.
Taking the logarithm base 5 of 900, we get log5(900) = 3x.
Using a calculator, the value of log5(900) is approximately 3.7075.
So, 3x = 3.7075.
Now, we can solve for x by dividing both sides of the equation by 3.
x = 3.7075 / 3 ≈ 1.2358.
Rounding to the nearest hundredth, the solution is 1.24.
Therefore, the correct answer is 1.24.
5. To find (g F)(-7), we need to plug -7 into the function g(x) and then use the result as the input for the function f(x).
Starting with g(x) = x + 8 / x, we substitute -7 for x.
g(-7) = -7 + 8 / -7 = 1 - 8/7 = -7/7 - 8/7 = -15/7.
Now, we have the value from g(-7) as -15/7, which becomes the input for f(x).
f(-15/7) = (-15/7)^2 + 6.
Simplifying, we get f(-15/7) = 225/49 + 294/49 = 519/49.
Therefore, (g F)(-7) = 519/49.
So, the correct answer is 519/49.
7. Looking at the table, we can observe that the relationship between x and y is not a direct variation or an inverse variation. In a direct variation, the ratio between x and y would remain constant, while in an inverse variation, the product of x and y would remain constant.
Since neither of these patterns is observed in the table, we can conclude that the relationship is neither a direct variation nor an inverse variation.
Therefore, the correct answer is D. Neither.
8. In an inverse variation, the product of the two variables is constant. In this scenario, the cost per person and the number of people on the trip have an inverse variation relationship.
Given that it costs $30 per person when 44 people go on the trip, we can determine the constant of variation (k) using the formula k = x * y.
k = 44 * 30 = 1320.
Now, we can use the constant of variation to find the cost per person when 55 people go on the trip.
Let x be the cost per person when 55 people go on the trip.
55 * x = 1320.
Solving for x, we have x = 1320 / 55 = 24.
Rounding to the nearest cent, the cost per person when 55 people go on the trip is $24.
Therefore, the correct answer is 24.00.
9. To translate the equation y = 6/x, we need to shift the graph horizontally and vertically according to the given asymptotes.
The equation y = 6/(x + 4) represents a horizontal translation of 4 units to the left.
Adding +5 to the equation represents a vertical translation of 5 units upward.
Therefore, the correct equation for the translation of y = 6/x with asymptotes x = -4 and y = 5 is:
y = 6/(x + 4) + 5.
So, the correct answer is y = 6/(x + 4) + 5.