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kiruha [24]
3 years ago
5

Given the function f(x) = 3x, find the value of f−1(81).

Mathematics
1 answer:
Shalnov [3]3 years ago
4 0
Given the function f (x) = 3x, find the value of f-1 (81).
 For this case, the first thing you should do is rewrite the function.
 We have then:
 y = 3 ^ x
 From here, we clear the value of x:
 log3 (y) = log3 (3 ^ x)
 log3 (y) = x
 Then, we rewrite the function again:
 f (x) ^ - 1 = log3 (x)
 Now, we evaluate the inverse function for x = 81:
 f (81) ^ - 1 = log3 (81)
 f (x) ^ - 1 = 4
 Answer:
 the value of f-1 (81) is: 
 f (x) ^ - 1 = 4
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7 0
3 years ago
What is the sum of 13+52 as the product of their GCF and another sum
vova2212 [387]
GCF(13; 52) = 13

13 = 13 · 1
52 = 13 · 4

13 + 52 = 13 · 1 + 13 ·4 = 13·(1 + 4)

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4 0
3 years ago
1. A set of weights includes a 5 lb barbell and 8 pairs of weight plates. Each pair, p,
lidiya [134]

Answer:

5 <= y <= 85

Step-by-step explanation:

Since the lowest weight possible is 5lbs (just the barbell and no weights) the lowest point of the range is 5lbs (the y intercept when x = 0)

The highest weight possible is 85lbs since, there is only 8 pairs of weight plates (8 is the input value) and the pairs each weigh 10lbs (the slope of the graph) + 5lbs from the barbell (y-intercept).

Using the function given, if you input 8 as the x value, you get

85 = 10(8) + 5

So the highest value of the range is 85lbs, therefore the range is 5 <= y <= 85.  

6 0
3 years ago
PLEASE I REALLY NEED HELP ON THIS​
saul85 [17]
Answer:
a) a= (3/4)t
4a = 3t
b = (5/2)t
2b = 5t
b)See explanation below
c) It will take 30.075 hours for the whole business to make at least $500 profit
Step-by-step explanation:
a) First we would represent the information given in terms of amount of bracelet produced and time spent in production with variables in order to convert to linear equations
Let number of bracelet Darrelle makes = a
Number of bracelet Danica makes = b
Let the time spent in producing them in hours = t
Darrelle takes 4 hours to make 3 bracelets:
Rate of producing bracelet = (number of bracelet produced)/time
Rate = a/t = 3/4
4a = 3t
Linear equation form: y = mx + c
a= (3/4)t
The above equation is in the slope-intercept form indicating the intercept = 0 and slope = 3/4
4a - 3t = 0 (equation in standard form )
Danica makes 5 bracelets every 2 hours:
Rate of producing bracelet = (number of bracelet produced)/time
Rate = b/t = 5/2
2b = 5t
Linear equation form: y = mx + c
b = (5/2)t
The above equation is in the slope-intercept form indicating the intercept = 0 and slope = 5/2
2b - 5t = 0 (equation in standard form)
b) The equations are linear equations, hence they can be graphed.
But as regards graphing using special functions, this answer can only be answered by you as I'm not aware of the special functions discussed in the course.
c) Darrelle makes $10.50 in profit per bracelet.
Danica makes $3.50 in profit per bracelet
Since Darrelle and Danica work the same amount of time, we have to find the relationship between their profit, the number of bracelets produced and the time.
Profit for Darrelle for 'a' number of bracelet product = $10.50 × a = $10.50a
Profit for Danica per 'b' number of bracelet product = $3.50 × b = $3.50b
Let P = total profit made by both
P = $10.50a + $3.50b
Relationship of profit in terms of time spent in production when they work same amount of time:
P = $10.50(3/4 ×t)+ $3.50(5/2 × t)
P = 16.625t
When P = $500, t = ?
500 = 10.50(3/4 ×t)+ 3.50(5/2 × t)
500 = 7.875t + 8.75t
500 = 16.625t
t = 30.075 hours
It will take 30.075 hours for the whole business to make at least $500 profit
7 0
3 years ago
If Trevor does a job in 392 hours and with the help of Kristen they can do it together in
lisabon 2012 [21]

Answer:

343 .................

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