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n200080 [17]
3 years ago
7

Remember to show work and explain. Use the math font.

Mathematics
1 answer:
fiasKO [112]3 years ago
6 0

Answer:

\large\boxed{1.\ f^{-1}(x)=3\log_5x}\\\boxed{2.\ f^{-1}(x)=\log_6(-x)}

Step-by-step explanation:

\log_ab=c\iff c=a^b\\\\\log_aa^n=n\\---------------------\\\\1.\\y=5^{\frac{x}{3}}\\\\\text{Exchange x and y}\\\\5^\frac{y}{3}=x\\\\\text{Solve for y:}\\\\5^\frac{y}{3}=x\qquad\log_5\text{of both sides}\\\\\log_55^\frac{y}{3}=\log_5x\Rightarrow\dfrac{y}{3}=\log_5x\qquad\text{multiply both sides by 3}\\\\y=3\log_5x\\---------------

2.\\y=-6^x\\\\\text{Exchange x and y:}\\\\-6^y=x\\\\\text{Solve for y:}\\\\-6^y=x\qquad\text{change the signs}\\\\6^y=-x\qquad\log_6\ \text{of both sides}\\\\\log_66^y=\log_6(-x)\Rightarrow y=\log_6(-x)

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Nick can do a certain job in 3 hours less than it takes bonnie to do the same job. If they complete the job together in 9 hours,
il63 [147K]

Answer:

Step-by-step explanation:

Let the number of hours Nick does the job alone to be x - 3 hours

Hence, in 1 hour, Nick has done 1/x - 3

Together they complete the job in 9 hours

Hence, let's represent the job as 1

9/x + 9/x - 3 = 1

Multiply through by (x)(x-3)

9(x- 3) + 9(x) = 1

9x - 27 + 9x = (x)(x-3)

-27 = x² - 3x

x² - 3x +27 = 0

4 0
3 years ago
Priscilla’s grandmother’s fruit salad recipe calls for one part apple, one part orange, four parts strawberry, two parts cherry,
damaskus [11]

Answer:

There are 11 parts of fruit: 4-strawberry, 3- grape, 2, cherry, 1- apple, 1-orange 4/11 from the entine quantity of fruits- strawberry

3/11-grapes

2/11- cherries

1/11- apples

1/11- oranges } ⇒ the quantity of oranges and apples are equal Hope it helps ;>

6 0
3 years ago
The hypotenuse of a right triangle is 15cm, and the shorter leg is 9cm. Find the length of the other leg
pishuonlain [190]

Hello!

If you add up the squares of the two legs, it will equal the square of the hypotenuse. As we already have the hypotenuse, we will subtract.

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Therefore, the other leg is 12 cm long.

I hope this helps!

3 0
3 years ago
Read 2 more answers
Do you think the equations (x−1)(x+3)=17+x and (x−1)(x+3)+500=517+x should have the same solution set? Why?
oksano4ka [1.4K]

Answer:

Those two pair of equations have the same solution set.

Step-by-step explanation:

There are two equations  

(x-1)(x+3)=17+x ..... (1) and  

(x-1)(x+3)+500=517+x ...... (2)

We have to check the same solution set will be there for equations (1) and (2) or not.

Now, we are going to rearrange the equation (2).

(x-1)(x+3)+500=517+x

⇒ (x-1)(x+3)=517-500+x

⇒(x-1)(x+3)=17+x

This is the same equation as equation (1).  

Therefore, there will be the same solution set for equations (1) and (2).  (Answer)

There are two equations  

(x-1)(x+3)=17+x ..... (3) and  

3(x-1)(x+3)+500=51+3x ...... (4)

We have to check the same solution set will be there for equations (3) and (4) or not.

Now, we are going to rearrange the equation (4).

3(x-1)(x+3)+500=51+3x

⇒ 3(x-1)(x+3)=3(17+x)

⇒(x-1)(x+3)=17+x

This is the same equation as equation (3).  

Therefore, there will be the same solution set for equations (3) and (4). (Answer)

7 0
3 years ago
An equation is given below.
docker41 [41]

Answer:

The correct option is  D.Any real number value of x satisfies the equation.

Hope it helps.............

6 0
3 years ago
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