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3 years ago

Solve the equation algebraically for all values of X

Mathematics

1 answer:

noname [10]3 years ago

5 0

This is a problem you need to solve using logs. When you use logs you can "pull" the exponents down in front of the log to get a new equation that looks like this: 2x^3 + x^2 log 81 = 6x - 3 log 27. Now divide both sides by log 81 and 6x - 3 simultaneously to get (2x^3 + x^2)/(6x - 3) = (log 27)/(log 81). If you do the log math on the right side you get .75. Now multiply both sides by 6x-3 to get 2x^3+x^2 = .75(6x-3). If you distribute that out on the left side you'll get 2x^3+x^2=4.5x-2.25. Now move everything over to the left side and set the whole thing equal to 0: 2x^3+x^2-4.5x+2.25=0. When you solve for x, you are in essence factoring, so do this by grouping: x^2(2x+1)-2.25(2x+1). Now finally factor out the 2x+1 to get (2x+1)(x^2-2.25). You're not done yet though cuz you need to solve each of those for x: 2x+1=0, and x= -1/2; x^2=2.25, and x=+/- 1.5. So all the values for x here are -1/2, 1.5, and -1.5

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Kelko will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $57 and cost an add

Delicious77 [7]

Questions (contd)

(a) For what amount of driving do the two plans cost the same?

(b) What is the cost when the two plans cost the same?

Answer:

(a) 100 miles

(b) $65

Step-by-step explanation:

Given

Plan 1:

$Initial\ Fee = \$57$

$Additional = \$0.08$ per mile

Plan 2:

$Initial\ Fee = \$50$

$Additional = \$0.10$ per mile

Solving (a): Number of miles when both plans are equal

Represent the distance with x and the cost with y

So:

Plan 1:

$y = 57 + 0.08 * x$

Plan 2:

$y = 50 + 0.10 * x$

To solve (a), we equate both plans together; i.e.

$y = y$

$57 + 0.08x = 50 + 0.10x$

Collect Like Terms

$0.08x - 0.10x= 50 - 57$

$-0.02x= -2$

Solve for x

$x = -2/-0.02$

$x = 100$

Hence, 100 mile would cost both plans the same

Solving (b): Cost when both plans are the same:

In this case, we simply substitute 100 for x in any of the y equation.

$y = 57 + 0.08 * x$

$y = 57 + 0.08 * 100$

$y = 57 + 8$

$y = 65$

Hence, the amount is $65

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2 years ago

San R APOR is a right triangle. IF RO = 8, what is PO? mios 16

attashe74 [19]

Answer:

PQ = 16

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos60° = $\frac{1}{2}$ , then

cos60° = $\frac{adjacent}{hypotenuse}$ = $\frac{RQ}{PQ}$ = $\frac{8}{PQ}$ = $\frac{1}{2}$ ( cross- multiply )

PQ = 8 × 2 = 16

6 0

3 years ago

According to a survey of adults, 64 percent have money in a bank savings account. If we were to survey 50 randomly selected adul

zheka24 [161]

Answer:

The mean number of adults who would have bank savings accounts is 32.

Step-by-step explanation:

For each adult surveyed, there are only two possible outcomes. Either they have bank savings accounts, or they do not. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$