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lisabon 2012 [21]
3 years ago
14

What is the value of x? Enter your answer in the box. x =

Mathematics
1 answer:
melisa1 [442]3 years ago
7 0

The two angles are vertical angles, which means they are the same.

Set the two equations to equal and solve:

2x +2 = 3x -52

Subtract 2x from each side:

2 = x -52

Add 52 to each side:

x = 54



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If log2 5 = k, determine an expression for log32 5 in terms of k.
lukranit [14]

Answer:

log_3_2(5)=\frac{1}{5} k

Step-by-step explanation:

Let's start by using change of base property:

log_b(x)=\frac{log_a(x)}{log_a(b)}

So, for log_2(5)

log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)

Now, using change of base for log_3_2(5)

log_3_2(5)=\frac{log(5)}{log(32)}

You can express 32 as:

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Using reduction of power property:

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log(32)=log(2^5)=5log(2)

Therefore:

log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)

As you can see the only difference between (1) and (2) is the coefficient \frac{1}{5} :

So:

\frac{log(5)}{log(2)} =k\\

log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k

6 0
3 years ago
Natasha is a bank teller. She received a 5% raise last year and a subsequent merit raise of 3% this year. What is the accumulati
Anvisha [2.4K]

Answer:

The correct answer is C. 8.15%.

Step-by-step explanation:

Given that Natasha is a bank teller, and she received a 5% raise last year and a subsequent merit raise of 3% this year, to determine what is the accumulative or compound effect of these two raises as a percentage, the following calculation must be performed, assuming, as an example, that her starting salary was $ 2,000:

(2,000 x 1.05) x 1.03 = X

2,100 x 1.03 = X

2,163 = X

2,000 = 100

2,163 = X

2,163 x 100 / 2,000 = X

216,300 / 2,000 = X

108.15 = X

108.15 - 100 = 8.15

Thus, the compound effect of both salary increases is a salary increase of 8.15%.

8 0
2 years ago
If (x+3)divided by 3 = 9 what is x
defon

Answer:

x = 24

Step-by-step explanation:

Given that:

(x+3)/3 = 9

multiplying both sides by 3

(x+3) = 9*3

(x+3)= 27

Subtracting 3 from both sides

x= 27-3

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I hope it will help you!

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