How to solve 12^r=13 in solving exponential equation with logarithms

Answers

Answer 1

Answer: 12^r = 13

Take the logarithm of each side of the equation:

r log(12) = log(13)

Divide each side by log(12) :

r = log(13) / log(12) = 1.03221,,, (rounded)

Answer 2

Answer: $12^r=13\n r=\log_(12)13$

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What scale factor was used when going from the grey triangle to the yellow triangle

Answers

Answer:

It was used $(1)/(3)$ as scale factor.

Step-by-step explanation:

The scale factor is the ratio of two corresponding side lengths of similar figures. Similar figures have the same shape but are of different sizes.

To find the scale factor that was used when going from the grey triangle to the yellow triangle we can work with any of the three sides of the grey triangle.

Let's work with the below side.

The below side is extended from the point $(-2,4)$ to the point $(7,4)$

The length of this side is 9 units.

In the yellow triangle, we can see that the below side is extended from the point $(2,0)$ to the point $(5,0)$

The length of this side is 3 units.

Working with the lengths and the scale factor ⇒

$(9units).(ScaleFactor)=3units$

$ScaleFactor=(3units)/(9units)=(1)/(3)$

We find that the scale factor that was used when going from the grey triangle to the yellow triangle is $(1)/(3)$

Answer:

Scale factor of 1/3

Step-by-step explanation:

Lm how many times does 177 go into 4

Answers

177 goes into 4 zero times because 177 is a larger number than 4, therefore it is impossible to fit 177 into 4.

What polynomial identity should be used to prove that 21 = 25 − 4

Answers

the complete question is

What polynomial identity should be used to prove that 21 = 25 − 4

A: Difference of cubes

B: Difference of Squares

C: Square of Binomial

D: Sum of Cubes

we know that

The difference of two squares is a squared number subtracted from another squared number

$(a^(2) -b^(2) )=(a+b)*(a-b)$

In this problem

then

$(5^(2) -2^(2) )=(5+2)*(5-2)$

$(5^(2) -2^(2) )=(7)*(3)$

$(5^(2) -2^(2) )=21$

$25-4=21$

therefore

the answer is the option

B: Difference of Squares

Choices:
A: Difference of cubes
B: Difference of Squares
C: Square of Binomial
D: Sum of Cubes

The polynomial identity used is B. DIFFERENCE OF SQUARES

21 = 25 - 4
21 = 5² - 2²

Help me please
!!!!!!!!!!!!!!!

Answers

S is in negative territory. So it is going to take you a distance to get to 0 and move further right to T.

You can do this without a formula just by adding 2 to get to zero and then 14 more to get to T. The distance between S and T is 14 + 2 = 16.

Now we should develop some kind of formula for these questions. When one point is on one side of zero on the number line and the other point is on the other side of zero then the formula for distance is

distance (as a formula for this question) = abs(S) + abs(T)

Distance = abs(-2) + abs(14) = 2 + 14 = 16

When both point are on the same side of zero then the formula becomes

Distance= abs(abs(S) - abs(T) )

For example if S = -2 and T = - 9

Then the distance = abs( abs(-2) - abs(-9) ) = abs(2 - 9) = abs(-7) = 7

If you have not taken abs value, then just take the answer that I have given above.

The distance between S and T:

|-2| + 14

= 2 + 14

= 16

Answer

16 units

The cost of $500,000 worth of 20-year term life insurance for Derek is $96.21 per month. If Derek's employer covers 85% of this cost, how much is deducted from Derek's gross income per year for life insurance?

Answers

Alright, the first thing we should have to do is find the total cost per year of his insurance. To do that, we multiply $96.21 by the 12 months in a year to get $1154.52. This is the cost of his insurance per year.

Next, we need to find out how much his boss covers, which we know is 85% of the total cost. SO what we can do is multiply the yearly cost ($1154.52) by the percent his boss covers (.85) to get $981.342. This is how much his boss covers per year.

Lastly, to find out how much Derek pays for insurance yearly, we just need to subtract how much his boss pays ($981.342) from the total yearly cost ($1154.52), which leaves us with $173.178, which is how much Derek pays yearly for his insurance, which should be your answer.

Final answer:

Derek pays 15% of the yearly cost of his life insurance, which amounts to $173.18 per year.

Explanation:

The total cost of Derek's life insurance for a year is calculated by multiplying the monthly fee by the number of months in a year (i.e. $96.21 x 12 = $1154.52). As Derek's employer is covering 85% of the cost, Derek is responsible for the remaining 15%. Therefore, the yearly cost deducted from Derek's gross income would be $1154.52 x 15% = $173.18. It's crucial to understand that these costs can vary depending on the insurance coverage, the employee benefits provided by the employer, and the individual's income.