Prove that x=2 if 4^x=8x...where ^ stands for "to the power of".

1 answer:

4 0

In order to prove this, you simply plug in the number 2 everywhere you see X:

4^(2) = 8(2).

Simplify

16 = 16 √

Since this checks out, x is proven to be 2.

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License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is

Helga [31]

Answer:

$26^3\times10^2 = 1757600$

option B is correct

Step-by-step explanation:

We have 5 spaces in the license plate:

_ _ _ _ _

we have 26 available letters, and 10 available numbers.

starting with letters:

how many choices do i have to place the 1st letter? 26.

26 _ _ _ _

how many choices do i have to place the 2nd letter? 26 (since we're allowed to repeat letters)

26 26 _ _ _

how many choices do i have to place the 3rd letter? 26

26 26 26 _ _

we've used all the places for letters, (note: the exact position of the letters doesn't matter here, the first letter could've been placed anywhere in _ _ _ _ _, but the amount of possible choices for letters would always be 26).

let's move on to numbers.

how many choices do i have to place the 1st number? 10

26 26 26 10 _

how many choices do i have to place the 2nd number? 10

26 26 26 10 10

we've completed our number plate. Next we'll simply multiply all these numbers to get all the possible arrangements in which numbers and letters can be displayed on a license place.

$26^3\times10^2 = 1757600$

option B is correct

8 0

3 years ago

Express 15.16 as a mixed number

kap26 [50]

If this is not a typo, and you mean 15.16 as in 15 and 16 hundredths, we can express this into a mixed number.
Mixed numbers are a whole number with the remainder of that number as a fraction.
For example, 1.25 as a decimal = 1 1/4 as a mixed number.
Since we already have our whole number, 15, we need to know what 16 hundredths is simplified as a fraction.
Currently, our mixed number is 15 16/100.
To simplify this, we need to find a common factor that 16 and 100 share.
Since they are both even numbers, let's divide by 2.
16/2 = 8
100/2 = 50.
Our new mixed number is 15 8/50.
Currently our fraction is still even, so divide by 2 again.
8/2 = 4
50/2 = 25
Your new mixed number is 15 4/25.
4 and 25 have no common factors, so the fraction is simplified.
Your answer is:
15.16 is 15 4/25 as a mixed number.
I hope this helps!

4 0

3 years ago

Read 2 more answers

Evaluateing expressions 9x-c

lyudmila [28]

Answer:

9x−c

= 9x + − c

=−c+9x

Step-by-step explanation:

3 0

3 years ago