Which fraction has a value that's equal to 3⁄4? A. 12⁄16 B. 12⁄12 C. 4⁄3 D. 9⁄16

Mathematics

2 answers:

Rus_ich [418]2 years ago

8 0

The fraction 12/16 has the same .75 value as the fraction 3/4

puteri [66]2 years ago

8 0

3/4 = 0.75

12/16 ÷ 4/4 = 3/4 = 0.75
12/12 = 1
4/3 = 1 1/3 = 1.333....
9/16 = already simplified = 0.5625

Thus, 12/16 is your answer.

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Please show ALL work!<br><br> Solve for x: log₂x+log₂(x-6)=4

Vlad [161]

Answer: x = 8

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I'm going to use the notation log(2,x) to indicate "log base 2 of x". The first number is the base while the second is the expression inside the log (aka the argument of the log)

log(2,x) + log(2,(x-6)) = 4
log(2,x*(x-6)) = 4
x*(x-6) = 2^4
x*(x-6) = 16
x^2-6x = 16
x^2-6x-16 = 0
(x-8)(x+2) = 0
x-8 = 0 or x+2 = 0
x = 8 or x = -2

Recall that the domain of log(x) is x > 0. So x = -2 is not allowed. The same applies to log(2,x) as well.

Only x = 8 is a proper solution.

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You can use the change of base rule to check your work
log base 2 of x = log(2,x) = log(x)/log(2)
log(2,(x-6)) = log(x-6)/log(2)

So,
(log(x)/log(2)) + (log(x-6)/log(2)) = 4
(log(8)/log(2)) + (log(8-6)/log(2)) = 4
(log(8)/log(2)) + (log(2)/log(2)) = 4
(log(2^3)/log(2)) + (log(2)/log(2)) = 4
(3*log(2)/log(2)) + (log(2)/log(2)) = 4
3+1 = 4
4 = 4
The answer is confirmed

5 0

2 years ago

Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic tit

Mamont248 [21]

Here, x - y = 2342
x = 2342 + y

Substitute this value into first equation,
2342 + y + y = 3500
2y = 3500 - 2342
y = 1158/2
y = 579

So, x = 2342 + 579 = 2921

In short, Your Answer would be 2921 contemporary titles

Hope this helps!

3 0

2 years ago

Read 2 more answers

What exponential function is the best fit for the data in the table?

gogolik [260]

Answer: fourth option

$\frac{1}{4} 4^{x-1}-4$

Explanation:

1) the pair x = 3 f(x) = 0, leads you to probe this:

f(3) = 0 = A [4 ^ (3 - 1) ] + C = 0

=> A [4^2] = - C

A[16] = - C

if A = 1/4

16 / 4 = 4 => C = - 4

That leads you to the function f(x) = [1/4] 4 ^( x - 1) - 4

2) Now you verify the images for that function for all the x-values of the table:

x = 2 => f(2) + [1/4] 4 ^ (2 - 1) - 4 = [1/4] 4 - 4 = 4 / 4 - 4 = 1 - 4 = - 3 => check

x = 3 => f(3) = [1/4] 4^ (3 - 1) - 4 = [1/4] 4^2 - 4 = 16 / 4 - 4 = 4 - 4 = 0 => check

x = 4 -> f(4) = [1/4] 4^ (4-1) - 4 = [1/4] 4^(3) - 4 = (4^3) / 4 - 4 = 4^2 - 4 = 16 - 4 = 12 => check.

Therefore, you have proved that the answer is the fourth option.

6 0

2 years ago

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Maya wants to know how many games the seventh grade students at her school play on their phones. Which is the BEST population fo

FrozenT [24]

Answer:

The best population for Maya's school would be all the seventh grade students at Maya's school, because that is who she wants to know how many games they play.

D. All the seventh grade students at Maya's school.

Hope this helps ;)

4 0

2 years ago

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Determine the next step for solving the quadratic equation by completing the square.

Studentka2010 [4]

Answer:

The solutions are $x=\frac{1+\sqrt{7}}{2}$ and $x=\frac{1-\sqrt{7}}{2}$