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Mrac [35]
2 years ago
11

What is the prime factorization for 192

Mathematics
1 answer:
ioda2 years ago
8 0
192|2
96|2
48|2
24|2
12|2
6|2
3|3
1

192=2^6\cdot3



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A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the
serious [3.7K]

Answer:

The equation is A=6000e^{-0.23t}  at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation A=A_0e^{rt}. We can find the rate at which it decays by using t=3 hours and A=3000. This means A_0=6000 in this context.

A=A_0e^{rt}\\3000=6000e^{r(3)}

0.5=e^{(24.5)r}

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r

We know lne=1 so we were able to cancel it out and divide both sides by 3.

We solve with a calculator \frac{ln0.5}{3} =r\\-0.23=r

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is A=6000e^{-0.23t}


5 0
3 years ago
The point P(-5,-8) is reflected across the x-axis to create point Q.
Ivahew [28]

Answer:

Answer: D. Q(5, −6) and R(−5, 6)

Step-by-step explanation:

3 0
3 years ago
PLEASE HELP!!!! WILL MARK BRAINLIEST!!!!
irga5000 [103]

Answer:

None of these.

Step-by-step explanation:

Let's assume we are trying to figure out if (x-6) is a factor. We got the quotient (x^2+6) and the remainder 13 according to the problem.  So we know (x-6) is not a factor because the remainder wasn't zero.

Let's assume we are trying to figure out if (x^2+6) is a factor.  The quotient is (x-6) and the remainder is 13 according to the problem.  So we know (x^2+6) is not a factor because the remainder wasn't zero.

In order for 13 to be a factor of P, all the terms of P must be divisible by 13.  That just means you can reduce it to a form that is not a fraction.

If we look at the first term x^3 and we divide it by 13 we get \frac{x^3}{13} we cannot reduce it so it is not a fraction so 13 is not a factor of P

None of these is the right option.

4 0
2 years ago
Read 2 more answers
Which expression represents the distance between the points (11, 4) and (5,8)?
antiseptic1488 [7]

Answer:

\displaystyle d = 2\sqrt{13}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Coordinates (x, y)

<u>Algebra II</u>

  • Distance Formula: \displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Step-by-step explanation:

<u>Step 1: Define</u>

Point (11, 4) → x₁ = 11, y₁ = 4

Point (5, 8) → x₂ = 5, y₂ = 8

<u>Step 2: Find distance </u><em><u>d</u></em>

Simply plug in the 2 coordinates into the distance formula to find distance <em>d</em>

  1. Substitute in points [Distance Formula]:                                                       \displaystyle d = \sqrt{(5-11)^2+(8-4)^2}
  2. [√Radical] (Parenthesis) Subtract:                                                                 \displaystyle d = \sqrt{(-6)^2+(4)^2}
  3. [√Radical] Evaluate exponents:                                                                    \displaystyle d = \sqrt{36+16}
  4. [√Radical] Add:                                                                                               \displaystyle d = \sqrt{52}
  5. [√Radical] Simplify:                                                                                         \displaystyle d = 2\sqrt{13}
4 0
3 years ago
If x - 10 = 15 then x = 25
masya89 [10]

Answer:

25-10=15

Step-by-step explanation:

5 0
2 years ago
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