All categories

3 years ago

Find the greatest common factor of 8m 3 and 6m 4

Mathematics

1 answer:

irina [24]3 years ago

5 0

ANSWER

$2{m}^{3}$

EXPLANATION

The expressions are

$8 {m}^{3} = {2}^{3} \times {m}^{3}$

and

$6 {m}^{4} = 2 \times 3 {m}^{4}$

The greatest common factor is the product the least powers of the common factors.

$= 2 {m}^{3}$

You might be interested in

Question 12<br> Simplify.<br> 54.8-6.9-12<br> 5-2.83.9-4.

trapecia [35]

Answer:

366.

-1493.

Step-by-step explanation:

54.8-6.9-12

You perform the multiplications first:

= 432 - 54 - 12

= 378 - 12

= 366.

5-2.83.9-4

= 5 - 166* 9 - 4

= 5 - 1494 - 4

= -1489 - 4

= -1493

8 0

3 years ago

A line segment has endpoints (-2,-3) and (4,4). Find the length of the segment and find the midpoint.

uysha [10]

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -2 &,& -3~) 
% (c,d)
&&(~ 4 &,& 4~)
\end{array}
\\\\\\
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{[4-(-2)]^2+[4-(-3)]^2}\implies d=\sqrt{(4+2)^2+(4+3)^2}
\\\\\\
d=\sqrt{36+49}\implies \boxed{d=\sqrt{85}}\\\\
-------------------------------$

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -2 &,& -3~) 
% (c,d)
&&(~ 4 &,& 4~)
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{4-2}{2}~~,~~\cfrac{4-3}{2} \right)\implies \left(\cfrac{2}{2}~~,~~\cfrac{1}{2} \right)\implies \boxed{\left(1~,~\frac{1}{2} \right)}$

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Chuge%5Cfbox%5Cgreen%7BQUESTION%7D%20" id="TexFormula1" title=" \huge\fbox\green{QUESTION

Anni [7]

$\huge \fbox \orange{♧Answer♧}$

$\mathcal\blue{METHOD\:1}$

$\mathsf \purple{ - ( \frac{y}{x} )}$

$\mathsf \purple{ - ( \frac{ - 4}{5})}$

$\mathsf \purple{( \frac{4}{5} )}$

$\mathcal\blue{METHOD\:2}$

$\mathsf\purple{m\:=\:(Y2\:-\:Y1)\:÷\:(X2\:-X1)}$

$\mathsf\purple{m\:=\:(-4\:-0)\:÷\:(0\:-\:5)}$

$\mathsf\purple{( \frac{4}{5})}$

$\mathcal\blue{METHOD\:3}$

$\mathsf\purple{m\:=\:rise\:÷\:run}$

$\mathsf\purple{m\:=\:( \frac{4}{5})}$

$\mathbb\pink{NOTE:}$

The difference between the y-coordinates of the two points is called the rise.
The difference between the x-coordinates of the same two points is called the run.
The slope can be calculated by dividing the rise by run.

3 0

2 years ago

Solve the equation for x: X^2=169

Lina20 [59]

Answer:

Step-by-step explanation:

Since x is squared, the inverse operation would be square root. So, the square root of 169 is 13.

5 0

2 years ago

A red die and a blue die are rolled. You win or lose money depending on the sum of the values of the two dice. If the sum is 6 o

olganol [36]

Answer:

The expected value of X is $0.0833.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

For each dice, there are 6 possible outcomes(values from 1 to 6). So for 2 dices, there are $6^2 = 36$ desired outcomes.

Desired outcomes:

Sum 5: (1,4), (2,3), (3,2), (4,1).

Sum 6: (1,5),(2,4),(3,3),(4,2),(5,1)

Sum of 9: (3,6), (4,5), (5,4), (6,3)

Sum of 10: (4,6), (5,5), (6,4)

Sum of 12: (6,6)

Probabilities:

5 + 3 = 8 outcomes in which the sum is 6 or 10, that is, 8/36 probability of winning $4.

4 + 4 + 1 = 9 outcomes in which the 5, 9, or 12, that is, 9/36 probability of winning $1.

36 - (8 + 9) = 36 - 17 = 19 remaining outcomes, that is, 19/36 probability of losing $2.

What is the expected value of X?

Multiplication of each outcome by its probability. So

$E(X) = \frac{8}{36}*4 + \frac{9}{36}*1 - \frac{19}{36}*2 = \frac{8*4 + 9*1 - 19*2}{36} = \frac{32 + 9 - 38}{36} = \frac{3}{36} = 0.0833$

The expected value of X is $0.0833.

4 0

3 years ago