How many quarts are there in 12 gallons and 3 quarts? enter the number only. Do not include units

What is the surface area of a cube with a side length of 5 yards?

Y_Kistochka [10]

Answer:

B 125. its basically 5 cubed

Step-by-step explanation:

5 times 5 times 5

8 0

3 years ago

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What is a solution to the equation 3 / m + 3 - M / 3 - M equals m^2 + 9 / m^2-9?

Mnenie [13.5K]

Answer: Last option.

Step-by-step explanation:

Given the equation:

$\frac{3}{m+3}-\frac{m}{3-m}=\frac{m^2+9}{m^2-9}$

Follow these steps to solve it:

- Subtract the fractions on the left side of the equation:

$\frac{3(3-m)-m(m+3)}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{9-3m-m^2-3m}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}$

- Using the Difference of squares formula ( $a^2-b^2=(a+b)(a-b)$ ) we can simplify the denominator of the right side of the equation:

$\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{(m+3)(m-3)}$

- Multiply both sides of the equation by $(m+3)(3-m)$ and simplify:

$\frac{(-m^2-6m+9)(m+3)(3-m)}{(m+3)(3-m)}=\frac{(m^2+9)(m+3)(3-m)}{(m+3)(m-3)}\\\\-m^2-6m+9=\frac{(m^2+9)(3-m)}{(m-3)}$

- Multiply both sides by $m-3$ :

$(-m^2-6m+9)(m-3)=\frac{(m^2+9)(3-m)(m-3)}{(m-3)}\\\\(-m^2-6m+9)(m-3)=(m^2+9)(3-m)$

- Apply Distributive property and simplify:

$(-m^2-6m+9)(m-3)=(m^2+9)(3-m)\\\\-m^3-6m^2+9m+3m^2+18m-27=3m^2+27-m^3-9m\\\\-m^3-3m^2+27m-27+m^3-3m^2+9m-27=0\\\\-6m^2+36m-54=0$

- Divide both sides of the equation by -6:

$\frac{-6m^2+36m-54}{-6}=\frac{0}{-6}\\\\m^2-6m+9=0$

- Factor the equation and solve for "m":

$(m-3)^2=0\\\\m=3$

In order to verify it, you must substitute $m=3$ into the equation and solve it:

$\frac{3}{3+3}-\frac{3}{3-3}=\frac{3^2+9}{3^2-9}\\\\\frac{3}{6}-\frac{3}{0}=\frac{18}{0}$

<em>NO SOLUTION</em>

7 0

3 years ago

What is the value of (2/3)-4

Angelina_Jolie [31]

Answer:

16/81

Step-by-step explanation:

as there is (-) sign so when we multiply even negative numbers it becomes positive

8 0

3 years ago

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Heather paid $2,022.30 for a computer. If the price paid includes a 7% sales tax, which if the following equation can be used to

andrey2020 [161]

Answer:

B

Step-by-step explanation:

3 0

3 years ago

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Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the g

jolli1 [7]

Answer:

D: The origin is not included in the shaded region, and the shaded area is above the line.

Step-by-step explanation:

First of all, let's find the shaded region for our given inequality:

y > ⅓x +4

To determine whether the origin is included in the shaded region, let's put in the value of x and y at the origin (0,0)

Plugging in x = 0 and y = 0 into the inequality gives;

0 > ⅓(0) + 4

0 > 4

0 is not greater than 4 like it states and thus it is false

Therefore, we conclude that the point (0,0) which is the origin is not included in the shaded region

In the inequality we have the symbol ">" which means greater than. For that symbol, we usually shade above the line on the inequality graph.

The only option that corresponds to our answers is option D

3 0

3 years ago

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