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3 years ago

Determine the rate of change of the following linear equation as it translates from (-5, -1) to any other point on the line.

1 answer:

4 0

The rate of change of a linear equation (first degree) is equivalent to the slope of a line. Slope is described as the vertical movement (rise) of the line over its horizontal counterpart (run). In determining the rate of change or slope (m) given 1 data point (x',y'), point-slope form is applicable. Point-slope form is: (y-y') = m (x-x'). Substitute the given point (-5,-1) in the equation. By substitution, [y-(-1)] = m [x-(-5)]. Re-arranging the equation, the rate of change or slope is, m = (y+1)/(x+5).

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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

Trapezoid ABCD and trapezoid JKLM are similar. What side corresponds to side BC? Side LM Side KL Side JK Side KJ

astraxan [27]

Answer: JK

Step-by-step explanation:

3 0

2 years ago

A car rental company rents cars for x dollars per day plus y dollars for each mile driven. Carlos rented a car for 4 days, drove

topjm [15]

Answer:

x = $20/day, y = $0.35/mile

Step-by-step explanation:

x = $/day, y = $/mile

4x + 160y = 136

1x + 240y = 104

You can solve by elimination or substitution.

4 0

2 years ago

By what percentage did the high temperature increase from friday to saturday ? round ur answer

monitta

Answer:

Step-by-step explanation:

First, you must find the actual decrease in temperature.

Decrease = Yesterday's temperature - Today's temperature

Decrease = 80 - 75

Decrease = 5 degrees

Now, find the percentage decrease.

% Decrease = Actual decrease / Yesterday's temperature x 100

% Decrease = 5/80 x 100

% Decrease = 0.0625 x 100

% Decrease = 6.25 %

So, the percent decrease in high temperature from yesterday to today is 6.25%

3 0

2 years ago

A store sells shirts at three prices only: $25, $30, and $35. How many different combinations are possible for the store to sell

Dvinal [7]

Answer:

Step-by-step explanation:

The average price of the 20 shirts is 600/20 = $30 each. So, we know that we can sell 20 shirts for $30 each to reach the goal.

For each $25 shirt we sell, we must also sell a $35 shirt to make the average price of the sale be $30 per shirt. That is any or all of the 10 pairs of $30 shirts can be replaced by a ($25, $35) pair. So, there are 10 additional ways to reach the goal.

The total number of possible combinations of shirt sales is 1 +10 = 11.

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3 years ago