1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alla [95]
3 years ago
11

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

Mathematics
1 answer:
Norma-Jean [14]3 years ago
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).
You might be interested in
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:

  11

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.

5 0
3 years ago
Other questions:
  • Marisol bought 20 peices of ribbion for $18. what would be the cost of 30 peices of ribbon
    10·1 answer
  • What point in the feasible region maximizes P for the objective function P = 2x + 3y? Constraints
    15·1 answer
  • What to do in the the following question
    13·1 answer
  • A rectangle has a length of 12 feet and a perimeter of 40 feet
    11·1 answer
  • Which set of three numbers could be the side lengths of a triangle?
    11·2 answers
  • What is the measure of m_A?
    9·1 answer
  • A color printer prints 19 pages in 8 minutes.<br> How many minutes does it take per page?
    5·1 answer
  • 135=18h what is the missing height
    12·2 answers
  • A teacher surveyed her class after they had taken a vocabulary test. Eighteen of the students claimed they had studied at least
    10·2 answers
  • If 2^2x = 2^3, what is the value of x?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!