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zlopas [31]
3 years ago
12

Peter works as a delivery person for a bike shipping company. The graph shows a linear model for his delivery times on different

days. Peter’s Deliveries What is the equation of the line, first written in point-slope form, and then written in slope-intercept form? Show how you determined the equation. Based on the linear model, predict how long it initially took Peter to deliver his packages (y-intercept). Approximately how much did his delivery time decrease per day (slope)? Complete sentences.I need this done before Monday, please!

Mathematics
1 answer:
aev [14]3 years ago
5 0

Answer/Step-by-step explanation:

✍️The equation of the line in point-slope form:

The equation is given as y - b = m(x - a), where,

(a, b) = a point on the line.

slope (m) = \frac{y_2 - y_1}{x_2 - x_1}

Let's find the slope (m) of the line, housing (3, 21) and (6, 12):

slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 21}{6 - 3} = \frac{-9}{3} = -3

Substitute a = 3 and b = 21, m = -3 into y - b = m(x - a).

Thus, the point-slope equation would be:

✅y - 21 = -3(x - 3)

✍️The equation of the line in slope-intercept form:

Rewrite y - 21 = -3(x - 3), so that y is made the subject of the formula.

y - 21 = -3x + 9

Add 21 to both sides

y = -3x + 9 + 21

y = -3x + 30

✅The slope-intercept equation of the line is y = -3x + 30

Where,

-3 = how much did his delivery time decrease per day (slope)

30 = how long it initially took Peter to deliver his packages (y-intercept)

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Answer:

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5 0
2 years ago
HELP HELP HELP<br> HELP HELP <br> HELP <br> (STEP BY STEP)
Marizza181 [45]

With some simple rearrangement, we can rewrite the numerator as

2x^3 - 3x^2 - x + 4 = 2(x^3 - x) - 3x^2 + x + 4 \\\\ ~~~~~~~~ = 2x(x^2-1) - 3(x^2 - 1) + x + 1 \\\\ ~~~~~~~~ = (2x-3)(x^2-1) + x+1

Then factorizing the difference of squares, x^2-1=(x-1)(x+1), we end up with

\dfrac{2x^3 - 3x^2 - x + 4}{x^2 - 1} = \dfrac{(2x-3)(x-1)(x+1) + x+1}{(x-1)(x+1)} \\\\ ~~~~~~~~ = \boxed{2x-3 + \dfrac1{x-1}}

3 0
2 years ago
Solve the equation X³+2X²-5X -6​
Natali [406]

Answer: x = {-1, -3, 2}

<u>Step-by-step explanation:</u>

x³ + 2x² - 5x - 6 = 0

Use the rational root theorem to find the possible roots:  ±1, ±2, ±3, ±6

Use Long division, Synthetic division, or plug them into the equation to see which root(s) work <em>(result in a remainder of zero)</em>.

I will use Synthetic division.  Let's try x = 1

1 |  1    2    -5     -6

  |<u>  ↓    1      3     -2 </u>      

     1     3    -2    -8   ← remainder ≠ 0 so x = 1 is NOT a root

 Let's try x = -1

- 1 |  1     2    -5    -6

   |<u>  ↓    -1     -1     6 </u>      

      1     1     -6     0   ← remainder = 0 so x = -1 is a root!

The coefficients of the reduced polynomial are: 1, 1, -6  -->   x² + x - 6

Factor: x² + x - 6

          (x + 3)(x - 2)

Set those factors equal to zero to solve for x:

x + 3 = 0   --> x = -3

x - 2 = 0    --> x = 2

Using Synthetic Division and Factoring the reduced polynomial, we found

x = -1, -3, and 2

6 0
3 years ago
You have 3 five dollar bills and 4 ten dollar bills in your pocket. If you pull out 2 bills, what is the probability they are bo
prohojiy [21]

Answer: I think its 4%

Step-by-step explanation: 3+4=7 7/2=3.5

3 0
3 years ago
Read 2 more answers
What’s an equation that passes through the ordered pair (3,7)and has a slope of -4
natita [175]

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

y = mx + b

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

According to the statement data we have:

m = -4\\(x, y) :( 3,7)

Then, the equation is of the form:

y = -4x + b

We substitute the given point and find "b":

7 = -4 (3) + b\\7 = -12 + b\\7 + 12 = b\\b = 19

Finally, the equation is of the form:

y = -4x + 19

Answer:

y = -4x + 19

6 0
2 years ago
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