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exis [7]
3 years ago
6

What is the slope of the line shown (4, 2) (-4, -2) m=?

Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
6 0

(4, 2) (-4, -2)


Slope is the change in Y over the change in X


From the two points given:

Slope =( -2 - 2 ) / ( -4 -4)

Slope = -4 / -8

Slope = 1/2

m = 1/2

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Determine the slope and vertical intercept of the following linear function below
Sedaia [141]

to get the slope of it, we simply need two points off the table, say (-4,-114) and (2,48).  Recall that the y-intercept, where the graph <u>intercepts</u> the y-axis, when that happens x = 0, so is right there on the table already.

\bf \begin{array}{rrll} x&y\\ \cline{1-2} -4&-114\\ -2&-60\\ 0&-6&\leftarrow y-intercept\\ 2&48\\ 4&102 \end{array}~\hfill (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-114})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{48})

\bf slope\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{48-(-114)}{2-(-4)}\implies \cfrac{48+114}{2+4}\implies \cfrac{162}{6}\implies 27 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(\stackrel{slope}{27}~~,~~\stackrel{y-intercept}{-6} \right)~\hfill

3 0
3 years ago
A maple syrup producer would like to increase production by 500 gallons per each consecutive year with a goal of producing at le
ipn [44]

Answer:

b) x ≥ 3000 gallons

Step-by-step explanation:

Part a)

Production of Year 1 = x gallons

By each year the producer will increase the production by 500 gallons. So,

Production in Year 2 = x + 500 gallons

Similarly,

Production in Year 3 = x + 500 + 500 = x + 1000 gallons

Production in Year 4 = x + 1000 + 500 = x + 1500 gallons

Production in Year 5 = x + 1500 + 500 = x + 2000 gallons

Part b)

The maple syrup producer wants to produced atleast 20,000 gallons in 5 years.

Total amount produced in 5 years = x + x + 500 + x + 1000 + x + 1500 + x + 2000

Total amount produced in 5 years = 5x + 5000

Since, producer wants total production to be atleast 20,000, we can set up the inequality as:

5x + 5000 ≥ 20000

Subtracting 5000 from both sides, we get:

5x ≥ 15000

Dividing both sides by 5, we get:

x ≥ 3000

This means, in the first year the production of maple syrup must be atleast 3,000 gallons i.e 3000 gallons or more to have a total of atleast 20,000 gallons in 5 years.

8 0
3 years ago
find the area of triangle qpm. round the answer to the nearest tenth. a. 5.2 square units b. 6.3 square units c. 6.5 square unit
viva [34]
Pls. see attachment. 

We need to solve for the angles of the smaller triangle in order to solve for the angle of the larger triangle which would help us solve the missing measurement of a side.

Given:

51 degrees.

Cut the triangle into two equal sides and it forms a right triangle. All interior angles of a triangle sums up to 180 degrees.

180 – 51 – 90 = 39 degrees

39 degrees * 2 = 78 degrees.

Angle Q is 78 degrees.

In the bigger triangle, 4.3 is the hypotenuse. We need to solve for the measurement of the long leg which is the opposite of the 78 degree angle.

We will use the formula:

Sine theta = opposite / hypotenuse

Sin(78 deg) = opposite / 4.3

Sin(78 deg) * 4.3 = opposite

4.21 = opposite. This is also the height of the triangle.

 

Area of a triangle = ½ * base * height

A = ½ * 3units * 4.21units

A = 6.315 square units.

7 0
3 years ago
I ONLY HAVE 5 MIN TO TURN THIS IN PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
DENIUS [597]

Answer:

132−15+12

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
a trapezoid has base lengths of (6x-1) units and 3 units. Its midsegment has a length of (5x-3) units. What is the value of x?
vodka [1.7K]
1. You have that:

 - The<span> lengths of the bases are (6x-1) units and 3 units.
 - The midsegment has a length of (5x-3) units.

 2. To solve this exercise, you must apply the formula for calculate the length of the midsegment of a trapezoid, which is shown below:

 Midsegment=Base1+Base2/2

 As you can see, the midsegment is half the sum of the bases of the trapezoid.

 3. When you substitute the values, you obtain:

 (5x-3)=[(6x-1)+3]/2

 4. Now, you can solve the problem by clearing the "x":
</span>
 (5x-3)=[(6x-1)+3]/2
 2(5x-3)=6x-1+3
 10x-6=6x+2
 10x-6x=2+6
 4x=8
 x=8/4
 x=2
3 0
3 years ago
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