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Alex73 [517]
3 years ago
8

What does the graph line look like with a slope of -2/3 passing through the point (-2,1)

Mathematics
1 answer:
ivolga24 [154]3 years ago
6 0
Slope is (change in y)/(change in x). If you have a slope of -2/3 the change in y is -2 and the change in x is 3. Find the point (-2, 1) on the xy plane. Change the y component by -2 (move down 2 grid lines) then change the x component by 3 (move to the right 3 grid lines). If you repeat this process in both directions then draw a line through the points you'll have a line with slope -2/3 which passes through the point (-2, 1). The equation of this line is: y=-2/3x-1/3
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Step-by-step explanation:

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A salesperson is paid an 8.25% commission on sales when the invoice is
son4ous [18]

Answer:

<em>The salesperson's commission for this month is $3,803</em>

Step-by-step explanation:

<u>Percentages</u>

Let's call x to the sales volume, not including commission.

The salesperson is paid an 8.25% commission on sales, thus the total invoice is x + 8.25%x = x + 0.0825x = 1.0825x

We are given this total invoice, thus:

1.0825x = $49,900

Dividing by 1.0825:

x = $46,097

The salesperson's commission is

0.0825*$46,097=$3,803

The salesperson's commission for this month is $3,803

7 0
2 years ago
3. At noon Lan is in his blue mini-van 300 km north of Makenna in her Bugatti. Lan heads south
LiRa [457]

Answer:

The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h

Step-by-step explanation:

At noon the location of Lan = 300 km north of Makenna

Lan's direction = South

Lan's speed = 60 km/h

Makenna's direction and speed = West at 75 km/h

The distance  Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km

The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km

The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km

Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.

By Pythagoras' theorem, we have;

s² = x² + y²

The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61

ds²/dt = dx²/dt + dy²/dt

2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt

2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900

ds/dt = 900/(2×30·√61) ≈ 1.92

The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h

5 0
3 years ago
Are the area of a square and the length of its side directly proportional quantities?
Angelina_Jolie [31]

Answer:

Yes they are directly proportional quantities.

Step-by-step explanation:

We find the area of a square by;

A = length squared or (L)² , where 'L' stands for length and 'A' stands for area.

So Area = L²

Assume the length is a units and increase the length by 2 units

The initial area before increasing the length is a²

After increasing the length, the area becomes: (a + 2)² = a² + 4a + 4

Now we subtract the initial area from the final area and get;

(a² + 4a + 4) - a² = 4a + 4

So the new area increases by 4a + 4 units.

Hence, the area increases as the length increases implying that the area of a square is directly proportional to its length.

We denote this proportionality as;

A ∝ L

7 0
3 years ago
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