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3 years ago

A student writes the equation for a line that has a slope of -6 and passes through the point (2, –8).

Mathematics

1 answer:

tester [92]3 years ago

3 0

Answer:

y -(-8) = -6(x - 2) or y - (-8) = -6x + 12

Step-by-step explanation:

gradient(m) = -6 point (2,-8)

equation of a line is given as;

y - y1 = m(x - x1)

y - (-8) = -6(x - 2)

y - (-8) = -6x - 12

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A hose dispenses 1,413 cm³ of water every minute into a cone with a radius of 60 cm and a height of 150 cm. How long will it tak

sergejj [24]

Hm. Have you ever dispensed water from a hose unto a cone? I know I haven’t, but math can give us a good idea of what it would be like — or at least, how long it would take.

We are told that the hose spills 1413 cm^3 of water every minute. We are also told the cone has a height of 150 cm and a radius of 60 cm. So far, so good.

First things first, we need to find out how much water can fit in the cone. That means volume. The volume of a cone is

π • r^2 • (h/3)

Let’s go ahead and plug in (remember we use 3.14 for π)

(3.14) • (60)^2 • (150/3)

The volume of the cone is 565,200 cm^3

Wait, I’m lost. What were we supposed to do again? Oh, right. We needed to find how long it would take for the hose to fill in the cone. Well, if we know the hose dispenses 1413 cm^3 per minute, and there is a total of 565,200 cm^3 the cone can take, we can divide the volume of the cone by the amount the hose dispenses per minute to get the number of minutes it’d take to fill it.

565200/1413

400 minutes. Wow, ok. I wouldn’t want to wait that long. That’s like watching 3 movies!

7 0

3 years ago

If the degree measure of an angle is 40° less than 3 times the degree measure of its supplementary angle, what is the degree mea

pishuonlain [190]

Let the measure of the unknown angle is x °
Supplementary angles sum up to 180°. So the supplementary angle of x° will be (180 - x)°

According to the given data, measure of x is 40° less than 3 times the measure of its supplementary angle (180 - x). So we can set up the equation for this scenario as:

$x = 3(180 - x ) - 40 \\ \\ 
x = 540 - 3x - 40 \\ \\ 
x + 3x = 500 \\ \\ 
4x = 500 \\ \\ 
x = 125$

So the degree measure of the required angle is 125°.

6 0

3 years ago

Read 2 more answers

Tanya [424]

Answer:

(A) 24 and 66

Step-by-step explanation

Complementary angles add up to 90 degrees

Supplementary angles add up to 180 degrees

(A) 24 + 60 = 90

These 2 angles sum to 90, so therefore they are complementary

(B) 56 + 124 = 180

These 2 angles sum to 180, so they are supplementary, not complementary

While 34 and 56 sum to 90 degrees, 34 and 66 sum to 100, so this answer does not satisfy the question

(D) 56 + 124 = 180; 66 + 114 = 180

Both of these angle pairs are supplementary, so they do not satisfy the answer to the question

5 0

4 years ago

Help i will give brainly pleasereee

irina1246 [14]

Answer:

the answer is 60

Step-by-step explanation:

please mark brainlts

5 0

3 years ago

Derek's design is a kite which starts with coordinates: A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he translates it 5 units to th

katrin [286]

Answer:

The answer is below

Step-by-step explanation:

Select the two answers

a.A would be at (-3,5)

b. B would be at (-1,5)

c.C would be at (-5,8)

d. It would end at the same spot if the original design was reflected across the x-axis,followed by a 180 degree rotation about the origin,followed by translation 1 unit to the left.

E.It would end at the same spot if the original design was reflected 180 degrees rotation about the origin,followed by a translation 3 unit up and translated 1 unit to the left

Select the two answers

a.A would be at (-3,5)

b. B would be at (-1,5)

c.C would be at (-5,8)

d. It would end at the same spot if the original design was reflected across the x-axis,followed by a 180 degree rotation about the origin,followed by translation 1 unit to the left.

E.It would end at the same spot if the original design was reflected 180 degrees rotation about the origin,followed by a translation 3 unit up and translated 1 unit to the left

Solution:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

If a point X(x, y) is translated b units up and a units right, the new point is X'(x + a, y + b). If a point X(x, y) is translated b units down and a units left, the new point is X'(x - a, y - b)

If X(x, y) is reflected across the y axis, the new point is X'(-x, y)

If X(x, y) is reflected across the x axis, the new point is X'(x, -y)

If X(x, y) is rotated 180 degrees, the new point is X'(-x, -y)

If A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he translates it 5 units to the left and 3 units down the new point is A'(-3, -3), B'(-1, -5), C'(-3, -8), D'(-5, -5). If it is then reflected across the y axis, the new point is A"(3, -3), B"(1, -5), C"(3, -8), D"(5, -5).

If A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he reflected across the x-axis the new point is A'(2,0), B'(4, 2), C'(2, 5), D'(0, 2). If it is then rotated 180 degrees, the new point is A"(-2, 0), B"(-4, -2), C"(-2, -5), D"(0, -2). If it is translated 1 unit left the point would be A"'(-3, 0), B"'(-5, -2), C"'(-3, -5), D"'(-1, -2)

If A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he rotated 180 degrees the new point is A'(-2, 0), B'(-4, 2), C'(-2, 5), D'(0, 2). If it is then translated it 3 units up and 1 units left, the new point is A"(-3, 3), B"(-5, 5), C"(-3, 8), D"(-1, 5).

8 0

3 years ago