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2 years ago

A direct variation function contains the points (-8, -6) and (12,9). Which equation represents the function?

Mathematics

1 answer:

bezimeni [28]2 years ago

3 0

Answer:

y = $\frac{3}{4} x$

Step-by-step explanation:

Each point is (x,y). So to find the equation, substitute both points into the given choices.

To test the first choice: y = $-\frac{4}{3}x$ substitute -8 into x and -6 into y

-6 = $-(\frac{4}{3})(-8)$

-6(3) = (-4)(-8)

-18 ≠ 32

Since the numbers are not equal this is not the correct equation. Move on to testing the next equation in the same manner.

The third equation y = $\frac{3}{4}x$ satisfies both points

Test for point (-8,-6)

-6 = $(\frac{3}{4})(-8)$

-6(4) = (3)(-8)

-24 = -24

Test for point (12,9)

9 = $(\frac{3}{4})(12)$

9(4) = (3)(12)

36 = 36

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Construct an equilateral triangle of side 7cm and construct circumcircle.

zalisa [80]

Answer:

To do this, all you need is to draw triangle with each side being 7 cm, and a circle that intersects all three of its corners.

Step-by-step explanation:

With a ruler and a pencil, draw a 7cm line.
With a compass set to a radius of 7cm draw an arc centered around the right end of the line.
With the same compass, still at 7cm, draw an arc centered around the left end of the line.
These two arcs will intersect on either side of the line (you only need one side, so you only need a small arc in the right place, roughly where you think the third point if the triangle is.
Where those arcs intersect is the third point on your triangle. Mark that, and then trace two lines from that point to either end of the line segment you started with.

<em>You now have an equilateral triangle with 7cm sides. Next you need to draw the circle</em>

Measure the halfway point on two of your three lines.
Draw a line from that each of those halfway points to the opposite corner. The new lines you're drawing will be perpendicular to the edge your measuring against.
You have now drawn two line segments, and they intersect in the center of the circle. Now take your compass and set its radius to the distance from that center point to one of the three corner points.
Centered on that middle point, trace a circle with the selected radius.

And you're done!

6 0

2 years ago

No links, No Wrong Answers, No Jokes, No Long Explanations.....

Harrizon [31]

Answer:

B (there is a negative correlation)

Step-by-step explanation:

the data set if you were put on a linear set, you be a negative and most of the points would fit through or around the slope. so it is a neagtive correlation

5 0

2 years ago

Read 2 more answers

A student dropped a textbook from the top floor of his dorm and it fell according to the formula s(t) = −16t 2 + 8√t , where t i

Sidana [21]

Answer:

Step-by-step explanation:

Given the distance of fall of the student in term of the time t expressed by the equation s(t) = −16t² + 8√t, to get the average speed of fall of the pencil after 2.8 secs, we will need to differentiate the given function first since Velocity is the change in distance of a body with respect to time i.e

V = d(s(t))/dt

s(t) = −16t² + 8t^1/2

V = -32t+1/2(8)t^(1/2 - 1)

V = -32t+4t^-1/2

The average speed of the fall Using the fact that the pencil hit the ground in exactly 2.8 seconds, will be gotten by substituting t = 2.8 into the resulting equation.

V = -32t+4(2.8)^-1/2

V = -32t+4/√2.8

V = -32+4/1.6733

V = -32+2.391

v = -29.61m/s

<em>Hence the average speed of the fall is -29.61m/s</em>

3 0

3 years ago

Find the missing length. The triangles are similar.

hodyreva [135]

Answer:

182

Step-by-step explanation:

First, we can say that ∠ACB and ∠BCF are opposite angles because they are not next to each other and are formed by intersecting lines. Therefore, ∠ACB = ∠BCF

Next, angles correspond with the side opposite of it. This means that, for example, ∠ACB corresponds with line AB and ∠BCF corresponds with line BF. Because ∠ACB and ∠BCF are equal and the triangles are similar, we can say that their corresponding sides have a ratio with each other. Similarly, ∠CAB corresponds to CB, ∠ABC corresponds to AC, ∠CWV corresponds to CV, and ∠CVW corresponds to CB.

Because the triangle CVW is isosceles, we can say that the angles whose corresponding sides are equal are equal as well, so ∠CAB = ∠ABC and ∠CVW = ∠CVW. Next, because ∠ACB and ∠BCF are equal and correspond to each other, and the other two angles in each triangle are equal to each other, we can say that the other two angles must be equal. Another way of putting this is like this:

Say that x = ∠CAB. Then,

∠CAB + ∠ABC + ∠ACB = 180

x + x + ∠ACB = 180

2x + ∠ACB = 180

subtract ∠ACB from both sides

180 - ∠ACB = 2x

Similarly, if y = ∠CWV,

180 - ∠WCV = 2y. Therefore, 2y=2x and y=x, so ∠CAB = ∠ABC = ∠CWV = ∠CVW.

Given this, we can say that sides CV and CW correspond with BC and AC. This means that the ratio between, for example, CV and BC is equal to the ratio between CW and AC. Therefore,

CV/BC = CW/AC

84/182 = 84/?

Filling in the blank, 84/182 is equal to 84/182, so ? = 182

8 0

3 years ago

An artist can sell 20 compies of a painting for $100 each, but for each additional copy he makes the value of each painting will

ki77a [65]

Answer:

40 copies for $3000

Step-by-step explanation:

First: The Equation

y=(20+x)(100-x)

This shows how for every new painting, the price will go down.

y=2000+80x-x²

Convert it to standard form: ax²+bx+c

You can now choose to graph it or find the vertex form. For the limit of time, I will just use a graph.

The vertex, (40,3000), is your answer, where the x value is the number of paintings and the y value the money made.

4 0

3 years ago