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Who answered Stacey's question correctly, Krista or Kevin? Based on the proportional relationship given, how much money will Sta

mariarad [96]

Answer:

Kristina will!

Step-by-step explanation:

Both Krista and Kevin found the right answer to Stacey’s question. Stacey will invest $108 in company A if she invests $24 in company B.

7 0

3 years ago

What is the period of the function y=-4sin (2/3x-pi?3)?

ad-work [718]

2/3 x = 2 pi
x = 2pi × 3/2 = 3pi

period = 3pi

7 0

3 years ago

All the factors of 21

ycow [4]

The factors of 21 are 1, 3, 7, and 21

3 0

3 years ago

Read 2 more answers

Pls help I am suffering

Fed [463]

Answer:

line l: x = -1

line m: x = 6

line n: y = 4

line p: y = -2

Step-by-step explanation:

All of these lines are parallel to either to y or x axis, so the slope is either zero or undefined. This means all you have to do is set x or y equal to the x intercept or y intercept. For lines that go vertically, they always have the same x coordinate and any y coordinate you put in will make a point that is on the line. The same thing with the horizontal lines, except they all have the same y coordinate and any x coordinate will make a point that is on that line.

All you have to do is set x or y, depending on which way the line is going, equal to the point is goes through on the axis it travels through, no need to worry about slope or y = mx + b.

6 0

2 years ago

Read 2 more answers

Find x so that the points (x,x+1), (x+2,x+3) and (x+3,2x+4) form a right-angled triangle.

azamat

Let a, b, and c be vectors each starting at the origin and terminating at the points (x, x + 1), (x + 2, x + 3), and (x + 3, 2x + 4), respectively.

Then the vectors a - b, a - c, and b - c are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.

If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:

(a - b) • (a - c) = 0

or

(a - b) • (b - c) = 0

or

(a - c) • (b - c) = 0

We have

a - b = (x, x + 1) - (x + 2, x + 3) = (-2, -2)

a - c = (x, x + 1) - (x + 3, 2x + 4) = (-3, -x - 3)

b - c = (x + 2, x + 3) - (x + 3, 2x + 4) = (-1, -x - 1)

Case 1: If (a - b) • (a - c) = 0, then

(-2, -2) • (-3, -x - 3) = (-2)×(-3) + (-2)×(-x - 3) = 2x + 12 = 0 ==> x = -6

which would make a - c = (-3, 3) and b - c = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).

Case 2: If (a - b) • (b - c) = 0, then

(-2, -2) • (-1, -x - 1) = (-2)×(-1) + (-2)×(-x - 1) = 2x + 4 = 0 ==> x = -2

which would make a - c = (-3, -1) and b = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).

Case 3: If (a - c) • (b - c) = 0, then

(-3, -x - 3) • (-1, -x - 1) = (-3)×(-1) + (-x - 3)×(-x - 1) = x ² + 4x + 6 = 0

but the solutions to x here are non-real, so we throw out this case.

So there are two possible values of x that make a right triangle, x = -6 and x = -2.

3 0

3 years ago