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Allisa [31]
3 years ago
11

Andrew walks along a road which can be modeled by the equation y=3x, where (0,0) represents his starting point. When he reaches

the point (12,36), he turns right, so that he is traveling perpendicular to the original road, until he stops at a point which is due east of his starting point (in other words, on the x-axis).
What is the point where Andrew stops?
Mathematics
1 answer:
Temka [501]3 years ago
7 0

Answer:

(120,0)

Steps:

y-36=-1/3(x-12)

(0)-36=-1/3(x-12)

(-3)(-36)=x-12

108=x-12

120=x

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1) Solve the following system of equations algebraically. Give your solution as two
Bad White [126]

For this case we have the following system of equations:

y = x ^ 2 + 7x + 12\\y = 2x + 8

Equating both equations we have:

x ^ 2 + 7x + 12 = 2x + 8\\x ^ 2 + 7x-2x + 12-8 = 0\\x ^ 2 + 5x + 4 = 0

We must find the solutions, for this we factor. We look for two numbers that, when multiplied, result in 4 and when added, result in 5. These numbers are 4 and 1:

4 + 1 = 5\\4 * 1 = 4

Then, the factorized equation is of the form:

(x + 4) (x + 1) = 0

Thus, the solutions are:

x_ {1} = - 4\\x_ {2} = - 1

We look for solutions for the variable "y":

y_ {1} = 2 (-4) + 8 = -8 + 8 = 0\\y_ {2} = 2 (-1) + 8 = -2 + 8 = 6

Thus, the system solutions are given by:(x_ {1}, y_ {1}): (- 4,0)\\(x_ {2}, y_ {2}): (- 1,6)

ANswer:

(x_ {1}, y_ {1}): (- 4,0)\\(x_ {2}, y_ {2}): (- 1,6)

8 0
3 years ago
in a small school, there are 60 boys and 80 girls. write down the ratio of the number of boys to the number of girls. give your
tester [92]
60:80
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3 0
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Plot and label all the points that are 4 units from point P AND that share the same x coordinate as point P. Write the coordinat
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The answers should be: (-2,5), (-2,-2), (-6,-1), (2,1)





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7 0
2 years ago
Consider a parallelogram in which one side is 3 inches long, another side measures 4 inches, and the measurement of one angle is
Musya8 [376]

9514 1404 393

Answer:

  (a) one parallelogram

  (b) opposite sides are 3 inches and 4 inches. Opposite angles are 45° and 135°

  (c) yes, all side lengths can be determined, see (b)

Step-by-step explanation:

Opposite sides of a parallelogram are the same length, so if one side is 3 inches, so is the opposite side. Similarly, if one side is 4 inches, so is the opposite side. If sides have different lengths, they must be adjacent sides. The given numbers tell us the lengths of all of the sides.

The 4 inch sides are adjacent to the 3 inch sides. Thus the angle between a 4 inch side and a 3 inch side must be 45°. Opposite angles are congruent, and adjacent angles are supplementary, so specifying one angle specifies them all.

Only one parallelogram can be formed with these sides and angles. (The acute angle can be at the left end or the right end of the long side. This gives rise to two possible congruent orientations of the parallelogram. Because these are congruent, we claim only one parallelogram is possible. Each is a reflection of the other.)

8 0
3 years ago
What are the relative minimum and relative maximum values over the interval [−4,4] for the function shown in the graph?
kobusy [5.1K]

Answer:

Relative minimum :  -36

Relative maximum :  64

The rate of change is 336 greater

Step-by-step explanation:

Relative minimum are the minimum values  in the interval

Looking at the graph, we find the lowest point in the interval

Relative minimum : (-3, -36) and (3,-36)  y value -36

Looking at the graph, we find the highest point in the interval

Relative maximum : (0,64)  y value 64

Average rate of change = f(x2) - f(x1)

                                          ---------------

                                            x2 - x1

                                       

                                         f(7) - f(5)     1469 - 549      920

                                        ------------- = ---------------   = ------- = 460

                                             7-5               7-5                2

                                         f(4) - f(2)     287 - 39         248

                                        ------------- = ---------------   = ------- = 124

                                             4-2               4-2                2

We need to subtract

460-124

336

6 0
3 years ago
Read 2 more answers
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