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MariettaO [177]
3 years ago
12

A line passes through the point (4, –3) and has slope m = 1. Find the equation in point–slope form.

Mathematics
1 answer:
timofeeve [1]3 years ago
8 0

Answer:

The expected answer is ...

  y +3 = x -4

Step-by-step explanation:

The line with slope m through point (h, k) can be written in point-slope form as ...

  y -k = m(x -h)

For (h, k) = (4, -3) and m=1, the filled-in form is ...

  y +3 = x -4

___

It happens that the same line can be described by ...

  y +4 = x -3 . . . . . matches the second choice

because that line also goes through the point (3, -4).

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3 years ago
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PLEASE HELP ME WITH THIS
Vedmedyk [2.9K]
Let's start with the drawing. (See the drawing at the bottom of this answer.)

Draw a vertical segment.
At the bottom endpoint, draw a horizontal segment to the right.
The angle at the bottom left is a right angle.
So far this should look like an "L" shape.
The vertical segment is the wall, and the horizontal segment is the ground.

Now draw a segment that connects the right endpoint of the horizontal segment and the top endpoint of the vertical segment. Now you have a right triangle. The diagonal segment represents the ladder. The diagonal segment is the hypotenuse. Label the diagonal segment, the hypotenuse, 12 ft.
Label the vertical segment, the wall, 11.8 ft.

The angle at the bottom right is A. It is the angle the ladder makes with the ground. This angle cannot be greater than 75 degrees.

Now we use trigonometry to find the measure of angle A.

For this right triangle, and its angle A, you have a hypotenuse that measures 12 ft, and an opposite leg that measures 11.8 ft.
We need to find angle A.
The trig ratio that relates the opposite leg and the hypotenuse is the sine.

\sin A = \dfrac{opp}{hyp}

\sin A = \dfrac{11.8}{12}

\sin A = 0.98333

Since the sine of angle A equals 0.98333, we use the inverse sine function to find the measure of angle A.

A = \sin^{-1} 0.98333

A = 79.5^\circ

Answer:
The angle the ladder makes with the ground is 79.5 degrees which is greater than 75 degrees, so the ladder it will be unsafe in this position.


           |\
           |  \
           |    \
           |      \
opp = |         \ hyp = 12
= 11.8  |           \
           |             \
           |_______\  A
3 0
3 years ago
8. There are 10 balls in a bag numbered from 1 to 10. Three balls are selected at random without replacement.
PIT_PIT [208]

Answer:

a. 720

b. 0.3

Step-by-step explanation:

a.

Three balls are selected at random without replacement.

First ball can be selected in 10 ways

Second ball can be selected in 9 ways

Third ball can be selected in 8 ways

Thus, there are 10×9×8 =720 different ways of selecting three balls.

b.

There are three cases that satisfy this condition

  1. first ball picked is 5, the others are not
  2. first ball is not 5, second is 5, third is not
  3. first and second ball is not five, third ball is 5

Each probabilities are:

  1. \frac{1}{10} * \frac{9}{9} *\frac{8}{8} =\frac{1}{10}
  2. \frac{9}{10} *\frac{1}{9} *\frac{8}{8} =\frac{1}{10}
  3. \frac{9}{10} *\frac{8}{9} *\frac{1}{8} =\frac{1}{10}

Thus, one of the balls selected is the number 5 is then \frac{1}{10} + \frac{1}{10} + \frac{1}{10} = \frac{3}{10}

5 0
3 years ago
488, 460, 520, 544, 535<br> What is the range of the data?
n200080 [17]

Answer:

84

Step-by-step explanation:

To find the range, find the difference between the largest value and the smallest value.

544 - 460 = 84

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Vinil7 [7]

Answer:

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Step-by-step explanation:

just distribute the 2 over to the 2x and the -6. That means multiply 2, to everything in the parentheses. Hope that's helpful

5 0
2 years ago
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