15 points

2 answers:

6 0

In this exercise is given that a triangle has a vertex R at the coordinate (-4,1) and it is says that this point was rotated 90 degrees counterclockwise from the origin. It is asked to find the rotation which is equivalent to 90 degree counterclockwise rotation.

First of all a 90 degree counterclockwise rotation is define by the rule
(x,y)--(-y,x), which means that every time a 90 degree counterclockwise rotation occurs the given point has to be changed according to the previous mention rule.

In the other hand, a 90 degree clockwise rotation is define by the rule (x,y)--(y,-x). A 360 degree counterclockwise rotation is define by (x,y)--(x,y), and a 270 degree clockwise rotation is represented by the rule (x,y)--(-y,x).

By the previous said, the rotation which is equivalent to a 90 degree counterclockwise rotation is a 270 degree clockwise rotation.

melisa1 [442]3 years ago

5 0

Clockwise 270 degrees is the answer

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The table represents the change in the boiling point of water at different altitudes. Altitude (in thousands of feet) Boiling Po

Anton [14]

Answers:

1) The dependent variable is the boiling point of water and the independent variable is the altitude.

2) The slope would represent the average decrease of the boiling point of water per every one thousand feet that the altitude increase.

Explanation:

1) given

Table:

<span>Altitude (in thousands of feet)    Boiling Point of Water (Fahrenheit)

(sea level) 0    212
0.5                                               211.1
1.0                                               210
2.0                                               208.4
2.5                                               207.5
3.0                                               206.6
4.0                                               204.8
4.5                                               203.9

2) The independent variable is the input of the function, and the dependent variable is the output of the function.

The input determines the output once the rule is established.

Therefore:

a) the independent variable is the altitude, and
b) the dependent variable is the boiling point of water in Farenheit.

3) The slope of the graph would be:

                 change in the dependent variable          change in boiling point
slope = --------------------------------------------------- = ---------------------------------
</span>                 change in the independent variable          change in altitude

Therefore, the slope represents the average change in the boiling boilin point of water every one thousand feet on change of altitude.

If the relationship is not linear, then the slope is not constant, and you will have different slopes for different parts.

If the slope is negative, means that as the altitude increase the boiling point of water decrease.

You can calculate the slope using any two pair of points (data)

              212 - 210           2
slope =---------------- =   ------- = - 2
                0 - 1            - 1

or, using other pair of points:

                204.8 - 210           -5.2
slope = --------------------- =   --------- = -2.6
                  4.0 - 2.0               2.0

As you see, the slope is not constant. So, the function is not linear.

5 0

3 years ago

Read 2 more answers

E Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? Select three options.

kozerog [31]

Answer:

6feet by 5feet by 4feet

7feet by 6feet by 4feet

8feet by 3feet by 7feet

7 0

2 years ago

Helpppppp plsssssssss

bekas [8.4K]

Answer:

Step-by-step explanation:

The right triangle on the right side of the figure has a height of 6 (two same sides lengths) and a base of 3.

x is the hypotenuse (side opposite of 90 degree angle).

We can use the pythagorean theorem to find x. The pythagorean theorem tells us to square each leg (height and base) of the triangle and add it. It should be equal to the hypotenuse square.

For this triangle it means, we square 6 and 3 and add it. It should be equal to x squared. Then we can solve. Shown below:

$6^2 + 3^2 = x^2\\36 + 9 = x^2\\45 = x^2\\x=\sqrt{45}$