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Gnom [1K]
3 years ago
8

1)The table below represents a linear function f(x) and the equation represents a function g(x):

Mathematics
2 answers:
irga5000 [103]3 years ago
6 0
<span>1)The table below represents a linear function f(x) and the equation represents a function g(x):

 x     y
-1  -11
 0   -1
 1    9


g(x) = 5x + 1

Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

slope of the data of the table:

slope = rise / run = Δy / Δx = [ 9 - ( - 1) ] / [1 - 0] = 10/1 = 10

Also Δy / Δx =  [-1 - (-11) ] / [ 0 - (-1) ] = 10 / 1 = 10

the slope of the function given in the form f(x) = mx + b is m, so the slope of g(x) = 5x - 1 is 5.

Comparisson: the slope of the function g(x) = 5x - 1 is half the slope of the function f(x) represented by the table.

Part B: Which function has a greater y-intercept? Justify your answer.

The y-intercept is the value of y when x = 0, so it is - 1 for the function represented by the table.

The y-intercept of a function given in the form f(x) = mx + b is b, so the y-intercept of g(x) = 5x - 1 is - 1.

So, both functions have equal y-intercept.

2)The table below shows the values of y for each value of x:

x  y
1  0
1 -1
2  1
2 -2

Part A: Does the table represent a relation that is a function? Justify your answer by using the values shown in the table. (4 points)

No, it is not a function, because the relation is ambiguous: the x-coordinate 1 may have two differente values, and the x-coordinate 2 may have two different. So you cannot determine the images of x = 1 and x = 2.

Part B: The function f(x) shown below represents the number of baskets Jess made at different distances, x, in meters, from the hoop:

f(x) = -x + 6

Calculate and interpret the meaning of f(4). (4 points)

f(4) = - 4 + 6 = 2

It means that Jess made 2 baskets at the distant of 4 meters.

Part C: Write an ordered pair to represent the input and output of the function in Part B when Jess is at a distance of p meters from the hoop. (2 points)

input, p         output, f(p)

6                       -6 + 6 = 0

So the ordered pair is (6,0)
</span>
yarga [219]3 years ago
5 0

Answer:

1)The table below represents a linear function f(x) and the equation represents a function g(x):

x     y

-1  -11

0   -1

1    9

g(x) = 5x + 1

Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

slope of the data of the table:

slope = rise / run = Δy / Δx = [ 9 - ( - 1) ] / [1 - 0] = 10/1 = 10

Also Δy / Δx =  [-1 - (-11) ] / [ 0 - (-1) ] = 10 / 1 = 10

the slope of the function given in the form f(x) = mx + b is m, so the slope of g(x) = 5x - 1 is 5.

Comparisson: the slope of the function g(x) = 5x - 1 is half the slope of the function f(x) represented by the table.

Part B: Which function has a greater y-intercept? Justify your answer.

The y-intercept is the value of y when x = 0, so it is - 1 for the function represented by the table.

The y-intercept of a function given in the form f(x) = mx + b is b, so the y-intercept of g(x) = 5x - 1 is - 1.

So, both functions have equal y-intercept.

2)The table below shows the values of y for each value of x:

x  y

1  0

1 -1

2  1

2 -2

Part A: Does the table represent a relation that is a function? Justify your answer by using the values shown in the table. (4 points)

No, it is not a function, because the relation is ambiguous: the x-coordinate 1 may have two differente values, and the x-coordinate 2 may have two different. So you cannot determine the images of x = 1 and x = 2.

Part B: The function f(x) shown below represents the number of baskets Jess made at different distances, x, in meters, from the hoop:

f(x) = -x + 6

Calculate and interpret the meaning of f(4). (4 points)

f(4) = - 4 + 6 = 2

It means that Jess made 2 baskets at the distant of 4 meters.

Part C: Write an ordered pair to represent the input and output of the function in Part B when Jess is at a distance of p meters from the hoop. (2 points)

input, p         output, f(p)

6                       -6 + 6 = 0

So the ordered pair is (6,0)

Step-by-step explanation:

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djverab [1.8K]

Step-by-step explanation:

10)

any triangle inscribed into a circle with the baseline being a diameter of the circle must be a right-angled triangle.

the arc angle of 84° means that also the angle at Q is 84°, because the arc angle is the same as the segment angle at the center of the circle (that is how arc sngles are defined).

that means the supplementary angle (together they have 180°) of Q at the inner top angle of the small left triangle is 180 - 84 = 96°.

as the legs of this small left triangle are both the radius of the circle, this triangle is an isoceles triangle (both legs are equally long, and both angles at its baseline are equally large).

remember, the sum of all angles in a triangle is always 180°.

so,

y = (180 - 96)/2 = 42°

x is a complimentary angle (together they are 90°, remember, the large triangle is inscribed and is right-angled) to the second 42° angle

x = 90 - 42 = 48°

11)

y is the supplementary angle to 126°

y = 180 - 126 = 54°

this inner segment angle is the mean value between the 2 outer angles.

54 = (57 + 2nd outer angle of y)/2

108 = 57 + 2nd outer angle of y

2nd outer angle of y = 108 - 57 = 51°

all arc angles around a circle must be 360°.

x = 360 - 57 - 104 - 51 = 148°

12)

again, all arc angles together must be 360°.

y = 360 - 148 = 212°

x is the same angle as the top angle of a triangle inscribed to the right of the chord.

and that angle is half of the opposing arc angle (148°).

it is therefore 148/2 = 74°

and so,

x = 74°

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