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yan [13]
3 years ago
14

If the graph of f(x) = 5x is shifted 8 units to the left, then what would be the equation of the new graph?

Mathematics
1 answer:
Vika [28.1K]3 years ago
4 0

The equation of the new graph would be f(x+8) = 5x + 8

<u>Explanation:</u>

Given:

f(x) = 5x

Graph is shifted 8 units to the left

Points on the graph of  y  =  f ( x )  are of the form  ( x ,  f ( x ) )

To shift a function left, add inside the function's argument: f (x + b) gives f (x)shifted b units to the left.

Thus,

f(x+8) = 5x + 8

The equation of the new graph would be f(x+8) = 5x + 8

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Help me pls this is very hard for me and plus i gotta turn this in tomorrow
faltersainse [42]

Answer: \Large\boxed{x=40^\circ}

Step-by-step explanation:

<u>Given information</u>

∡ 1 = 90°

∡ 2 = 50°

∡ 3 = x°

Total Angle = 180° <em>(Triangle angle sum theorem)</em>

<u>Given formula</u>

∡ 1 + ∡ 2 + ∡ 3 = Total Angle

<u>Substitute values into the formula</u>

(90) + (50) + (x) = (180)

<u>Combine like terms</u>

140 + x = 180

<u>Subtract 140 on both sides</u>

140 + x - 140 = 180 - 140

\Large\boxed{x=40^\circ}

Hope this helps!! :)

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6 0
2 years ago
In a study commuting patterns of people in a large metropolitan area, respondents were asked to report the time they took to tra
natali 33 [55]

Answer:

b. a person

Step-by-step explanation:

The conducted study demonstrates the commuting patterns of people. Here, the information is collected from a person about amount of time consumes in travel to their work on a certain day of the week. Thus, here the individual is "a person" because the information is collected from a person about their time travel.

6 0
3 years ago
How many ways can Marie choose 2 pizza toppings from a menu of 6 toppings if each topping can only be chosen once?
m_a_m_a [10]

Answer:

30 different ways

Step-by-step explanation:

Hi

for the first topping she can choose 1 of 6 items

so she has 6 choices

and then the second topping she has 5 choices as each topping can only be chosen once

so it comes 6 * 5 = 30

5 0
3 years ago
What percent of the data lie inside the box on a box plot?
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Answer:

50%

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3 0
3 years ago
1) Let f(x)=6x+6/x. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relat
brilliants [131]

Answer:

1) increasing on (-∞,-1] ∪ [1,∞), decreasing on [-1,0) ∪ (0,1]

x = -1 is local maximum, x = 1 is local minimum

2) increasing on [1,∞), decreasing on (-∞,0) ∪ (0,1]

x = 1 is absolute minimum

3) increasing on (-∞,0] ∪ [8,∞), decreasing on [0,4) ∪ (4,8]

x = 0 is local maximum, x = 8 is local minimum

4) increasing on [2,∞), decreasing on (-∞,2]

x = 2 is absolute minimum

5) increasing on the interval (0,4/9], decreasing on the interval [4/9,∞)

x = 0 is local minimum, x = 4/9 is absolute maximum

Step-by-step explanation:

To find minima and maxima the of the function, we must take the derivative and equalize it to zero to find the roots.

1) f(x) = 6x + 6/x

f\prime(x) = 6 - 6/x^2 = 0 and x \neq 0

So, the roots are x = -1 and x = 1

The function is increasing on the interval (-∞,-1] ∪ [1,∞)

The function is decreasing on the interval [-1,0) ∪ (0,1]

x = -1 is local maximum, x = 1 is local minimum.

2) f(x)=6-4/x+2/x^2

f\prime(x)=4/x^2-4/x^3=0 and x \neq 0

So the root is x = 1

The function is increasing on the interval [1,∞)

The function is decreasing on the interval (-∞,0) ∪ (0,1]

x = 1 is absolute minimum.

3) f(x) = 8x^2/(x-4)

f\prime(x) = (8x^2-64x)/(x-4)^2=0 and x \neq 4

So the roots are x = 0 and x = 8

The function is increasing on the interval (-∞,0] ∪ [8,∞)

The function is decreasing on the interval [0,4) ∪ (4,8]

x = 0 is local maximum, x = 8 is local minimum.

4) f(x)=6(x-2)^{2/3} +4=0

f\prime(x) = 4/(x-2)^{1/3} has no solution and x = 2 is crtitical point.

The function is increasing on the interval [2,∞)

The function is decreasing on the interval (-∞,2]

x = 2 is absolute minimum.

5) f(x)=8\sqrt x - 6x for x>0

f\prime(x) = (4/\sqrt x)-6 = 0

So the root is x = 4/9

The function is increasing on the interval (0,4/9]

The function is decreasing on the interval [4/9,∞)

x = 0 is local minimum, x = 4/9 is absolute maximum.

5 0
3 years ago
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