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viktelen [127]
2 years ago
12

\begin{aligned} f(x)&=|x| \\\\ g(x)&=|x | + 1 \end{aligned} f(x) g(x) ​ =∣x∣ =∣x∣+1 ​ We can think of ggg as a translate

d (shifted) version of fff. Complete the description of the transformation. Use nonnegative numbers. To get the function ggg, shift fff by units.
Mathematics
1 answer:
Tema [17]2 years ago
7 0

Answer:

To get the function g, shift f by 1 unit.

Step-by-step explanation:

Given

\begin{aligned} f(x)&;=|x| \\ g(x)&;=|x | + 1 \end{aligned}

Required

How do f(x) translates to g(x)

In terms of f(x), g(x) can be represented as:

g(x) = f(x) + k

Where

f(x)= |x|

and

k = 1

<em>This implies that f(x) is vertically shifted 1 unit up to get g(x)</em>

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A heated piece of metal cools according to the function c(x) = (.5)x − 11, where x is measured in hours. A device is added that
e-lub [12.9K]
16.5 degrees below the starting temp, whatever that is. If its 0, then -16.5 degrees.

The first equation would be (.5)5-11=-8.5, because the metal has been cooling for 5 hours.

The device that 'aids' in the cooling would be -5-3=-8, because it is a separate variable that cools the metal, so the amount the device cools is independent of the natural cooling amount, and the equation is independent of the natural cooling equation.
You then add -8.5 and -8, because the device has lowered 8.5 degrees and 8 degrees. This equals -16.5 degrees, or a decrease of 16.5 degrees.
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3 years ago
Somebody pls!! “Write the equation of the line in fully simplified slope-<br> intercept form.”
zhannawk [14.2K]

Answer:

y = 3/5x + 5

Step-by-step explanation:

Slope-intercept form is y = mx + b where m is the slope (rise / run of the line) and b is y-intercept (y value of where the line intersects with the y-axis.

The line is rising up 3 and run to the right 5 and so it's slope is 3/5. The line intersects with the y-axis at a y value of 5 and so it's y-intercept is 5.

Therefore, your answer in slope-intercept form is y = 3/5x + 5.

8 0
3 years ago
If (2,3) is reflected over the y axis what is the new coordinates
Andrei [34K]

Answer:

(-2,3)

Step-by-step explanation:

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). Notice that B is 5 horizontal units to the right of the y-axis, and B' is 5 horizontal units to the left of the y-axis. the y-axis is the point (-x,y).

3 0
3 years ago
Yuto and Riko went for a bike ride on the same path. When Riko left their house, Yuto was 5.25 miles along the path. If Yuto’s a
Nimfa-mama [501]

Answer:

Step-by-step explanation:

When Riko left his house, Yuto was 5.25 miles along the path.

Average speed of Riko = 0.35 miles per minute

Average speed of Yuto = 0.25 miles per minute

First we will calculate the time in which Riko will catch Yuto on the track.

Relative velocity of Riko as compared to Yuto will be = velocity of Riko - velocity of Yuto

= 0.35 - 0.25

= 0.10 miles per minute

Now we this relative velocity tells that Riko is moving and Yuto is in static position.

By the formula,

Average speed = \frac{Distance}{Time}

0.10 = \frac{5.25}{t}

t = \frac{5.25}{0.1}

t = 52.5 minutes

Now we know that Rico will catch Yuto in 52.5 minutes. Before this time he will be behind Yuto.

So duration of time in which Rico is behind Yuto will be 0 ≤ t ≤ 52.5

Here time can not be less than zero because time can not be with negative notation. It will always start from 0.

3 0
3 years ago
Read 2 more answers
Translate the given phrase into an algebraic expression and simplify if possible: the product of -13 and the difference of c
Musya8 [376]

Answer:  -13c+13d

Step-by-step explanation:

For this exercise it is important to remember the following:

1. By definition, the "Product" is the result of a multiplication.

2. The "Difference" is defined as the result of a subtraction.

3. The Distributive property states that:

a(b+c)=ab+ac\\\\a(b-c)=ab-ac

Keeping the above on mind, you know that:

"The difference of c and d" can be represented with the following expression:

c-d

Therefore, "The product of -13 and the difference of c and d" can be represented with this expression:

-13(c-d)

Finally, you must apply the Distributive property in order to simplify the expression. You get:

=-13c+13d

7 0
3 years ago
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