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kumpel [21]
2 years ago
13

The graph of f (x) = x + 5 is a vertical translation 5 units

Mathematics
1 answer:
irakobra [83]2 years ago
7 0

Answer:

A horizontal translation of 5 units to the left.

Step-by-step explanation:

Given the parent linear function:

\displaystyle f(x)=x

To shift vertically n units, we can simply add n to our function. Hence:

f(x)=x+n

So, a vertical shift of 5 units up implies that n=5. So:

f(x)=x+5

As given.

However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:

f(x-n)=(x-n)

Where n is the horizontal shift.

For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:

f(x-1)=(x-1)

Or:

f(x)=x-1

We notice that this is also a vertical shift of 1 unit downwards.

Therefore, we want a number n such that -n=5.

So, n=-5.

Therefore, it we shift our function 5 units to the left, then n=-5.

Then, our function will be:

f(x-(-5))=(x+5)\text{ or } f(x)=x+5

Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.

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What is the length of EF?
pantera1 [17]

Answer:

  (a)  3.8

Step-by-step explanation:

The Law of Sines can be used to find a missing side length in a triangle where the angles are known and at least one side is given. It tells you the ratio of side lengths is equal to the ratio of the sines of their opposite angles. In effect, longer sides are opposite larger angles.

__

<h3>compare angles</h3>

The given side length (DE=3) is opposite given angle F=50°. The unknown side length EF is opposite larger angle D=75°.

<h3>compare sides</h3>

Since the unknown side is opposite a larger angle than the other angle given, the length of the unknown side will be longer than the side given.

  EF > DE

  EF > 3

Only one answer choice satisfies this inequality.

  EF = 3.8

__

<em>Additional comment</em>

If you want to do the actual computation, we have ...

  EF/sin(D) = DE/sin(F)

  EF = DE·sin(D)/sin(F) = 3·sin(75°)/sin(50°) ≈ 3.7828

  EF ≈ 3.8

7 0
1 year ago
If 246 is a multiple of a
garik1379 [7]

Answer:

FALSE

Step-by-step explanation:

246=2*3*41

If n=2 then 123=3*41 is not a multiple of n

FALSE

6 0
3 years ago
The diameter of the pan is 9 inches. What is the approximate circumference of a lid that will fit his frying pan? (Use 3.14 for
konstantin123 [22]

Answer:

28.26

Step-by-step explanation:

the equation for circumference is 2pi*r or pi*d

3.14*9 (the diametre) is 28.26

Answer 28.26

6 0
2 years ago
6x+14x+5=5(4x+1) what is x in this equation
andrew-mc [135]
Infinite many solutions
8 0
3 years ago
Read 2 more answers
Mrs. Jones is building wooden picture frames. She has 1 5/8 of wood and needs 3/4 for each frame. How many frames can she make w
jonny [76]

Answer:

2\frac{1}{6}\ frames

Step-by-step explanation:

we know that

To find out how many frames she can  make with the exiting material, divide 1 5/8 by 3/4

so

1\frac{5}{8}:\frac{3}{4}

Convert mixed number to an improper fraction

1\frac{5}{8}=\frac{1*8+5}{8}=\frac{13}{8}

substitute

\frac{13}{8}:\frac{3}{4}=\frac{52}{24}\ frames

Simplify

\frac{13}{6}\ frames

Convert to mixed number

\frac{13}{6}\ frames=\frac{12}{6}+\frac{1}{6}=2\frac{1}{6}\ frames

6 0
3 years ago
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