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laiz [17]
3 years ago
15

Show why, for linear functions, a vertical translation is equivalent to a horizontal translation. For a linear function, what ho

rizontal translation is equivalent to a vertical translation of 3 units up?
Mathematics
1 answer:
V125BC [204]3 years ago
8 0

Explanation:

A) For the function ...

f(x) = mx + b

the vertical translation by k makes the function ...

g(x) = f(x) + k = mx + b + k

This can be rewritten as ...

g(x) = m(x +k/m) +b = f(x+k/m)

That is, the vertical translation by k is equivalent to a horizontal translation by -k/m, where m is the slope of the linear function.

___

B) For a vertical translation of 3, the equivalent horizontal translation is ...

-k/m for k=3

= -3/m . . . . . where m is the slope of the function

_____

Please note that there is no equivalent for m=0.

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What is the average rate of change from x = -3 to x = 3
andrey2020 [161]
I believe it is -1 since -3 times -1 equals 3 and the rate of change is based on the slope of a line 
5 0
3 years ago
In a right triangle, the measure of one acute angle is 12 more than twice the measure of the other acute angle. Find the measure
soldi70 [24.7K]

Given:

In a right triangle, the measure of one acute angle is 12 more than twice the measure of the other acute angle.

To find:

The measures of the 2 acute angles of the triangle.

Solution:

Let x be the measure of one acute angle. Then the measure of another acute is (2x+12).

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees. So,

x+(2x+12)+90=180

3x+102=180

3x=180-102

3x=78

Divide both sides by 3.

x=\dfrac{78}{3}

x=26

The measure of one acute angle is 26 degrees. So, the measure of another acute angle is:

2x+12=2(26)+12

2x+12=52+12

2x+12=64

Therefore, the measures of two acute angles are 26° and 64° respectively.

8 0
3 years ago
Solve the equation <br><br> 5 | 2-3x |= 7x + 2
igor_vitrenko [27]

Answer:

Check the ppicture i sent you i think it would help

5 0
2 years ago
Matters has 456:8 What s his rate
Olegator [25]

We are given ratio 456:8.

The given ratio can be written in fraction form as \frac{456}{8}

In order to find the rate, we need to divide 456 by 8, because it would give the unit value.

When we divide 456 by 8, we first take multiple of 8 closer to the number 45.

8*6=48 but it's greater than 45, so we would take 8*5 =40.

Subtracting 40 from 45, we get 5.

Getting 6 down, we get 56. Take multiple of 8 upto 56.

8*7= 56.

56 -56=0.

So, on dividing 456 by 8 we got 57.

Therefore, rate is 57 per unit.


3 0
3 years ago
Greatest common factor for 40,10
horrorfan [7]
The greatest common factor of 40&10 is 10
8 0
3 years ago
Read 2 more answers
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