1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
notka56 [123]
3 years ago
6

The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): A graph with two linear

functions; f of x passes through 5, 0 and 10, 10, and g of x passes through negative 3, 0 and 2, 10. Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Mathematics
1 answer:
Julli [10]3 years ago
5 0

Answer:

First, let's find the equations for our lines:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

f(x) passes through (5,0) and (10, 10), then the slope is:

a = (10 - 0)/(10 - 5) = 10/5 = 2.

then we have:

y = 2*x + b

And when x = 5, we have y = 0.

0 = 2*5 + b

0 = 10 + b

b = -10

Then the equation for f(x) is:

y = f(x) = 2*x - 10.

Now for g(x) we have the points:

(3, 0) and (2, 10)

a = (10 - 0)/(2 - 3) = -10

y = -10*x + b

0 = -10*3 + b

b = 30.

y = g(x) = -10*x + 30.

A) Ok, the transformations:

Transformation 1 or T1.

f(x) = 2*x - 10

g(x) = -10*x + 30.

Then, we start with f(x):

First, we can move f(x) up 4 units and get:

f'(x) = 2*X - 6

Now we can dilate f(x) with a scale factor of -5 from the origin, now we get:

f''(x) = -5*f'(x) = -10*x + 30.

And this is g(x).

Transformation 2 or T2.

Move f(x) up 10 units, so now we have:

f'(x) = 2*x

Do a reflection over the x-axis, so the sign of y changes, and now we get:

f''(x) = -2*x

Do a dilation of scale factor 5

f'''(x) = 5*-2*x = -10*x

Now do a vertical translation of 30 units up.

f''''(x) = -10*x + 30 = g(x).

These are two transformations that start with f(x) and end with g(x).

B) Ok, as i was writting the transformations i already solved them, so this part is already done.

C) the equation for the transformations are:

T1) g(x) = -5*(f(x) + 4)

T2) g(x) =  -(f(x) + 10)*5 + 30

You might be interested in
A family buys 5 airline tickets and travel insurance that costs $17 per ticket. The total cost is $850. Let x represent the pric
otez555 [7]

Answer:

850+5(x+17) (D)

153

3 0
3 years ago
Read 2 more answers
Lena is converting 2/25 to a percent. What should she multiply the numerator and denominator of the fraction by to find the perc
NNADVOKAT [17]
A percent is a number out of 100, so you'd want to multiply the denominator to get 100. In this case, 25 would have to be multiplied by 4 to get 100. To keep the fractions equal to each other, you have to multiply the numerator by the same thing. 2*4=8. Therefore, your fraction would be 8/100 or 8%
7 0
3 years ago
Read 2 more answers
The diagram shows a solid formed by joining a hemisphere, of radius rcm, to a cylinder, of radius rcm and height hcm. The total
posledela

Answer:

Step-by-step explanation:

The total surface area of the sphere = 2πr²

Total surface area of the cylinder = 2πr²+2πrh

Total surface area of the solid = 4πr²+2πrh

r is the radius of the sphere and the cylinder

h is the height of the cylinder

Total surface area of the solid = 2πr(r+h)

If the total height of the solid is 18 cm, then r+h = 18cm

Given the Total surface area of the solid = 205π cm

205π = 2πr(r+h)

205π = 2πr(18)

205π = 36πr

205 = 36r

Divide both sides by 36

205/36 = 36r/36

r = 5.69cm

Since  r+h = 18cm

5.69+h = 18

h = 18-5.69

h = 12.31cm

6 0
3 years ago
What is 15 increased by 60%
vazorg [7]
What is 15 increased by 60 percent? Let's work it out!

First, you must know what 60 percent of 15 is.

<u>60 percent of 15
</u>   15 times .60 
<u />equals
9.

So 60% of 15 is 9.


<u /><u>Increased</u> is a word which<u> means added</u>.

So, 15 plus 9 (15+9) is 24.

Final Answer = 24.




Hope I could help!
Ossashi(◔ ͜ʖ◔)









7 0
3 years ago
Read 2 more answers
Which expression has an estimated product of 45?<br>44.7x2.1<br>7.5x84<br>8.7x5.28<br>38.1 x 7.3​
Anni [7]

Answer: 8.7 x 5.28

We have to find that expression , which has an estimated product of

1.→44.7 x 2.1

2.→7.5 x 8.4

3.→8.7 x 5.28

4.→38.1 x 7.3

We will start from option 1.

→44.7 x 2.1

44.7 when estimated to nearest tenth=45

2.1, when estimated to nearest tenth=2

44.7 × 2.1=45×2=90

Option 2

7.5 x 8.4

7.5 when estimated to nearest tenth=8

8.4, when estimated to nearest tenth=8

⇒7.5 × 8.4=8×8=64

Option 3

8.7 × 5.28

8.7, when estimated to nearest tenth=9

5.28, when estimated to nearest tenth=5

⇒8.7 × 5.28=9×5=45

Option D

38.1 × 7.3

38.1 when estimated to nearest tenth=38

7.3, when estimated to nearest tenth=7

⇒38×7=266

Option C:⇒8.7 × 5.28 has an estimated product of 45

6 0
3 years ago
Read 2 more answers
Other questions:
  • On a test, mean score was 70 and the standard deviation of the scores was 15.
    5·1 answer
  • Plz help me number 4 thanks
    12·1 answer
  • The graph of y = -3+4 is:
    6·1 answer
  • 5-6n=2n+5 <br>Solve for n
    12·2 answers
  • Let sin t = a​, cos t = b​, and tan t = c. Write the expression in terms of​ a, b, and c.
    14·1 answer
  • Describe how you can tell that a fraction is reapeating and not terminating
    13·1 answer
  • To what power must you raise the expression <br> 7<br> 1<br> 2<br> to get 7 as the result?
    5·1 answer
  • Please help i will give brainest to correct answer
    15·2 answers
  • Select the three problems below in which the solution would be a negative number.
    12·1 answer
  • At a local print shop, 18 copies can be made for $6. At this rate, how much would it
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!