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
Oxana [17]
3 years ago
15

4) The line -3x + 4y = 8 is transformed by a dilation centered at the origin. Which linear equation could represent its image?

Mathematics
1 answer:
Dimas [21]3 years ago
3 0

Answer:

4) The linear equation which could represent its image is y = \frac{3}{4} x + 8 ⇒ (2)

5) The equation of the image of the line is y = \frac{3}{2} x - 3 ⇒ (4)

Step-by-step explanation:

Dilation does not change the slope of a line but changes the y-intercept

Dilation of a line segment is longer or shorter by ratio that equal to the scale factor of dilation

4)

The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b its y-intercept

Let us put the given equation in the slope-intercept form to find its slope

∵ The line -3x + 4y = 8 is transformed by a dilation centered at

   the origin

- Add 3x to both sides

∴ 4y = 3x + 8

- Divide both sides by 4

∴ y = \frac{3}{4} x + 2 ⇒ the equation of the line before dilation

- By comparing it with the form above, then m =  \frac{3}{4} , so the

   equation after dilation has the same slope

∵ The slope of the line before dilation is  \frac{3}{4}

∴ The slope of the line after dilation is  \frac{3}{4}

∵ The equation that has the slope  \frac{3}{4}  is y =

∴ The equation of the image of the line is y = \frac{3}{4} x + 8

The linear equation which could represent its image is y = \frac{3}{4} x + 8

5)

∵ The equation of the line is y = \frac{3}{2} x - 4

∵ The scale factor of dilation is \frac{3}{4}

- Dilation dose not change the slope of the line

∴ The slope of the image after dilation is \frac{3}{2}

- Dilation changes the y-intercept, to find it multiply the scale

  factor of dilation by the y-intercept of the line before dilation

∵ The y-intercept of the line is (0 , -4)

- Multiply it by \frac{3}{4}

∵  \frac{3}{4} × -4 = -3

∴ The y-intercept of the image is (0 , -3)

∴ The equation of the image of the line is y = \frac{3}{2} x - 3

You might be interested in
Find the length of the arc.
Bezzdna [24]

Answer:

18.84 ft

Step-by-step explanation:

¼×2×3.14×12 = 18.84 ft

5 0
3 years ago
Read 2 more answers
I need to know how to solve this question please help!
lorasvet [3.4K]

Answer:

-3

Step-by-step explanation:

log7 (1/343)

log7(7^-3)

-3

3 0
3 years ago
Based on FAA estimates the average age of the fleets of the 10 largest U.S. commercial passenger carriers is 13.4 years with a s
Aliun [14]

Answer : 0.0129

Step-by-step explanation:

Given : Based on FAA estimates the average age of the fleets of the 10 largest U.S. commercial passenger carriers is \mu=13.4 years and standard deviation is \sigma=1.7 years.

Sample size : n=40

Let X be the random variable that represents the age of fleets.

We assume that the ages of the fleets of the 10 largest U.S. commercial passenger carriers are normally distributed.

For z-score,

z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}

For x=14

z=\dfrac{14-13.4}{\dfrac{1.7}{\sqrt{40}}}\approx2.23

By using the standard normal distribution table , the probability that the average age of these 40 airplanes is at least 14 years old will be :-

P(x\geq 14)=P(z\geq2.23)\\\\=1-P(z

Hence, the required probability = 0.0129

6 0
3 years ago
Can someone please help me with this math problem
IrinaK [193]

Answer:

y = 10x + 7

Step-by-step explanation:

5 0
2 years ago
Given the table of candy distributions below, find P(Not orange), the probability of selecting anything but an orange candy at r
patriot [66]
The probability to pick anything other then orange is 0.86
6 0
3 years ago
Read 2 more answers
Other questions:
  • The sum of twice a number and five is greater than three times the number minus three
    10·1 answer
  • An electrical pole breaks at a height of 6m from its base due to a thunderstorm. Its top touches the ground at a distance of 8m
    5·1 answer
  • Rewrite it as a function and isolate Y. ​
    14·1 answer
  • Test the claim that the mean GPA of Orange Coast students is smaller than the mean GPA of Coastline students at the 0.005 signif
    7·1 answer
  • I will mark brainliest!!
    8·1 answer
  • The table shows the proportional relationship between the number of hours biked,t, and the miles traveled,d create an equation u
    7·2 answers
  • Use the graph to find the slope.
    9·1 answer
  • Mhanifa Please help find angle 1,2,3,4 and 5 thanks!
    12·2 answers
  • I NEED HELP PLEASE ITS A SOLVE FOR X PROBLEM :(
    5·1 answer
  • A = h/b =, solve for b
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!