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Llana [10]
3 years ago
10

An architect is sketching a blueprint of a patio for a new fence. On the blueprint, C is the midpoint of segment AD. Point B is

the midpoint of segment AC. If BC = 8 feet, what is the length of AD?
Mathematics
1 answer:
Slav-nsk [51]3 years ago
3 0

The length of AD is 32 feet

Step-by-step explanation:

An architect is sketching a blueprint of a patio for a new fence

  • On the blueprint, C is the midpoint of segment AD
  • Point B is the midpoint of segment AC
  • BC = 8 feet

We need to find the length of AD

A mid-point divides a line segments into two equal parts in length

∵ C is the mid-point of AD

- The mid-point C divides the line segments AD into two equal parts

∴ AC = CD

∵ B is the mid point of AC

∴ AB = BC

∵ BC = 8 feet

∴ AB = 8 feet

- AC contains AB and BC

∵ AC = AB + BC

∴ AC = 8 + 8 = 16

∵ AC = CD

∵ AC = 16

∴ CD = 16

- AD contains AC and CD

∵ AD = AC + CD

∴ AD = 16 + 16 = 32

The length of AD is 32 feet

Learn more:

You can learn more about the mid-point in brainly.com/question/3269852

#LearnwithBrainly

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Answer:

# The transformation of f(x) to be g(x) is

- Reflected across the x-axis

- Translated 7 units to the left

- Translated 6 units up

# The transformation of f(x) to be g(x) is

- Reflected across the y-axis

- Translated 7 units down

Step-by-step explanation:

* Lets revise some transformation rules

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Lets solve the problems

# f(x) = 2^x ⇒ g(x) = -(2)^(x + 7) + 6

- There is a -ve sign in-front of the 2

∵ f(x) will be -f(x)

∴ f(x) will reflect across the x-axis ⇒ (1)

- The power x becomes x + 7

∵ -f(x) will be -f(x + 7)

∴ -f(x) will translate 7 units to the left ⇒ (2)

- after that -f(x + 7) add by 6

∴ -f(x + 7) will translate 6 units up ⇒ (3)

- From (1) , (2) , (3)

∴ The transformation of f(x) to be g(x) is

- Reflected across the x-axis

- Translated 7 units to the left

- Translated 6 units up

# f(x) = ㏒(x) ⇒ g(x) = ㏒(-x) - 7

- The (x) will be (-x)

∵ f(x) will be f(-x)

∴ f(x) will reflect across the y-axis ⇒ (1)

- after that f(-x) subtracted by 7

∴ f(-x) will translate 7 units down ⇒ (2)

- From (1) , (2)

∴ The transformation of f(x) to be g(x) is

- Reflected across the y-axis

- Translated 7 units down

* For more understand look to the attached graphs

# First function:

- f(x) is the red

- g(x) is the blue

# Second function:

- f(x) is the black

- g(x) is the green

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