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marissa [1.9K]
3 years ago
9

A ray is a portion of a line that begins at a point and extends endlessly in one direction.

Mathematics
1 answer:
viva [34]3 years ago
4 0

Answer: T

Step-by-step explanation:

cuz i practice geometry.

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The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new functio
kap26 [50]

Answer:

The new function is (x + 7)² - 47 ⇒ the 3rd answer

Step-by-step explanation:

* Lets put the function f(x) in the vertex form at first and then make

 the translation

∵ The general form of the quadratic function is

  f(x) = ax² + bx + c

∵ The x-coordinate of the vertex of the function is -b/2a

∵ The y-coordinate of the vertex of the function is f(-b/2a)

- Lets find a , b from the function two find the vertex point

∵ f(x) = x² + 22x + 58

∴ a = 1 , b = 22 , c = 58

∵ x-coordinate of the vertex = -b/2a

∴ x-coordinate of the vertex = -22/2(1) = -11

∵ y-coordinate of the vertex = f(-11)

∴ f(-11) = (-11)² + 22(-11) + 58 = 121 - 242 + 58 = -63

∴ The vertex point is (-11 , -63)

- The vertex form of the quadratic function is f(x) = (x - h)² + k , where

  (h , k) are the coordinates of the vertex point

∵ The vertex point is (-11 , -63)

∴ h = -11 , k = -63

∴ f(x) = (x - -11)² + -63

∴ f(x) = (x + 11)² - 63

* lets revise the rules of the translation

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

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

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

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

- If the function f(x) translated vertically up  

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

- If the function f(x) translated vertically down  

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

∵ f(x) will translate 4 units to the right

∴ m = 4

∵ f(x) ⇒ f(x - m)

∴ (x + 11)²  ⇒ (x + 11 - 4)² = (x + 7)²

∵f(x) will translate 16 units up

∴ -63 will add by 16

∴ n = 16

∴ f(x) ⇒ f(x) + n

∵ -63 + 16 = -47

∴ The new function is (x + 7)² - 47

5 0
3 years ago
Read 2 more answers
What segment is congruent to AC?<br> A. BD<br> B. BE<br> C. CE<br> D. none
Phoenix [80]
You can find the segment congruent to AC by finding another segment with the same length. So first, you need to find the length of AC.

   C - A = AC
0 - (-6) = AC   Cancel out the double negative
  0 + 6 = AC
        6 = AC

Now, find another segment that also has a length of 6.

   D - B = BD
2 - (-2) = BD   Cancel out the double negative
  2 + 2 = BD
        4 = BD
        4 ≠ 6

   E - B = BE
4 - (-2) = BE   Cancel out the double negative
  4 + 2 = BE 
        6 = BE
        6 = 6

So, the segment congruent to AC is B. BE . 
8 0
3 years ago
Help with this algebra problem? 12y+6=6y+12?
Anika [276]
First, combine like terms.
12y+6=6y+12 turns into
12y-6y=12-6, which is
6y=6. Now divide both sides by 6.
y=1

now do a quick check (cause that's always a good idea).
12(1)+6=6(1)+12
12+6=6+12
18=18  ; )
7 0
3 years ago
Help!! PLEASE ANSWER ASAP. Please provide why the statement is wrong and give an example!! Math
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1. false because the GCF of 101 and 102 is 1 whereas the GCF of 33 and 99 is 33.

2. idk

3. false because the GCF of 1 and 2 is 1
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What is the volume of the truck bed which is
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Answer:

120 ft cubed

Step-by-step explanation:

V=lwh

V=10(4)(3)

V=120 ft cubed

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