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densk [106]
3 years ago
11

If b2 + 2b − 24 = 0, and b < 0, what is the value of b?

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

Answer: b = -6, 4

Step-by-step explanation:

Convert into factored form :

(b+6)(b-4)

Then make one of the terms 0.

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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
Raul and Athena make bumper stickers. They know that their fixed costs are $145 and the cost of each bumper sticker is $2. Write
alexandr1967 [171]

Answer:

145 + 2c = X

Step-by-step explanation:

Fixed cost: 145

PLUS

2 dollars per bumper sticker (c)

After you write this out, you can put this as an actual equation.

8 0
2 years ago
Determine the linear factors. 18x3 − 34x2 + 16x
wlad13 [49]

Answer:

C

Step-by-step explanation:

5 0
3 years ago
Given f(x) = x^4 -3x^3 +10x^2 -9x +1. Is (x-2) a factor? Is x=-3 a zero? Find f(-1) show all work.
gizmo_the_mogwai [7]

Step-by-step explanation:

(x-2) is not a factor

x = -3 is not a zero

<h2>Please mark my answer as the brainliest for further answers :)</h2>

3 0
3 years ago
Matt and Ben are baking. Matt needs 5 5/6 cups of flour and Ben needs 3 1/3 cups of flour. How many cups of flour do Matt and Be
mario62 [17]
C is the answer be 5 5/6+3 1/3=9 1/6
7 0
3 years ago
Read 2 more answers
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