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Jobisdone [24]
1 year ago
11

Given that 2x³-5x² - 4x+8 = (Ax - 1)(x-B)(x + 1) + C for all values of x, find the

Mathematics
1 answer:
vfiekz [6]1 year ago
8 0

Answer:

A=2, B=3, C=5

Step-by-step explanation:

Two polynomials are equal for all values of the variable if the corresponding coefficients are the same. The way to solve the problem is to multiply the RHS, rewrite it in a more orderly way

(Ax-1)(x-B)(x+1)+C = \\Ax^3+(A-AB-1)x^2+(B-AB-1)x +B+C

Now, for the two polynomials to be the same we need to have, at the same time

x^3: A=2\\x^2: A-AB-1= -5\\x:B-AB-1=-4\\1: B+C=8

You might notice that we have more conditions than variables, but you can consider one of the two in the middle as a "check" option.

Now, grabbing the value from the first condition into the second we get B=3. Replacing both value in the third we see that the equality still holds, and replacing into the fourth we get C =5.

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PLEASE HELP ASAP
BaLLatris [955]

The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.

<h3>How to find the find the dilation factor</h3>

In this problem we have the following relationship bewteen the two <em>quadratic</em> equations: g(x) = f(k · x), which means that for all y the following relationship between f(x) and g(x):

k = \frac{x_{g}}{x_{f}}

Let suppose that y = 3, then x_{f} = - 5.5 and x_{g} = - 1.8, then the value k is:

k = (- 5.5)/(- 1.8)

k = 3.056

The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.

To learn more on transformations: brainly.com/question/11709244

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6 0
1 year ago
If f(x)=x and g(x)=2, what is (f o g)(x)?
IgorC [24]

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Step-by-step explanation:

6 0
2 years ago
Solving by elimination <br> 5x+2y= -3<br> 3x+3y=9<br> please help me solve x and y
-Dominant- [34]
1) -3(5x+2y=-3)⇒ -15x-6y=9
                                             ⇒ -9x=27
     2(3x+3y=9)⇒ 6x+6y=18

2) -9x/-9=27/-9 ⇒ x=-3 

3) 3(-3)+3y=9⇒ -9+9+3y=9+9⇒ 3y/3=18/3⇒ y=6

Answer: (-3,6)

Reasoning:
Step 1) In order to eliminate, first I had to multiple the first equation by -3 and the second by 2 so that when combining the equations y would cancel each other out so that I could solve for x. <em>Note: There are many combinations as to how you could multiple the equations so that either the x or y would cancel out.
</em>
Step 2) Once y is eliminated, solve for x.

Step 3) Now plug x back into one of the original equations and solve for y. <em>Note: Plug x back into one of the original equations, not the equations that were changed by multiplication,</em> 

6 0
3 years ago
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