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Ymorist [56]
3 years ago
13

Given that f(x) = x^2 - 4x +1, find the value of m if f(m) = -3

Mathematics
1 answer:
iragen [17]3 years ago
3 0

a. Answer:  m = 2

<u>Step-by-step explanation:</u>

f(x) = x² - 4x + 1

f(m) = m² - 4m + 1 = -3

         m² - 4m + 4 = 0

         (m - 2)(m - 2) = 0

               m = 2

***************************************************

b. Answer:  k = 2 and k = 5

<u>Step-by-step explanation:</u>

f(x) = x² - 7x + 14

f(k) = k² - 7k + 14 = 4

        k² - 7k + 10 = 0

        (k - 2)(k - 5) = 0

        k = 2   k = 5

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PLEASE HELP!! Algebra 2
lawyer [7]

Answer:

No

Edit:

Yes, based on original equation. (Credit to greenpumpkin for correction)

Step-by-step explanation:

For this problem, we simply need to find the values of x that can make the equation true.  So, let's begin by isolating the "x" variable.

sqrt(2x + 13) = x + 5

[sqrt(2x + 13)]^2 = (x + 5)^2

2x + 13 = x^2 + 10x + 25

0 = x^2 + 8x + 12

Note, we can remove the sqrt method by squaring both sides of the equation.  Doing this, we see we have a quadratic equation meaning we can apply the quadratic formula to find solutions for x.

[-b +/- sqrt( b^2 - 4(a)(c) ) ] / 2a

Let a = 1, b = 8, and c = 12

[-8 +/- sqrt( (8)^2 - 4(1)(12) ) ] / 2(1)

= [-8 +/- sqrt( 64 - 48 ) ] / 2

= [-8 +/- sqrt(16) ] / 2

= [ -8 +/- 4 ] / 2

So, x = [ -8 + 4 ] / 2  and x = [-8 - 4 ] / 2

x = [-4] / 2 = -2  and x = [-12] / 2 = -6

Hence, the two values of x that can solve this quadratic equation are x = -2 and x = -6.

Therefore, we know that x = -6 is not extraneous, meaning it is a solution to our equation.

Cheers.

----------------------------------------------------

Edit:

Plugging the value of -6 back into the original equation, we get the following:

sqrt(2x + 13) = x + 5

sqrt(2(-6) + 13) = (-6) + 5

sqrt (1) = -1

1 != -1

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8 0
3 years ago
joe and james are selling pies for a school fundraiser. Customers can buy blueberry pies and blackberry pies. Joe sold 5 blueber
dimulka [17.4K]
This is a system of equations problem.

Blueberry = X, blackberry = Y

Joe:
5x + 10y = 135

James:
x + 9y = 104

Let’s isolate x from James’ equation.
x = 104 - 9y

Now substitute that into the first equation.
5(104 - 9y) + 10y = 135

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y = -385/-35. The negatives cancel out, leaving us with $11 for blackberries.

Now we can substitute that value into James’s equation.

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Final answer: Blueberry pies cost $5, blackberry pies cost $11.
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Step-by-step explanation:

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