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3 years ago

Rewrite the equation by completing the square. x^2+10x+24 = 0

Mathematics

1 answer:

ser-zykov [4K]3 years ago

3 0

Answer:

(x+5)^2 = 1

Step-by-step explanation:

x^2+10x+24 = 0

Subtract 24 from each side

x^2+10x+24 -24 = 0-24

x^2+10x = -24

Take the coefficient of x

Divide by 2

10/2 =5

Square it

5^2 = 25

Add it to each side

x^2+10x+25 = -24+25

Take the coefficient divided by 2 inside the factor

(x+10/2) ^2 = -24+25

(x+5)^2 = 1

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3 years ago

Find the maximum value or minimum value for the function f(x) = 0.15(x + 1)² - 3.

il63 [147K]

Answer:

The minimum value for $f(x) = 0.15(x + 1)^2 - 3$ is $-3$ .

Step-by-step explanation:

Given function is $f(x) = 0.15(x + 1)^2 - 3$

We need to find the maximum value or the minimum value for the function.

Now, differentiate $f(x) = 0.15(x + 1)^2 - 3$ w.r.t $x$ .

$f'(x) =\frac{d}{dx}(0.15(x + 1)^2 - 3)\\f'(x)=\frac{d}{dx}(0.15(x+1)^2-\frac{d}{dx}(3)\\$

$f'(x)=2\times 0.15(x+1)\frac{d}{dx}(x+1)-0\\f'(x)=0.3(x+1)(1)\\f'(x)=0.3(x+1)$

Now, we will equate $f'(x)=0$ to find critical point.

$0.3(x+1)=0\\x=-1$

Plug this critical point in to the function $f(x) = 0.15(x + 1)^2 - 3$ we get,

$f(-1) = 0.15(-1 + 1)^2 - 3\\f(-1)=-3$

Also, $f''(x)=0.3$ which is positive, We have minimum value.

So, the minimum value for $f(x) = 0.15(x + 1)^2 - 3$ is $-3$ .

7 0

3 years ago

F(x) =x^2+6x and g(x)=7-x find (f-g)(x) and (f-g)(9)

liq [111]

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(f-g)(9) = 81 + 63 - 7
(f-g)(9) = 137

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alexandr1967 [171]

Answer:

Step-by-step explanation: see attachment

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liraira [26]

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