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Andreyy89
3 years ago
11

Factor by completing the square 5x^2-21=10x

Mathematics
1 answer:
velikii [3]3 years ago
4 0
Solve for x over the real numbers:
5 x^2 - 21 = 10 x

Subtract 10 x from both sides:
5 x^2 - 10 x - 21 = 0

Divide both sides by 5:
x^2 - 2 x - 21/5 = 0

Add 21/5 to both sides:
x^2 - 2 x = 21/5

Add 1 to both sides:
x^2 - 2 x + 1 = 26/5

Write the left hand side as a square:
(x - 1)^2 = 26/5

Take the square root of both sides:
x - 1 = sqrt(26/5) or x - 1 = -sqrt(26/5)

Add 1 to both sides:
x = 1 + sqrt(26/5) or x - 1 = -sqrt(26/5)

Add 1 to both sides:
Answer:  x = 1 + sqrt(26/5) or x = 1 - sqrt(26/5)
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Find the HCF using prime factors of 36 and 54​
nataly862011 [7]

Answer:

18

Step-by-step explanation:

2x18 is 36 and 3x18 is 54

8 0
2 years ago
HELP with these questions
zlopas [31]

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

transform the parent graph of f(x) = ln x        into f(x) = - ln (x - 4)  by shifting the parent graph 4 units to the right and reflecting over the x-axis

(???, 0): 0 = - ln (x - 4)

            \frac{0}{-1} = \frac{-ln (x - 4)}{-1}

            0 = ln (x - 4)

            e^{0} = e^{ln (x - 4)}

             1 = x - 4

          <u> +4 </u>  <u>    +4 </u>

             5 = x

(5, 0)

(???, 1): 1 = - ln (x - 4)

            \frac{0}{-1} = \frac{-ln (x - 4)}{-1}

            1 = ln (x - 4)

            e^{1} = e^{ln (x - 4)}

             e = x - 4

          <u> +4 </u>   <u>    +4 </u>

         e + 4 = x

          6.72 = x

(6.72, 1)

Domain: x - 4 > 0

                <u>  +4 </u>  <u>+4  </u>

               x       > 4

(4, ∞)

Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that

No vertical asymptotes

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

transform the parent graph of f(x) = 3ˣ        into f(x) = - 3ˣ⁺⁵  by shifting the parent graph 5 units to the left and reflecting over the x-axis

Domain: there is no restriction on x so domain is all real number

(-∞, ∞)

Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0.  the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.

(-∞, 0)

Y-intercept is when x = 0:

f(x) = - 3ˣ⁺⁵

      = - 3⁰⁺⁵

      = - 3⁵

      = -243

Horizontal Asymptote: y = 0  <em>(explanation above)</em>

5 0
3 years ago
The function f(x) = x2 + 6x + 3 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).
garri49 [273]

Answer:

(-1,-6)

Step-by-step explanation:

f(x)=x^2+6x+3

g(x)=f(x-2)

g(x)=(x-2)^2+6(x-2)+3  (Replaced x in f with (x-2))

g(x)=x^2-4x+4+6x-12+3 (Used (x+b)^2=x^2+2bx+b^2 and distributive property)

g(x)=x^2-4x+6x+4-12+3 (Gathered like terms)

g(x)=x^2+2x-5  (Simplified)

The vertex of a parabola occurs at (\frac{-b}{2a},g(\frac{-b}{2a}).

Let's find \frac{-b}{2a} first.

\frac{-2}{2(1)}=-1

Now we can obtain g(\frac{-b}{2a}) which is g(-1) in this case:

g(x)=x^2+2x-5

g(-1)=(-1)^2+2(-1)-5

g(-1)=1-2-5

g(-1)=-1-5

g(-1)=-6.

The vertex is (-1,-6).

6 0
3 years ago
Solve n + 5(n - 1) = 7
Nina [5.8K]

Answer:

N = 2

Step-by-step explanation:

n + 5(n-1) = 7

n + 5n - 5 = 7

6n - 5 = 7

6n = 12

n = 2

HOPE THIS HELPS

PLZZ MARK BRAINLIEST!!!

7 0
3 years ago
Read 2 more answers
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
elena-14-01-66 [18.8K]

Answer:

yes

Step-by-step explanation:

I think sorry if I am wrong

8 0
2 years ago
Read 2 more answers
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