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3 years ago

Katie solved the equation by completing the square.

1 answer:

7 0

Katie has equation $x^2+12x-7=0$ and wants to solve it completing the perfect square. In order to do it, first rewrite 7 in right side:

$x^2+12x=7.$

Then note that $12x=2\cdot 6\cdot x,$ so Katie has to add $6^2=36$ to both sides (because $x^2+12x+36=x^2+2\cdot 6\cdot x+6^2=(x+6)^2$ ):

$x^2+12x+36=7+36,\\ \\(x+6)^2=43.$

Answer: correct choice is C.

You might be interested in

A submarine descends at a rate of 2.6 kilometers per hour. If the ocean floor is 6.24 kilometers below sea level, how long will

navik [9.2K]

Answer

Find out the how long will it take the submarine to descend to the ocean floor

To proof

Formula

$r = \frac{d}{t}$

where d = distance traveled (or descended),

r = rate of travel , t = time

As given

A submarine descends at a rate of 2.6 kilometers per hour. If the ocean floor is 6.24 kilometers below sea level .

put all the values in the above formula

$2.6 = \frac{6.24}{t}$

$t = \frac{6.24}{2.6}$

t = 2.4 hour

it take 2.4 hours the submarine to descend to the ocean floor .

Hence proved

8 0

3 years ago

Max lost 128 pounds in 16 weeks on his new weight-loss plan. What was his average change in weight per week?

Alex

Answer:

8 pounds per week

Step-by-step explanation:

AVG= total/time span

AVG= 128/16

AVG= 8 pounds per week

Hope this helps!

7 0

2 years ago

I will mark brainlest

vodka [1.7K]

20 Square units jit. now give me brainliest.

3 0

2 years ago

Exponential functions

Rainbow [258]

Answer:

An exponential function is a Mathematical function in form f (x) = ax.

 $f(x) = ax$ 

Step-by-step explanation:

 where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

NoTe: The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

if u need any help, just tell me know

6 0

2 years ago

Find the roots of:

Elena-2011 [213]

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

| 2 -7 8 -3

1 | 2 -5 3

| 2 -5 3 0

1 | 2 -3

2 -3 0

So the factorization is (x-1)² (2x-3)=0. So:

$\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

| 1 -1 0 -4

2 | 2 2

1 2 2 0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

$\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

| 6 7 9 2

-2 | -12 10 -2

6 -5 1 0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

$\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}$

$\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}$

6 0

2 years ago