PLLSS HELP ME ty :)))

Detmermine the best method to solve the following equation, then solve the equation. (3x-5)^2=-125

liq [111]

For the given equation;

$(3x-5)^2=-125$

We shall begin by expanding the parenthesis on the left side, after which we would combine all terms on and move all of them to the left side, which shall yield a quadratic equation. Then we shall solve.

Let us begin by expanding the parenthesis;

$\begin{gathered} (3x-5)^2\Rightarrow(3x-5)(3x-5) \\ (3x-5)(3x-5)=9x^2-15x-15x+25 \\ (3x-5)^2=9x^2-30x+25 \end{gathered}$

Now that we have expanded the left side of the equation, we would have;

$\begin{gathered} 9x^2-30x+25=-125 \\ \text{Add 125 to both sides and we'll have;} \\ 9x^2-30x+25+125=-125+125 \\ 9x^2-30x+150=0 \end{gathered}$

We shall now solve the resulting quadratic equation using the quadratic formula as follows;

$\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Where;} \\ a=9,b=-30,c=150 \\ x=\frac{-(-30)\pm\sqrt[]{(-30)^2-4(9)(150)}}{2(9)} \\ x=\frac{30\pm\sqrt[]{900-5400}}{18} \\ x=\frac{30\pm\sqrt[]{-4500}}{18} \\ x=\frac{30\pm\sqrt[]{-900\times5}}{18} \\ x=\frac{30\pm\sqrt[]{-900}\times\sqrt[]{5}}{18} \\ x=\frac{30\pm30i\sqrt[]{5}}{18} \\ \text{Therefore;} \\ x=\frac{30+30i\sqrt[]{5}}{18},x=\frac{30-30i\sqrt[]{5}}{18} \\ \text{Divide all through by 6, and we'll have;} \\ x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3} \end{gathered}$

ANSWER:

$x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3}$

3 0

10 months ago

Are these rates equivalent, 96 words typed for 3 minutes; 160 words typed for 5 minutes

monitta

<h2>Greetings</h2>

Answer:

Yes, they are.

Step-by-step explanation:

Lets simplify both rates to the rate typer per minute.

(m is minutes)

3m = 96

Divide both sides by 3:

$\frac{3m}{3} = \frac{96}{3}$

m = 32

So the rate is 32 words per minute.

5m = 160

Divide both sides by 5:

$\frac{5m}{5} = \frac{160}{5}$

m = 32

<h3>So because the rates per minute are the same, they are equivalent.</h3>
<h2>Hope this helps!</h2>

3 0

2 years ago

What is the gcf to 36 k and 144km

leonid [27]

The GCF is 36 since 36 can go into 144 (:
x

7 0

2 years ago

Read 2 more answers

Write the number of measures (sides/angles/diagonals) needed to construct the following :

gladu [14]

Square :4 sides,each side 90 degrees ..

:each angle is 90 degrees

: 4 diagonals

Rectangle: 4 sides..4 angles..2 diagonals..
Rhombus : 4 sides..2 angles...2 diagonals..
Parallelogram : 4 sides..4 angles..2 diagonals..
Quadrilateral: 4 sides...4 angles...4 diagonals..

If this answer helps you plz mark as brainlist..

3 0

2 years ago

What is the missing value in the equation shown □ x1/10=0.034

grin007 [14]

Answer:

0.34

Step-by-step explanation:

Do the inverse operation so;

0.034 / 1/10 = 0.34

Now go back and subsitute,

0.34 * 1/10 = 0.034

4 0

3 years ago