$\displaystyle x^2 - 8x + 41 = 0 \\\\ \Delta=b^2-4ac \\ \Delta=(-8)^2-4\cdot1\cdot41 \\ \Delta=64-164 \\ \Delta=-100 \\ \\ X_{1,2}= \frac{-b\pm i \sqrt{-\Delta} }{2a} = \frac{8 \pm 10i}{2} \\ \\ X1=4-5i \\ \\ X2=4+5i$

5 0

3 years ago

Given: ⅓ (18x + 27) = 81 Prove: x = 12

sasho [114]

Answer:

Firstly, rewrite the equation:

⅓ (18 + 27) = 81

Substitute x for the given number of it's supposed equivalent.

In this case x = 12.

⅓ (18(12) + 27) = 81

Solve using PEMDAS and simplify what is in the parenthesis first. Then, multiply.

(18 x 12) + 27 = 243

Now, solving using PEMDAS, multiply the total of what you got that was originally in the parenthesis by ⅓ .

⅓ (243) = 81

When you multiple these number they are equivalent to 81.

81 = 81

Since the equation given, when substituted x for 12, is equivalent to 81, this proves that substituting x for 12 makes this equation true.

4 0

3 years ago

Solve -5 + w divided by 3 = -1. 12 -12 2 -2

son4ous [18]

Hello!

Answer:

w=12

*The answer must have a positive sign.*

Step-by-step explanation:

First, you add by 5 from both sides of an equation.

$-5+\frac{w}{3}+5=-1+5$

Then, you simplify.

$\frac{w}{3}=4$

Next, you multiply by 3 from both sides of an equation.

$\frac{3w}{3}=4*3$

And finally, simplify and solve. You can also multiply by the numbers from left too right.

$4*3=12$

Final answer: → $w=12$

Hope this helps!

Thanks!

-Charlie

Have a great day!

3 0

3 years ago