1st Step: 3 - 4x - 7 = -24<br> 2nd Step: 3- 7 - 4x = -24<br> What property justifies the 2nd step

Solve the equation <img src="https://tex.z-dn.net/?f=8x%5E2%3D-36" id="TexFormula1" title="8x^2=-36" alt="8x^2=-36" align="absmi

chubhunter [2.5K]

Answer: 4(2x²+9) or $i\frac{3\sqrt{2} }{2}$

Step-by-step explanation:

To solve the equation by factoring, we want to set the equation to zero. In order to have the equation equal to zero, we want to add both sides by 36.

8x²=-36 [add both sides by 36]

8x²+36=0

When it comes to factoring, we want to pull out numbers or variables that are common in each term.

8x²+36=0 [take out a 4 in each term]

4(2x²+9)=0

It may seem that 2x²+9 can be factored further, it actually can't. This tells us that the factored form of the equation is 4(2x²+9)=0.

To solve the equation, we want to find the value of x. We already know the graph does not cross the x-axis because the y-intercept or vertex is (0,9).

4(2x²+9)=0 [divide both sides by 4]

2x²+9=0 [subtract both sides by 9]

2x²=-9 [divide both sides by 2]

x²=-9/2 [square root both sides]

$x=\sqrt{-\frac{9}{2} }$ or $x=i\frac{3\sqrt{2} }{2}$

6 0

3 years ago

Read 2 more answers

Simplify

melomori [17]

Answer: $4\sqrt{3}$

Step-by-step explanation:

For this exercise it is important to remember the following:

$i=\sqrt{-1} \\\\i^2=-1$

Given the following expression:

$-2i\sqrt{-12}$

You can notice that the radicand (the number inside the square root) is negative. Therefore, in order to simplify the expression, you need to follow these steps:

1. Replace $\sqrt{-1}$ with $i$ and simplify:

$(-2i)(i)\sqrt{12}=-2i^2\sqrt{12}=-2(-1)\sqrt{12}=2\sqrt{12}$

2. Descompose 12 into its prime factors:

$12=2*2*3=2^2*3$

3. Substitute into the expression:

$=2\sqrt{2^2*3}$

4. Since $\sqrt[n]{a^n}=a$ , you can simplify it:

$=(2)(2)\sqrt{3}=4\sqrt{3}$

4 0

2 years ago

If I bought shoes for 32.30 with 15% off 7%sales tax a 25dollar gift card but had a coupon that was forgotten for 5%off the orig

Otrada [13]

Answer:

$4.37 cash outlay

$29.37 total amount paid, partly with gift card

Step-by-step explanation:

The discount was ...

0.15 × $32.30 = $4.845 ≈ $4.85

So the price to which tax is added is ...

$32.30 -4.85 = $27.45

The amount of tax is 7% of this value, or ...

tax = $27.45 × 0.07 = $1.9215 ≈ $1.92

So, payment is made on the amount ...

$27.45 + 1.92 = $29.37

$29.37 is the total amount paid.

If $25 is paid using a gift card, then the cash outlay is $4.37.

_____

Usually only a single coupon can be applied to a given purchase. Since the 15% store discount exceeds the amount of the 5% coupon left at home, it makes more sense to claim the 15% store discount and save the 5% coupon for another time.

__

<em>Alternate interpretation</em>

If, by some magic, both discounts could be applied, then the amount to be paid is $27.65, of which $2.65 exceeds the gift card amount. The calculation proceeds the same way, except that 20% is used instead of 15%.

4 0

3 years ago

Is n^2+50n+25 a perfect square

elixir [45]

Answer:

yes

Step-by-step explanation:

5 0

2 years ago

What is an explicit formula for the following sequence 1,5,9,13,17 ? plssss helppp mee

morpeh [17]

Answer:

plus 4 every time

Step-by-step explanation:

1+4=5+4=9+4=13+4=17

7 0

3 years ago

1st Step: 3 - 4x - 7 = -24 2nd Step: 3- 7 - 4x = -24 What property justifies the 2nd step