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cupoosta [38]
9 months ago
13

PLEASE HELP ME!!!!!!!!!

Mathematics
1 answer:
vitfil [10]9 months ago
8 0
<h2>1)</h2>

(x - 4) {}^{2}  - 28 = 8 \\ (x - 4) {}^{2}  = 8 + 28 \\ (x - 4) {}^{2}  = 36

This must be true for some value of x, since we have a quantity squared yielding a positive number, and since the equation is of second degree,there must exist 2 real roots.

\sqrt{(x - 4) {}^{2} }  =  ± \sqrt{36}  \\x - 4 = ±6 \\ x _{1}- 4 = 6 \:  \:  \:  \:  \:  \:  \: \:  \:  \:  x _{2}- 4 =  - 6 \\ x_{1} = 6 + 4 \:  \:  \:  \:  \:  \:  \:  \:  \:  \: x_{2} =  - 6 + 4 \\ x_{1} = 10 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \: \:  \: x_{2} =  - 2

<h2>2)</h2>

Well he started off correct to the point of completing the square.

(x - 3)  {}^{2}  = 16 \\ x - 3 = ±4 \\  \: x_{1}  - 3 = 4 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: x_{2}  - 3 =  - 4 \\ x_{1}  = 7 \:  \:  \:  \:  \:  \:  \:  \:  \:  \: x_{2}  =  - 1

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Step-by-step explanation:

x + 2\frac{1}{2} > - \frac{1}{2}      First turn 2\frac{1}{2} into an fraction since its easier. So it becomes \frac{5}{2}

x + \frac{5}{2} > - \frac{1}{2}

<u>   - </u>\frac{5}{2}<u>     - </u>\frac{5}{2}<u>  </u>       Do inverse operations, so subtract \frac{5}{2} from both sides.

    x > - \frac{6}{2}          Combine  - \frac{5}{2} with - \frac{1}{2}, which gives us - \frac{6}{2}

    x > - 3          Since we know that 6 divided by 2 is 3.

This would not allow me to attach an image so I am going to type a visual representation f what the graph would look like below)

<-------------O--------------------------------------------------->

-5    -4     -3      -2       -1     0     1     2    3    4     5

So, the number line would be a solid line rather than dashed (but I was not able to attach an image so I kind of had to improvise). When using ≥ ≤ sings the circle of the point is closed. When using < and > signs, the circle of the point is open. Thus, in this scenario since he sign is >, then the circle of the point is open. The direction of the arrow and ray for this equality is going to the right because the answer is that x is greater than - 3, Therefore any values greater than - 3 are a possibility which is why the arrow goes on indefinitely.

 

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