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Olin [163]
3 years ago
14

Use completing the square to solve (x-12)(x+4)=9 for x

Mathematics
2 answers:
Kay [80]3 years ago
6 0
X= 4 + \sqrt{73}

x= 4 - \sqrt{73}
cestrela7 [59]3 years ago
6 0

we have

(x-12)(x+4)=9\\ x^{2} +4x-12x-48=9\\ x^{2} -8x-48=9

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2} -8x=9+48\\ x^{2} -8x=57

Complete the square. Remember to balance the equation by adding the same constants to each side

x^{2} -8x+16=57+16\\ x^{2} -8x+16=73

Rewrite as perfect squares

x^{2} -8x+16=73\\ (x-4)^{2} =73\\ (x-4)=(+/-)\sqrt{73}

x1=4+\sqrt{73} \\ x2=4-\sqrt{73}

therefore

the answer is

x1=4+\sqrt{73} \\ x2=4-\sqrt{73}



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If T(x, y) = (x + 5, y + 6) and Pris the image of P, what is the rule for the translation in which P is the image of P'? T(x, y)
xxTIMURxx [149]

Answer:

The translation is;

T(x,y)=(x-5,y-6)

Explanation:

Given the translation rule;

T(x,y)=(x+5,y+6)

when P' is the image of P.

For the inverse, when P is the image of P', the Translation rule would become;

\begin{gathered} x=x^{\prime}+5 \\ x^{\prime}=x-5 \\ y=y^{\prime}+6 \\ y^{\prime}=y-6 \\ So,\text{ the translation rule becomes;} \\ T(x,y)=(x-5,y-6) \end{gathered}

The translation is;

T(x,y)=(x-5,y-6)

3 0
1 year ago
A General Motors buyer-incentive program offered a 5.5% rebate on the selling price of a new car. What rebate (in dollars) would
Mashcka [7]

Answer: he would receive a rebate of $1677.5

Step-by-step explanation:

A General Motors buyer-incentive program offered a 5.5% rebate on the selling price of a new car. This means that if the selling price of the new car is $x, the rebate (in dollars) that a customer would receive is

5.5/100 × x = 0.055 × x = 0.055x

Therefore, for a customer who purchased a $30,500 car under this program, the rebate that he would receive is

0.055 × 30500 = $1677.5

6 0
3 years ago
there is a direct path from gayle's house to the store. due to construction, the direct route is closed and gayle must travel 6
NikAS [45]

Answer:

c2=10

Step-by-step explanation:

8^2+6^2=c2

64+36=120

c2=square root of 120..which is 10

4 0
3 years ago
Read 2 more answers
In this lesson, you learned new formulas to find the area of a triangle. How are these formulas different from the commonly know
Yuki888 [10]
Aside from the conventional formula for triangle, A=<span>½bh which is only applicable to problems where the base and height are already given and the triangle is a right triangle having a degree of 90. There are some formulas in getting the area of a triangle:

>Given three sides of the triangle, use Heron's Formula
A= sqrt(s(s-a)(s-b)(s-c))
s= (a+b+c)/2
>Given two sides with an included angle
</span>Area = <span>1/2 </span><span>ab sin (tetha)
</span><span>tethat should be in degrees



</span>
3 0
4 years ago
Translate each phrase and select the one that is DIFFERENT from the others. two more than a number, n the total of n and 2 twice
tensa zangetsu [6.8K]

Answer:

Option C.

Step-by-step explanation:

We need to translate each phrase and find the different expression.

"+" sign is used for sum, more and total.

Twice means two times of a number.

Let n be the unknown number.

Two more than a number = n+2

The total of n and 2 = n+2

Twice the number n = 2n

Sum of n and 2 = n+2

From the above expressions it is clear that only 2n is different from other.

Therefore, the correct option is C.

7 0
3 years ago
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