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Likurg_2 [28]
2 years ago
7

(x+16)²=12 plz help me and show work

Mathematics
1 answer:
Readme [11.4K]2 years ago
6 0

Answer:

The answer is x=-16 ±2\sqrt{3} in exact form or x=-12.535898, x=-19.464102 in decimal form.

Step-by-step explanation:

To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring x+16, which will look like x^{2} +32x+256-12=0. Next, simplify the equation again, which will look like x^{2} +32x+244=0.

Then, use the quadratic formula to find the solutions. The quadratic formula looks like\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}.

For this problem, the quadratic variables are as follows:

a=1

b=32

c=244

The next step is to substitute the values a=1, b=32, and c=244 into the quadratic formula and solve. The quadratic formula will look like \frac{-32(+-)\sqrt{32^2-4(1*244)} }{2*1}. To simplify the equation, start by simplifying the numerator, which will look like x=\frac{-32(+-)4\sqrt{3} }{2*1}. Then, multiply 2 by 1 and simplify the equation, which will look like x=-16(+-)2\sqrt{3}. The final answer is x=-16 ±2\sqrt{3} in exact form. In decimal form, the final answer is x=-12.535898, x=-19.464102.  

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A beacon is flashing on top of a 50 foot tower. A 6 foot tall man walks constantly away from the tower at 5 feet/sec. At the ins
Viefleur [7K]

Answer:\frac{253}{44}

Step-by-step explanation:

ignore the "at the instant the man is 30 feet away" part, set it as X and the man's shadow as Y.

Similar triangles so we can do \frac{50}{x+y}  = \frac{6}{y}.

Solve for it we get 44y = 6x

Differentiate relative to time t, we get 44y' = 6x'.

change in x (x') is equal to 5. And we get the answer y' = \frac{33}{44}.

the \frac{33}{44} ft/sec is the rate of which the length of the shadow is changing. add 5 to it for the rate of the tip of his shadow moving away from the tower.

7 0
2 years ago
5x -10x- 30= 10x solve for x
Andru [333]

Answer:

x=-2

Step-by-step explanation:

5x -10x- 30= 10x

-5x -30 = 10x

-30=15x

x=-2

8 0
3 years ago
Read 2 more answers
A child is hopping along a sidewalk. The ratio table below shows the comparison between the number of hops and the distance trav
natima [27]
First we rewrite the table:
 20    30
 50    75
 80    120
 150   ?
 We observe that for each 30 number of hops, the distance increases by 45 feet.
 We must find the slope of the line:
 m = (y2-y1) / (x2-x1)
 m = (75-30) / (50-20)
 m = 1.5
 Then, the line is:
 y = 1.5x
 We substitute x = 150
 y = 1.5 * (150)
 y = 225
 Answer:
 
Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.
3 0
3 years ago
Read 2 more answers
Two sides of a triangle are equal in length and double the length of the shortest side. The perimeter of the triangle is 36 inch
chubhunter [2.5K]

Answer:

Two equal sides = 14.4 inches each

Shortest side = 7.2 inches

Step-by-step explanation:

a + b + c = 36

a = b

a = 2c

then:

c = a/2

a + a + a/2 = 36

2a + a/2 = 36

4a/2 + a/2 = 36

5a/2 = 36

a = 2*36/5

a = 72/5

a = 14.4

a = 2c

14.4 = 2*c

c = 14.4/2

c = 7.2

a = b

b = 14.4

Check:

14.4 + 14.4 + 7.2 = 36

3 0
3 years ago
1. What number, when substituted for x in the following problem, will make the problem true?
riadik2000 [5.3K]

Answer:

x = 17.82

Step-by-step explanation:

6x + 8% = 107    

      -8%    -8%

or

107 - 0.08 = 106.92

-----------------------------------

6x = 106.92

÷6      ÷6

x = 17.82

------------------------------------

I hope this helps!

8 0
2 years ago
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