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AlexFokin [52]
3 years ago
9

Express the function f(x) =3x^2-6x-18 in the form a(x + h)^2=k, where a, h and k are constants.Hence state the :

Mathematics
1 answer:
ololo11 [35]3 years ago
6 0

Answer:

The minimum value of f(x) is -21 and it occurs at x = 1

Step-by-step explanation:

f(x) =3x^2-6x-18

Factor out the greatest common factor out of the first two terms

f(x) =3(x^2-2x)-18

Complete the square

-2x/2 =-1  (-1)^2 = 1

Add 1  (But remember the 3 out front so we are really adding 3  so we need to subtract 3 to remain balanced)

f(x) = 3(x^2 -2x+1) -3 -18

f(x) = 3(x-1)^2 -21

This is vertex form

f(x) = a(x-h)^2 +k  where (h,k) is the vertex and a is a constant

The vertex is (1,-21)  

Since a > 0 this opens upward and the vertex is a minimum

The minimum value of f(x) is -21 and it occurs at x = 1

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Liula [17]
3/20 is the same as 15/100 or 15%
so 10×3/20 would be the same as 10×15% or 150%
Is that what you were asking?
6 0
3 years ago
Find the measure of the exterior angle.
PtichkaEL [24]

Answer:

1) 128°

2) 126°

3) 108°

<h2>Question one:</h2>

   The square in the corner means 90°. If you add the interior angles of any triangle together, you get 180. in this case, x is in exterior angle, so you subtract it from 180 to get the interior angle.  

38 + 90 + (180-x) = 180

38 + 90 + 180 - x = 180

38 + 90 + 180 - 180 - x = 0

38 + 90 + 180 - 180 = x

128 = x

<h2>Question two:</h2><h2></h2>

again, adding all the interior angles makes 180°. use this to make the equation.

3x + (5x-6) + 90 = 180

3x + 5x - 6 = 90

8x = 96

x = 12.

   x isn't the answer the question wants, however. if you look at the drawing, the angle that's supplementary to 5x-6 is the exterior angle. so,

180 - (5x-6) = the answer

180 - 5x + 6 = the answer

substitute x for 12

180 - 60 + 6 = the answer

126 = x

<h2>Question three</h2>

again, adding all the interior angles together makes 180°.

(a + 10) + 44 + (180-2a) = 180

a + 10 + 44 + 180 - 2a = 180

-a + 234 = 180

234 - 180 = a

54 = a

however, the question is looking for the exterior angle, not a. in this case, the exterior angle is 2a, so just multiply 54 by 2.

x = 108

8 0
3 years ago
Hugo drove 26 miles on
Sergio [31]

Answer:

70

Step-by-step explanation:

26 times 2 the plus 18 and you get 70 hope this helps

6 0
2 years ago
Read 2 more answers
There are two balance beams at the gym.one is 15 feet long ,theother is 162 inches long.which beam is longer?
Oduvanchick [21]
12 inches = 1 foot

Let x=length of 2nd balance beam in feet

by ratio and proportion

1/12 = x/162

multiply noth sides by 162 to isolate x

(1/12)(162) = (x/162)(162)

162/12 = x

13.5 = x

Source -->https://socratic.org/questions/at-the-gym-one-balance-beam-is-15-feet-long-while-the-other-is-162-in...<--

can you help me? brainly.com/question/3131429 
7 0
3 years ago
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In the figure, j | k and mZ2 = 117°<br> What is the mZ3?
DIA [1.3K]

Answer:

if angle 2 is 117 degrees, angle 3 is supplemental and would be 63 degrees.

180-117=63

4 0
3 years ago
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