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zavuch27 [327]
3 years ago
15

Rewrite the function by completing the square. h(x)= x^{2} +3 x -18 left parenthesis, x, right parenthesis, equals, x, squared,

plus, 3, x, minus, 18 h(x)=h(x)=h, left parenthesis, x, right parenthesis, equals (x+(x+left parenthesis, x, plus )^2+) 2 +right parenthesis, squared, plus
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
4 0

Answer:

  h(x) = (x +1.5)^2 -20.25

Step-by-step explanation:

We assume you want to rearrange h(x)= x^2 +3x -18.

Recognize the coefficient of x is 3. Add and subtract the square of half that. (3/2)^2 = 9/4 = 2.25

  h(x) = (x^2 +3x +2.25) -18 -2.25

Now, write the expression in parentheses as a square, simplify the constant.

  h(x) = (x +1.5)^2 -20.25 . . . . . . . . vertex form

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Graph the following lines and write the equation in slope-intercept form. Through the point (2,−4) with y-intercept of −2.
CaHeK987 [17]

For this case we have that by definition, the equation in the form of slope-intersection is given by:


y = mx + b

Where

  • m is the slope
  • b is the cut point

Substituting the given point: (x, y) = (2, -4) and the cutoff point b = -2 we can find the slope,


We have:


-4 = m * 2-2\\-4 = 2m-2\\-4 + 2 = 2m\\-2 = 2m

m =-\frac{2}{2}\\m = -1

Thus, the equation is given by:


y = -x-2

Answer:


y = -x-2

See attached image


3 0
3 years ago
Limit of x^2-81/x+9<br> As x goes toward -9
Semmy [17]
Hello,

Use the factoration

a^2 - b^2 = (a - b)(a + b)

Then,

x^2 - 81 = x^2 - 9^2

x^2 - 9^2 = ( x - 9).(x + 9)

Then,

Lim (x^2- 81) /(x+9)

= Lim (x -9)(x+9)/(x+9)

Simplity x + 9

Lim (x -9)

Now replace x = -9

Lim ( -9 -9)

Lim -18 = -18
_______________

The second method without using factorization would be to calculate the limit by the hospital rule.

Lim f(x)/g(x) = lim f(x)'/g(x)'

Where,

f(x)' and g(x)' are the derivates.

Let f(x) = x^2 -81

f(x)' = 2x + 0
f(x)' = 2x

Let g(x) = x +9

g(x)' = 1 + 0
g(x)' = 1

Then the Lim stay:

Lim (x^2 -81)/(x+9) = Lim 2x /1

Now replace x = -9

Lim 2×-9 = Lim -18

= -18




7 0
3 years ago
if ( in one month ) I make a total of 15 calls at standard hours, what is the difference in cost between the two contracts ? ans
Olenka [21]

Answer:

Voice over Internet Protocol (VoIP), also called IP telephony, is a method and group of technologies for the delivery of voice communications and multimedia sessions over Internet Protocol (IP) networks, such as the Internet. The terms Internet telephony, broadband telephony, and broadband phone service specifically refer to the provisioning of communications services (voice, fax, SMS, voice-messaging) over the Internet, rather than via the public switched telephone network (PSTN), also known as plain old telephone service (POTS).

5 0
3 years ago
283838383838382828 + 83838383888282ab
natta225 [31]

2.8392222e+17

Step-by-step explanation:

283838383838382828 + 83838383888282=2.8392222e+17

5 0
2 years ago
One day at football practice, Darrell, the kicker, punted the ball so that its height in feet above the ground was given by the
nika2105 [10]

When the football is 81 feet high, it will be √  3 / 8 seconds

<h3>Function</h3>

Function relates input to output. Therefore,

  • h(t)  = - 16t² + 75

Therefore,

t = number of seconds

h(t) = - 16t² + 75

h(t) = 81 ft

Therefore,

81 = - 16t² + 75

- 16t²  = 81 - 75

- 16t²  = 6

divide both sides by -16

t² = 6 / -16

t² = - 3 / 8

square root both sides

t = √  3 / 8 seconds

learn more on function here: brainly.com/question/4418459

6 0
2 years ago
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