1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nataliya [291]
3 years ago
7

The height of water shooting from a fountain is modeled by the function f(x) = −4x2 + 24x − 29 where x is the distance from the

spout in feet. Complete the square to determine the maximum height of the path of the water.
−4(x − 3)2 − 29; The maximum height of the water is 3 feet.

−4(x − 3)2 − 29; The maximum height of the water is 29 feet.

−4(x − 3)2 + 7; The maximum height of the water is 7 feet.

−4(x − 3)2 + 7; The maximum height of the water is 3 feet.
Mathematics
2 answers:
kirza4 [7]3 years ago
8 0
Below is the solution:

f(x)=−4(x2−6x+9−9)−29

<span> (</span>x2−6x+9)=(x−3)(x−3)

f(x)=−4((x−3)2−9)−29

f(x)=−4(x−3)2−4(−9)−29

f(x)=−4(x−3)2+36−29

f(x=−4(x−3)2+7

f(x)=−4(x−3)2+7

That's the equation we got by completing the square.

y=a(x−h)2+k

That's the formula of a parabola in "vertex" form. Notice the similarity? The two are equal if we say

y=f(x)

a=−4

h=3

k=7


Therefore the answer is C, <span>−4(x − 3)2 + 7; The maximum height of the water is 7 feet.</span>


attashe74 [19]3 years ago
7 0

Answer:

Option 3 - y= -4(x-3)^2+7; The maximum height of the water is 7 feet.

Step-by-step explanation:

Given : The height of water shooting from a fountain is modeled by the function f(x) = -4x^2+24x-29 where x is the distance from the spout in feet.

To find : Complete the square to determine the maximum height of the path of the water.

Solution :

f(x) = -4x^2+24x-29

f(x) = -4(x^2-6x)-29

Completing the square by adding and subtracting (\frac{6}{2})^2=3^2=9 in the bracket,

f(x) = -4(x^2-6x+9-9)-29

f(x) = -4((x-3)^2-9)-29

f(x) = -4(x-3)^2+36-29

f(x) = -4(x-3)^2+7

The general vertex form is y=a(x-h)^2+k

On comparing,

a=−4, h=3, k=7

The maximum height of the water is given by y-intercept i.e. k,

The maximum height of the water is 7 feet.

Therefore, Option 3 is correct.

You might be interested in
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?
sertanlavr [38]

y = ( 48 *2 ) / 6

Step-by-step explanation:

If y varies directly as x they are directly proportional, which means they relate to each other in the same way....

2 : y = 6: 48

what is y if x = 2?

The value of y can be found if you write it a two fracrions

2 : y = 6 : 48

2 / y = 6 / 48

cross multiply the fractions gives

6*y = 48 *2

divide left and right of the = sign by 6 gives the answer:

y = ( 48 *2 ) / 6

(if you solve it you get y = 12 but that was not the question).

Other method:

multiply left and right of the = sign by y

2 * y/y = y *6 / 48

6y / 48 = 2 * 1

multiply left and right of the = sign by 48

6y * 48/48 = ( 48 *2 )

6y = ( 48 *2 )

divide left and right of the = sign by 6

6/6* y = ( 48 *2 )/6

y = ( 48 *2 ) / 6

(if you solve it you get y = 12 but that was not the question).

4 0
3 years ago
Write the equation of a line in standard form that has x-intercept (P,0) and y-intercept (0,R).
ExtremeBDS [4]

Answer:

Rx+Py=RP

Step-by-step explanation:

The points on the straight line are (P, 0) and (0, R).

The slope would be

m=\frac{R-0}{0-P}=-\frac{R}{P}

And b=R, because the y-intercept is at (0, R).

So, the equation of this line would be

y=-\frac{R}{P} x+R

Where we multiply the equation by P

Py=-Rx+RP

Therefore, the equation that represents this line is

Rx+Py=RP

<h2>So, the right answer is B.</h2>
7 0
2 years ago
WILL GIVE BRAINIEST What is the solution set to log(x+4) &lt; log6 x
Svetllana [295]

It is B.

the question is so tough

8 0
3 years ago
Perform the following calculation. Express your answer in scientific notation. (2×105) + (6×105) Write your answer in scientific
ZanzabumX [31]
Answer:

8.4x10^1
Thanks
7 0
3 years ago
Read 2 more answers
Aria paid $75,000 for her house. its property value increased by 2.2% per year. when aria sold her house after eleven years, how
Wewaii [24]

Answer:

D

Step-by-step explanation:

Converting percent to decimal : 2.2/100 = 0.022

Finding 2.2$ of $75k : 75,000 x 0.022 = $1,650 (also the increase in one year)

Finding how much it was worth after 11 years :

(75,000 x 0.022) x 11 = $18,150 or 1,650 x 11 = $18,150

Now add the product to the regular amount to find out the answer:

75,000 + 18,150 = $93,150 (which is how much it increased after 11 years)

3 0
2 years ago
Other questions:
  • What is the square root of 25/9?
    8·2 answers
  • Find S15 for the series -1 + -3 + -5 + -7 +...
    9·1 answer
  • 53.02 in expanded notation
    15·2 answers
  • 2) -84 = 6(4a – 2)<br> A) {2}<br> C) No solution.<br> B) {1}<br> D) -3)
    12·1 answer
  • Ted's class collects aluminum cans to sell to the recycling center. The center pays $0.002 for each kilogram of aluminum.Write a
    7·1 answer
  • Help Please I'm Out Of Time ;(
    6·1 answer
  • Helen Sanchez's checking account had a balance of $678.22. She wrote a check to pay her gasoline charge
    14·1 answer
  • Can someone pls help me ? I really need help
    7·1 answer
  • Please both the question please ​
    9·2 answers
  • If x=5 and y=2 workout the value of
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!