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
mote1985 [20]
3 years ago
14

The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 12 feet, represented by a v

ertex of (8,12)​ , and lands 16 feet from the water jet, represented by (16,0)​ . Write a function in vertex form that models the path of the stream
Mathematics
2 answers:
tia_tia [17]3 years ago
8 0

Answer:

y=-3/16(x-8)^2+12

Step-by-step explanation:

Refer to the vertex form equation for a parabola:

y=a(x-h)^2+k where (h,k) is the vertex.

Therefore, we have y=a(x-8)^2+12 as our equation so far. If we plug in (16,0) we can find a:

0=a(16-8)^2+12

0=64a+12

-12=64a

-12/64=a

-3/16=a

Therefore, your final equation is y=-3/16(x-8)^2+12

Stels [109]3 years ago
7 0

Answer:

y = (-5.33)(x - 8)^2 + 12

Step-by-step explanation:

The graph is a parabola which opens down and has its vertex at (8, 12).  We can immediately write y = a(x - 8)^2 + 12, knowing that if x = 8, y = 12.  To find the coefficient '1', substitute 16 for x and 0 for y:

0 = a(16 - 8)^2 + 12, or

-64a = 12, or a = -64/12 = 5.33

Then the desired function is:

y = (-5.33)(x - 8)^2 + 12

You might be interested in
Find all solutions to the equation.<br><br> 7 sin2x - 14 sin x + 2 = -5
cestrela7 [59]

\bf 7sin^2(x)-14sin(x)+2=-5\implies 7sin^2(x)-14sin(x)+7=0 \\\\\\ \stackrel{\textit{notice, this is just }ax^2+bx+c}{\stackrel{\stackrel{ax^2}{\downarrow }}{sin^2(x)}\stackrel{\stackrel{bx}{\downarrow }}{-2sin(x)}\stackrel{\stackrel{c}{\downarrow }}{+1}}=0\implies [sin(x)-1][sin(x)-1]=0 \\\\\\ sin(x)-1=0\implies sin(x)=1\implies \measuredangle x=sin^{-1}(1)\implies \measuredangle x=\cfrac{\pi }{2} \\\\\\ ~~~~~~~~~~~~~~\stackrel{\textit{and for all solutions using }n \in \mathbb{Z}}{\cfrac{\pi }{2}+2\pi n}

7 0
4 years ago
Read 2 more answers
Can someone help me with this ASAP
Vika [28.1K]

Answer:

1.4 is the slope

Step-by-step explanation:

comment if you want me to explain

3 0
3 years ago
How to factor the trinomial 3 x^{2} + 8 -3
IgorLugansk [536]
3x² + 8x - 3 = (3x - 1) (x + 3)
6 0
3 years ago
6. Triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form
joja [24]

Given:

Consider triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C'.

To find:

The transformation that can be used to map each point (x,y) on Triangle ABC to its corresponding point on Triangle A'B'C'.

Solution:

If a figure rotated 90 degrees counterclockwise, then

(x,y)\to (-y,x)

P(x,y)\to P_1(-y,x)

If a figure translated 3 units up, then

(x,y)\to (x,y+3)

P_1(-y,x)\to P'(-y,x+3)

If  triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C', then the rule of transformation is

(x,y)\to (-y,x+3)

Therefore, the required rule of transformation is (x,y)\to (-y,x+3).

Note: Option are not in proper form.

7 0
3 years ago
Find the area of a triangle whose vertices are (0,0), (4,2), (-1,2)​
Yakvenalex [24]

Answer:

Therefore area of a triangle whose vertices are (0,0), (4,2), (-1,2) is

5 units².

Step-by-step explanation:

Given:

Let the vertices be,

point A( x₁ , y₁) ≡ ( 0 , 0)

point B( x₂ , y₂) ≡ (4 , 2)

point C(x₃ , y₃ ) ≡ (-1 , 2)

To Find:

Area of Triangle = ?

Solution:

If the Vertices A( x₁ , y₁), B( x₂ , y₂) and C(x₃ , y₃ ) then the Area of Triangle is given by

\textrm{Area of Triangle}=\dfrac{1}{2}(x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2}))

Substituting the values we get

\textrm{Area of Triangle}=\dfrac{1}{2}(0(2-2)+4(2-0)+(-1)(0-2))

\textrm{Area of Triangle}=\dfrac{1}{2}(0+8+2))=\dfrac{10}{2}=5\ units^{2}

Therefore area of a triangle whose vertices are (0,0), (4,2), (-1,2) is

5 units².

7 0
3 years ago
Other questions:
  • A line contains the points (82, −96) and (87, −86) .
    10·2 answers
  • What is the difference in the place value between the 2 in 324 and the 2 in 0.324?
    5·2 answers
  • The costs of Brand A and Brand B coffee beans are $400/kg and
    6·1 answer
  • Ms. Johnson earns $47,000 per year. She is paid weekly and puts 8% of her salary
    8·1 answer
  • Sally can paint a room in 7 hours while it takes Steve 6 hours to paint the same room. How long would it take them to paint the
    7·2 answers
  • The correlation coefficient r between a child’s age, x, and the number of minutes spent doing homework each day, y, is 0.694. Wh
    12·1 answer
  • Answer correctly please
    10·2 answers
  • Imagine that each of these 40 students then made their choices from the list of four personality
    5·1 answer
  • Care to comment? I need help this... Please. (This is a word docx)
    6·2 answers
  • 1.99x+6=2.50x can someone help me
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!