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
mylen [45]
3 years ago
15

Henry is designing a model for a dome shaped glasshouse. He creates the model and records the horizontal distance from the edge

of the greenhouse of the dome over its vertical height from the base of the model. The table shows the horizontal distance from the edge of the greenhosue, in inches, x, over its verital height from the base, in inches, f(x). Use data in table to create standard form of the function that models this situation.

Mathematics
2 answers:
dolphi86 [110]3 years ago
8 0

Answer:

Correct choice is B

Step-by-step explanation:

All given options represent quadratic function. Let the equation of this quadratic function be

f(x)=ax^2+bx+c.

Then

1. f(0)=2=a\cdot 0^2+b\cdot 0+c\Rightarrow c=2;

2. f(1)=7.5=a\cdot 1^2+b\cdot 1+c\Rightarrow 7.5=a+b+2;

3. f(2)=12=a\cdot 2^2+b\cdot 2+c\Rightarrow 12=4a+2b+2.

Solve the system of two equations:

\left\{\begin{array}{l}a+b+2=7.5\\4a+2b+2=12\end{array}\right.\Rightarrow\left\{\begin{array}{l}a=5.5-b\\4(5.5-b)+2b=10\end{array}\right.

Then

22-4b+2b=10,\\ \\-2b=-12,\\ \\b=6,\\ \\a=5.5-6=-0.5.

Thus, the equation of the function is

f(x)=-\dfrac{1}{2}x^2+6x+2.

Note that

f(3)=-\dfrac{1}{2}\cdot 3^2+6\cdot 3+2=-4.5+20=15.5;

f(4)=-\dfrac{1}{2}\cdot 4^2+6\cdot 4+2=18.

lara31 [8.8K]3 years ago
5 0

Answer:

Step-by-step explanation:

You might be interested in
Which one is bigger 30% or 4 /15<br>???
Nikolay [14]
I believe 30% is bigger than \frac{4}{15}.

To find the answer, you'd have to convert both the fraction and the percent into decimal form to see which one is truly bigger. Converting the percent is fairly easy. 30% would become 0.30 is decimal form. To find the fraction in decimal form, you'd have to divide the numerator by the denominator, which would be 4 ÷ 15, which makes : 2.6666666666666666666666667. 

Now you compare easily. Which one is bigger? 2.666666666666666666666667 or 0.30? 

0.30 is bigger. So 30% is bigger out of both of them.
5 0
2 years ago
Read 2 more answers
HELP PLEASE?????????????????
Yakvenalex [24]
It’s d the students
8 0
2 years ago
Jade can do 65 push ups in 5 minutes. At the same rate, how many push ups can you expect her to do in 7 minutes?
hram777 [196]

Answer:

91

Step-by-step explanation:

Set up a proportion, where x is the number of push ups she can do in 7 minutes

\frac{65}{5} = \frac{x}{7}

Cross multiply and solve for x:

5x = 455

x = 91

So, Jade can do 91 push ups in 7 minutes

3 0
3 years ago
Read 2 more answers
What is the equation in slope intercept form for (2,5) (3,12)
kondaur [170]

Slope formula: y2-y1/x2-x1

= 12-5/3-2

= 7/1

= 7

_____

Best Regards,

Wolfyy :)

7 0
3 years ago
Find the slope of the line that passes through the points (2, 1) and (-1, -1).
Natali5045456 [20]

Answer:

In the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)

5 0
3 years ago
Other questions:
  • Help please im confused
    14·2 answers
  • Find the value of x for which x²-3x - 10 /<br>x² + 12x + 36<br>is equal to zero, undefined​
    14·1 answer
  • If a 6 foot tall man casts a 9 foot shadow what is the approximate from top of his head to the top of his shadow
    11·1 answer
  • Find the radical equivalent of 272/3 and compute it?
    6·2 answers
  • Help me please thank you
    8·2 answers
  • A theater company charges $9.50 per ticket for people of all age groups. If c represents the total number of children who bought
    6·1 answer
  • The points (-5, -1) and (11, r) lie on a line with slope 1/4<br> Find the missing coordinate r.
    13·1 answer
  • Help my sister please
    8·1 answer
  • Help please! What is the slope?
    8·1 answer
  • Select the graph of the equation y + x + 3 = 0.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!