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

dolphi86 [110]

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

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

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

8 0

3 years ago

Read 2 more answers

Solving a One-Variable Linear Equation

vitfil [10]

Answer:

$\Longrightarrow:\boxed{\sf{h=14}}$

Step-by-step explanation:

Isolate the term of h from one side of the equation.

Use the distributive property.

Distributive property:

→ A(B+C)=AB+AC

First, multiply expand.

⇒ -5(3h-8)

⇒ -5*3h=-15h

⇒ -5*8=40

Rewrite the problem.

→ -15h+40

⇒ 7h-15h+40=-72

⇒ 7h-15h=-8h

→ -8h+40=-72

Subtract by 40 from both sides.

⇒ -8h+40-40=-72-40

Solve.

⇒ -72-40=-112

⇒ -8h=-112

Then, you divide by -8 from both sides.

⇒ -8h/-8=-112/-8

Solve.

Divide the numbers from left to right.

→ -112/-8=14

$\Longrightarrow: \boxed{\sf{h=14}}$

Therefore, the correct answer is h=14.

I hope this helps! Let me know if you have any questions.

5 0

2 years ago

27 x and 45y Find the GCF of the terms: b. 3 a. 1 d. 9xy b. 9

Luden [163]

Answer:

d. 9

Step-by-step explanation:

it can't be the rest... ion even know how to explain it.

3 0

3 years ago

Beatrice has at least one quarter, one dime, one nickel, and one penny. She has exactly 13 coins total. Beatrice also has a tota

prohojiy [21]

Answer:

(Q, D, N, P) = (0, 7, 4, 2) or (1, 3, 7, 2)

Step-by-step explanation:

Let the numbers of coins be Q, D, N, P

We have:

Q + D + N + P = 13

25Q + 10D + 5N + P = 92

Obviously, P = 2, so

Q + D + N = 11 (1)

25Q + 10D + 5N = 90

Divide by 5 and get

5Q + 2D + N = 18 (2)

(2) - (1), get

4Q + D = 7

Let D = 7, Q = 0, from (1), N = 4, so the set is (Q, D, N, P) = (0, 7, 4, 2)

Let D = 3, Q = 1, from (1), N = 7, so the set is (Q, D, N, P) = (1, 3, 7, 2)

If D = 6, 5, 4, 2, 1, 0, Q is not an integer, these can be ignored.

6 0

2 years ago

The ratio of boys to girls in the 9th grade is 5 to 6 there are 312 girls how many boys are there?

bija089 [108]

Answer:

260 boys

Step-by-step explanation:

multiply 312 by 5/6

(312/6) * 5 = 260

4 0

3 years ago