6)
A quadratic function has the form
y = ax^2 + bx + c
Use point (3, 5) in the equation above:
5 = a(3^2) + 3b + c
5 = 9a + 3b + c
9a + 3b + c = 5 Equation 1
Use point (4, 3) in the equation above:
3 = a(4^2) + 4b + c
16a + 4b + c = 3 Equation 2
Use point (5, 3) in the equation above.
5 = a(5^2) + 5b + c
25a + 5b + c = 5 Equation 3.
Now solve the system of equations of equations 1, 2, and 3 to find the coefficients, a, b, and c.
9a + 3b + c = 5
16a + 4b + c = 3
25a + 5b + c = 5
Subtract the first equation from the second equation.
Subtract the second equation from the third equation.
You get
7a + b = -2
9a + b = 2
Subtract the first equation above from the second equation to get.
2a = 4
a = 2
Substitute:
7a + b = -2
7(2) + b = -2
b = -16
9a + 3b + c = 5
9(2) + 3(-16) + c = 5
18 - 48 + c = 5
c - 30 = 5
c = 35
The equation in standard form is
y = 2x^2 - 16x + 35
We can find it in vertex form:
y = 2(x^2 - 8x) + 35
y = 2(x^2 - 8x + 16) + 35 - 32
y = 2(x - 4)^2 + 3
Answer:
38
Step-by-step explanation:
f(-9) is the value of f(x) when x = -9. Therefore, f(-9) = 4 from the graph. Doing the same with g(6), we can see that g(6) = 6. Our expression becomes:
-1 * 4 + 7 * 6
= -4 + 42
= 38
Answer:
B and D
Step-by-step explanation:
B because if you dont and it is a real cop you would get an even bigger fine. D because you never know.
Answer:
The inequality which represents the graph is y ≤ -2x + 1 ⇒ A
Step-by-step explanation:
To solve the question you must know some facts about inequalities
- If the sign of inequality is ≥ or ≤, then it represents graphically by a solid line
- If the sign of inequality is > or <, then it represents graphically by a dashed line
- If the sign of inequality is > or ≥, then the area of the solutions should be over the line
- If the sign of inequality is < or ≤, then the area of the solutions should be below the line
Let us study the graph and find the correct answer
∵ The line represented the inequality is solid
∴ The sign of inequality is ≥ or ≤
→ That means the answer is A or B
∵ The shaded area is the area of the solutions of the inequality
∵ The shaded area is below the line
∴ The sign of inequality must be ≤
→ That means the correct answer is A
∴ The inequality which represents the graph is y ≤ -2x + 1
Answer:
59/20 cups
Step-by-step explanation:
5 3/10
8 1/4
Common denimainator is 40
5 3/10 = 5 12/40
8 1/4 = 8 10/40
Now we can subtract:
330/40-212/40=118/40
118/40= 59/20 cups
Sorry if I spelled some words wrong
