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
Y directly proportional to WX and inversely to Z.
Y=k(WX)/Z
Where k is the constant of proportionality.
So, the first thing is to find the value of this constant.
k = YZ/WX
= (32×3)/(6×20)
= 96/120
= 0.8
The <span>equation that models the relationship will be;
Y = 0.8(WX/Z)</span>
Step-by-step explanation:
question number 2 first part X + 2 is equal to 7 .. x is equal to 7 - 2x is equal to 5 ..second part 3 x minus 1 is equal to 3 x is equal to 23 - 1 = 3x=24 x=24÷3=x=8ans
<em>y-intercept</em><em> </em><em>is</em><em> </em><em>where</em><em> </em><em>the</em><em> </em><em>line</em><em> </em><em>on</em><em> </em><em>your</em><em> </em><em>graph</em><em> </em><em>crosses</em><em> </em><em>through</em><em> </em><em>the</em><em> </em><em>y-axis</em>
Answer:
Muercury 3
Venus 6
Mars 2
pluto 5
Jupiter 1
Nucleus4
Step-by-step explanation:
