The given data is proportional because, we get 3.15 when Quantity y is divided by Quantity x, y/x = 3.15
Given,
The data;-
Quantity x; 2 , 6 , 9 , 5 , 1
Quantity y; 6.3, 18.9, 28.35, 15.75, 3.15
We have to find the proportionality between the data set given;-
Lets see the proportionality;-
Quantity y ÷ Quantity x
6.3 ÷ 2 = 3.15
18.9 ÷ 6 = 3.15
28.35 ÷ 9 = 3.15
15.75 ÷ 5 = 3.15
3.15 ÷ 1 = 3.15
Here,
The given data is proportional because, we get 3.15 when Quantity y is divided by Quantity x, y/x = 3.15
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<h2>
For a = 1 and b = 10 x+1 and x+2 factors of x³-ax²-bx-8 = 0</h2><h2>
Other factor is (x-4)</h2>
Step-by-step explanation:
We have
x³-ax²-bx-8 = 0
Its factors are x+1 and x+2
That is x = -1 and x = -2 are its roots
Substituting x = -1
(-1)³-a(-1)²-b(-1)-8 = 0
-1 - a + b - 8 = 0
b - a = 9 ---------------------eqn 1
Substituting x = -2
(-2)³-a(-2)²-b(-2)-8 = 0
-8 - 4a + 2b - 8 = 0
2b - 4a = 16 ---------------------eqn 2
eqn 1 x -2
-2b + 2a = -18 ---------------------eqn 3
eqn 2 + eqn 3
-2a = -2
a = 1
Substituting in eqn 1
b - 1 = 9
b = 10
For a = 1 and b = 10, x+1 and x+2 factors of x³-ax²-bx-8 = 0
The equation is x³-x²-10x-8 = 0
Dividing with x + 1 we will get
x³-x²-10x-8 = (x+1)(x²-2x-8)
Dividing (x²-2x-8) with x + 2 we will get
x²-2x-8 = (x+2)(x-4)
So we have
x³-x²-10x-8 = (x+1)(x+2)(x-4)
Other factor is (x-4)
The slope intercept form of the line whose points are (1,5) and (-2,-4) is y=3x+2.
Given two points of a line (1,5) and (-2,-4).
We have to form an equation in slop intercept form.
Equation is relationship between two or more variables which are expressed in equal to form.Equations of two variables looks like ax+by=c.
Point slope form of an equation is y=x+mc where m is slope of the line.
From two points the formula of equation is as under:
(y-
)=
*(x-
)
where 
are the points.
Putting the values of =1, 
=-2, =5 and 
=-4.
y-5=(-4-5/-2-1)*(x-1)
y-5=-9/-3*(x-1)
y-5=3(x-1)
y-5=3x-3
y=3x-3+5
y=3x+2
Hence the slope intercept form of the line having points (1,5)(-2,-4) is y=3x+2.
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