Answer: a = 4
Step-by-step explanation: Area of a triangle is calculated as: .
The triangle formed by the parabola has base (b) equal to the distance between the points where the graph touches x-axis and height (h) is the point where graph touches the y-axis.
The points on the x-axis are the roots of the quadratic equation:
a(x-3)(x+2)=0
(x-3)(x+2)=0
x - 3 = 0
x = 3
or
x + 2 = 0
x = -2
So, base is the distance between (-2,0) and (3,0).
Since they are in the same coordinate, distance will be:
b = 3 - (-2)
b = 5
Area of the triangle is 10. So constant a is
5a = 10.2
a = 4
The constant a of the function y = a(x-3)(x+2) is 4.
Answer:
DNE
Step-by-step explanation:
The left limit is +1; the right limit is -1. These are different, so the limit does not exist.
7x + 15x + 27 = 247
22x = 247 -27
22x =225
X= 10.22
Answer:
(25,19)
Step-by-step explanation:
We are to find the location of the train station.
Using the formula for calculating midpoint given as:
M(X,Y) = [(x1+x2)/2, (y1+y2)/2]
X = x1+x2/2
Y = y1+y2/2
Given
M(X,Y) = (11,11)
Bus station (x1, y1) = (-3,3)
Substituting the given parameters into the formula.
11 = -3+x2/2
Cross multiply
11×2 = -3+x2
22 = -3+x2
x2 = 22+3
x2 = 25
Similarly
Y = y1+y2/2
11 = 3+y2/2
Cross multiply
11×2 = 3+y2
22 = 3+y2
y2 = 22-3
y2 = 19
Hence the location of the train station is at (25,19)
Answer:
x=29
Step-by-step explanation:
(x+3)+(x-1)+(x+1)=90
x+3+x-1+x+1=90
3x+3=90
3x=90-3
x=87/3
x=29
x+3=32
x+1=30
x-1=28
Checking
(x+3)+(x-1)+(x+1)=90
(29+3)+(29-1)+(29+1)=90
32+28+30=90
90=90