Answer: The graph decreases, then increases. c.The graph remains constant. d.The graph increases, then decreases.
Step-by-step explanation:
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
![10=\frac{5.a}{2}](https://tex.z-dn.net/?f=10%3D%5Cfrac%7B5.a%7D%7B2%7D)
5a = 10.2
a = 4
The constant a of the function y = a(x-3)(x+2) is 4.
Answer:
![\boxed{225}](https://tex.z-dn.net/?f=%5Cboxed%7B225%7D)
.
Step-by-step explanation:
Arithmetic sequence
![Un = a + (n - 1)b](https://tex.z-dn.net/?f=Un%20%3D%20a%20%2B%20%28n%20-%201%29b)
.
First step, find its difference
![b = U_2 - U_1](https://tex.z-dn.net/?f=b%20%3D%20U_2%20-%20U_1)
![b = 6 - 3](https://tex.z-dn.net/?f=b%20%3D%206%20-%203)
![b = 3](https://tex.z-dn.net/?f=b%20%3D%203)
.
So, we get
![a = 3](https://tex.z-dn.net/?f=a%20%3D%203)
![b = 3](https://tex.z-dn.net/?f=b%20%3D%203)
.
Finally, Let's find the 75th term
![U_{75} = 3 + (75 - 1)3](https://tex.z-dn.net/?f=U_%7B75%7D%20%3D%203%20%2B%20%2875%20-%201%293)
![U_{75} = 3 + (74)3](https://tex.z-dn.net/?f=U_%7B75%7D%20%3D%203%20%2B%20%2874%293)
![U_{75} = 3 + 222](https://tex.z-dn.net/?f=U_%7B75%7D%20%3D%203%20%2B%20222)
![U_{75} = 225](https://tex.z-dn.net/?f=U_%7B75%7D%20%3D%20225)
Answer:
AB = 11.5mm
Step-by-step explanation:
let the hypotenuse be AC = 23mm
Angle of elevation = 30degrees
Required
Opposite AB
Using the SOH CAH TOA identity
Sin theta = opp/hyp
Sin 30 = AB/AC
Sin 30 = AB/23
0.5 = AB/23
AB = 0.5 * 23
AB = 11.5mm