The expression given by f(x)=a(x-h)^2+k is a the equation of a vertex where (h,k) is the vertex. The importance of h is that it represents the x-intercept, the lowest or the highest point of the graph of the expression. This is a very important factor when determining the turning points of parabolas
Answer:
<B = 47°
<C = 28°
b = AC = 28.0
Step-by-step explanation:
Given:
∆ABC
AB = c = 18
BC = a = 37
<A = 105°
Required:
Length of AC = b
measure of angle B and angle C
SOLUTION:
==>Use the sine rule, sin A/a = sinC/c to find the angle of C:
SinA = sin(105) = 0.9659
a = 37
sinC = ?
c = 18
0.9659/37 = sinC/18
Cross multiply
0.9659*18 = 37*sinC
17.3862 = 37*sinC
Divide both sides by 37
17.3862/37 = sinC
0.4699 = sinC
sinC = 0.4699
C = Sin-¹(0.4699)
C = 28.0° (nearest tenth)
==>Find angle B using sum of angles in a triangle:
Angle B = 180 - (105+28)
Angle B = 180 - 133
Angle B = 47°
==>Find length of b using sine rule, b/sinB = c/sinC:
SinC = sin(28) = 0.4695
SinB = sin(47) = 0.7314
c = 18
b = ?
b/0.7314 = 18/0.4695
Cross multiply
b*0.4695 = 18*0.7314
b*0.4695 = 13.1652
Divide both sides by 0.4695
b = 13.1652/0.4695
b = 28.0 (nearest tenth)
Answer:
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form 
or 
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Let
x -----> the number of hours worked
y ----> the amount paid in dollars
In this problem we have a proportional variation, between two variables, x, and y
<em>Find out the constant of proportionality k</em>
For (5,300) -----> 
----> 
For (4,240) -----> ----> 
For (6,360) -----> ----> 
The constant k is
The equation is equal to
The unit rate of change of dollars with respect to time is equal to the constant of proportionality or slope of the linear equation
therefore
By using a graphing calculator, the solutions are:
(-3, 4) and (1, 0)
Answer: 86
Step-by-step explanation:
