Can you help me with this
2 answers:
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Answer:
Step-by-step explanation:
see the attached figure to better understand the problem
Let
c -----> the cost of some taxi journeys
n ----> the number of miles
we know that
The graph is a line
The equation of a line in slope intercept form is
where
m is the slope
b is the c-intercept (value of c when the value of n is equal to zero)
Observing the graph we have the points
(0,2.5), (5,5.5)
<em>Find the slope</em>
The formula to calculate the slope between two points is equal to
substitute the values
we have
-----> because the point (0,2.5) is the c-intercept
substitute in the equation of slope-intercept form
Answer:
Option A: b must equal 7 and a second solution to the system must be located at the point (2, 5)
Step-by-step explanation:
<u><em>The complete question is</em></u>
Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.
Equation 1: (x – 3)2 = y – 4
Equation 2: y = -x + b
In order for Tom’s thinking to be correct, which qualifications must be met?
A: b must equal 7 and a second solution to the system must be located at the point (2, 5).
B: b must equal 1 and a second solution to the system must be located at the point (4, 5).
C: b must equal 7 and a second solution to the system must be located at the point (1, 8).
D: b must equal 1 and a second solution to the system must be located at the point (3, 4).
step 1
Find the vertex of the quadratic equation
The general equation of a vertical parabola in vertex form is
where
(h,k) is the vertex
we have
so
The vertex is the point (3,4)
step 2
Find out the value of b in the linear equation
we know that
If the vertex is a solution of the system of equations, then the vertex must satisfy both equations
substitute the value of x and the value of y of the vertex in the linear equation
For x=3, y=4
so
step 3
Find out the second solution of the system of equations
we have
-----> equation A
----> equation B
solve the system of equations by graphing
Remember that the solutions are the intersection points both graphs
The second solution of the system of equations is (2,5)
see the attached figure
therefore
b must equal 7 and a second solution to the system must be located at the point (2, 5)
