Identify the function that best models the given data
1 answer:
You might be interested in
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)
Answer: y= - 4x+18
Step-by-step explanation:
Equation: y=mx+b
***remember: b is the y-intercept and m is the slope.
m=
3= x1
2= x2
6= y1
10=y2
m==
= -4
m=-4
Now we have y=-4x+b , so let's find b.
You can use either (x,y) such as (3,6) or (2,10) point you want..the answer will be the same:
(3,6). y=mx+b or 6=-4 × 3+b, or solving for b: b=6-(-4)(3). b=18.
(2,10). y=mx+b or 10=-4 × 2+b, or solving for b: b=10-(-4)(2). b=18.
Equation of the line: y=-4x+18
Answer:
The price of the television before taxes is $420
Step-by-step explanation:
* Lets explain how to solve the problem
- The purchased price = cost price + taxes
- A new television set was recently purchased for the common room
in a residence hall for $436.80
- This price including tax
- The tax rate is 4%
- We need to find the price of the television before taxes
* <em>Lets solve the problem</em>
- Assume that the price of the television before tax is 100%
∵ The tax rate is 4%
∵ The price after tax = price before tax + tax
∵ The price before tax = 100%
∴ The price after tax = 100% + 4% = 104%
∵ 104% equivalent to $436.80
∴ 100 ⇒ ?
104 ⇒ 436.80
- <em>By using cross multiplication</em>
∴ ? =
∴ The price of the television before taxes is $420