<u>Given</u>:
Given that the circle is graphed with center (-1,1)
We need to determine the equation of the circle.
<u>Radius</u>:
To determine the radius of the circle, let us simply count the number of units between the center point to any point on the circle.
Hence, from the figure, it is obvious that there are 5 units between the center and any point on the circle.
Thus, radius of the circle is 5 units.
<u>Equation of the circle:</u>
The standard form for the equation of the circle is given by
where the center is (h,k) and radius is r.
Substituting the center (-1,1) and r = 5 in the above formula, we get;
Thus, the equation of the circle is
Answer:
Step-by-step explanation:
<u>Initial coordinates and transformations:</u>
- (x, y) → (4x, 4y) → (3x, 3y)
- A(-1, -1) → A'(-4, -4) → A''(-3, -3)
- B(1, 1) → B'(4, 4) → B''(3, 3)
- C(2, 0) → C'(8, 0) → C''(6, 0)
Answer:
x = 125
Step-by-step explanation:
4 hrs : 200 mi
2.5 hrs : x mi
4/2.5 = 1.6 hrs
200/1.6 = 125 mi
x = 125 mi
Answer:
<em>Student 2 is incorrect because he didn't use the formula properly</em>
Step-by-step explanation:
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The initial value of the item is Co=$1000, the rate of decay is r=40%=0.4, and the time is t=3 years.
Substituting into the formula:
C(3)=$216
Student 2 is incorrect because he didn't use the formula properly
<h2>
Answer:</h2>
The graph is shown in the Figure below
<h2>
Step-by-step explanation:</h2>
In this exercise, we have an equation. On the left side we have a straight line with slope 
and there is no any y-intercept. On the right side, on the other had, we also have a straight line, but the slope here is 
. Therefore, by plotting these two straight lines, we have that the solution is the origin, that is, the point 
.
