We are told that circle C has center (-4, 6) and a radius of 2.
We are told that circle D has center (6, -2) and a radius of 4.
If we move circle C's center ten units to the right and eight units down, the new center would be at (-4 + 10), (6 - 8) = (6, -2). So step 1 in the informal proof checks out - the centers are the same (which is the definition of concentric) and the shifts are right.
Let's look at our circles. Circle C has a radius of 2 and is inside circle D, whose radius is 4. Between Circle C and Circle D, the radii have a 1:2 ratio, as seen below:
If we dilate circle C by a factor of 2, it means we are expanding it and doubling it. Our circle has that 1:2 ratio, and doubling both sides gives us 2:4. The second step checks out.
Translated objects (or those that you shift) can be congruent, and dilated objects are used with similarity (where you stretch and squeeze). The third step checks out.
Thus, the argument is correct and the last choice is best.
Answer:6
Step-by-step explanation:
-7+10-(-3)
Using BODMAS
-7+10+3
3+3=6
D. Plug the first number into “n” to get the second number
Answer:
The time it takes for the cannonball to hit the ground is 6.49 seconds.
Step-by-step explanation:
You know that the height of the cannonball above the ground, h, in meters, in time, t, in seconds, is found by the function h(t) = -4.9t² + 30.5t + 8.4. You want to calculate the time it takes for the cannonball to hit the ground, that is, the time it takes for the bullet to reach zero height. So, being h(t) = 0 you have:
0 = -4.9t² + 30.5t + 8.4
To solve a quadratic function 0=a*x² + b*x +c, the expression is applied:
In this case, being a = -4.9, b =30.5 and c =8.4 you have:
Solving you get:
t1= -0.26 seconds and t2=6.49 seconds
Since time does not have a negative value, then <u><em>the time it takes for the cannonball to hit the ground is 6.49 seconds.</em></u>
To solve this problem, let us first assign variables. Let
us say that:
A = runner
B = cyclist
d = distance
v = velocity
time = t
The time in which the cyclist overtakes the runner is the
time wherein the distance of the two is the same, that is:
dA = dB
We know that the formula for calculating distance is:
d = v t
therefore,
vA tA = vB tB
Further, we know that tA = tB + 2, therefore:
vA (tB + 2) = vB tB
4 (tB + 2) = 14 tB
4 tB + 8 = 14 tB
10 tB = 8
tB = 0.8 hours = 48 min
Therefore the cyclist overtakes the runner after 0.8
hours or 48 minutes.
