Answer:
16
Step-by-step explanation:
1) Plug x=1 into equation
f(x) = -2(1)²+4(1)+6
f(x) = -2²+4+6
f(x) = 4+4+6
y = 14
(1,14)
2) Plug in x=2 into equation
f(x) = -2(2)²+4(2)+6
f(x) = -4²+8+6
f(x) = 16+8+6
y = 30
(2,30)
3) Use slope formula ()
16
3 screws 3/32 times 4 long.
1 answer:
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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:
- <em><u>12 tickets</u></em>
Explanation:
You must assume that the ratio of the number of tickets in row 7 is a constant.
That permits you to set a proportion with the ratio of the number of tickets in row 7 for the first batch of tickets and the ratio of the number of tickets in row 7 for the next 33 tickets sent out:
<u>1. Ratio of number of tickets in row 7 for the first batch.</u>
- Number of tickets in row 7: 20
- Total number of tickets: 20 + 19 + 16 = 55
- Ratio: 20/55
<u>2. Ratio of number of tickets in row 7 in the next 33 tickets sent out:</u>
- Number of tickets in row 7: x
- Total number of tickets sent out: 33
- Ratio: x/33
<u>3. Proportion</u>
Set the proportion and solve for x:
Answer: 12 tickets