Answer:
(3, 0 )
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c (a ≠ 0 )
Then the x- coordinate of the vertex is
= - 
y = 5x² - 30x + 45 ← is in standard form
with a = 5, b = - 30 , then
= - 
= 3
Substitute x = 3 into the function for corresponding value of y
y = 5(3)² - 30(3) + 45 = 45 - 90 + 45 = 0
vertex = (3, 0 )
The transformations that would prove that circles A and C are similar are:
- A. Reflect A over the line y=x
- C. Dilate A by 3/2
<h3>How to prove that circle A and circle C are similar?</h3>
The circles are given as:
Circle A and B
Assume the following parameters:
- The center of circle A is (2,3) with a radius of 2
- The center of circle B is (3,2) with a radius of 3
To start with;
The circle A must be reflected across the line y = x with the following transformation rule:
(x,y) -> (y,x)
So, we have:
(2,3) -> (3,2)
Next, the radius of A must be dilated by 3/2 as follows:
New Radius = 3/2 * 2 = 3
After the transformations, we have the following parameters:
- The center of circle A is (3,2) with a radius of 3
- The center of circle B is (3,2) with a radius of 3
Notice that both circles now have the same center and radius.
Hence, both circles are similar
Read more about similar circles at:
brainly.com/question/9177979
The probability that a person wins the game is 32.1%
<h3>How to illustrate the probability?</h3>
Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.
Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:
= 24 + 4 = 28
The frequency table will be such that 28 or more has a relative frequency of 9. Therefore, the probability that a person wins the game will be:
= 9/28 = 32.1%
When you win 25% of the time, this illustrates that the number of products picked will be:
= 25% × 28
= 7 products.
The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:
= 1/6⁴
= 1/1296
Learn more about probability on:
brainly.com/question/24756209
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Answer:
C.
{− 4 1/2, −3/4, 0}
Step-by-step explanation:
domain
-1/2;1/4; 2/5
range
-5 1/2; (5/4-2);0
{-1/2, 1/4, 2/5}
take the derivative of the equation 4 times. f 4 (x)=0.
