Answer:
Radius:
Step-by-step explanation:
Given
Solving (a): The radius of the circle
First, we express the equation as:
Where
So, we have:
Divide through by 9
Rewrite as:
Group the expression into 2
Next, we complete the square on each group.
For
1: Divide the
2: Take the
3: Add this
So, we have:
Factorize
Apply the same to y
Add the fractions
Recall that:
By comparison:
Take square roots of both sides
Split
Rationalize
Solving (b): The center
Recall that:
Where
From:
and
Solve for h and k
and
Hence, the center is:
The graph that shows the proportional relationship y = 0.7x is Graph A.
<h3>What is a proportional relationship?</h3>
A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, 7 out of 10 customers preferred the restaurants new spaghetti sauce, hence the constant is given by:
k = 7/10 = 0.7.
And the equation is:
y = 0.7x.
When x = 0, y = 0, which already eliminates graphs C and D. When x = 10, y = 7, which means that Graph A is the answer to this question.
More can be learned about proportional relationships at brainly.com/question/10424180
Measure the distance between the two end points, and divide the result by 2. This distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates.
1. Make a frequency distribution table. Draw a histogram. Age frequency. 2 4 6 8 10 12 14 16... make a tally in the appropriate class. 5... frequency is 50, which is the number of entries in sample data set.