7.) the equation of the circle is
(x - 3)^2 + (y - 4)^2 = 25
If you substitute the point in you get
(6-3)^2 + (8-4)^2 = 25
3^2 + 4^2 = 25
9 + 16 = 25
25 = 25
Both sides of the equation are the same so it proves it lies on the circle
8.) you add the x coordinates together and divide by 2
7 + 4 = 11
11/2 = 5.5
You use +7 because you need to find the midpoint.
You then add 5.5 to - 7 or - 5.5 from 4
-7 + 5.5 = - 1.5
You do the same for y coordinates
6+5 = 11
11/2 = 5.5
6-5.5 = 0.5
So the coordinates of Rachel's house are
(-1.5, 0.5)
x+y = 47
x-y = 21
------------ add together
2x =68 divide by 2
x=34
x+y = 47
34+ y = 47
subtract 34 from each side
y = 13
the two numbers are 34 and 13
Answer:
$16.40
Step-by-step explanation:
Answer:
Option (C)
Step-by-step explanation:
There are two inequalities,
t - 4 ≥ 4t + 8 ------(1)
3t > 14 - 4t ------(2)
By simplifying inequality (1),
t - 4 ≥ 4t + 8
t ≥ 4t + 8 + 4
t ≥ 4t + 12
t - 4t ≥ 12
-3t ≥ 12
t ≤ 
t ≤ -4
By solving inequality (2),
3t > 14 - 4t
3t + 4t > 14
7t > 14
t > 
t > 2
From the given graphs, Option (C) will be the answer.
We have that the total length of paper needed to cover all the tables is

From the question we are told that:
Number of tables 
Length of table
Extension 
Generally, the equation for the Total length tables is mathematically given by


Therefore with an extension of 0.25ft at both end we have the Total length of tablecloths to be


In conclusion
The total length of paper needed to cover all the tables is

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