Answer:
(x+12)(x-15)
Step-by-step explanation:
Answer:
(x − 4)² + (y − 3)² = 25
Step-by-step explanation:
The equation of a circle is:
(x − h)² + (y − k)² = r²
Given three points on the circle, we can write three equations:
(1 − h)² + (7 − k)² = r²
(8 − h)² + (6 − k)² = r²
(7 − h)² + (-1 − k)² = r²
Expanding:
1 − 2h + h² + 49 − 14k + k² = r²
64 − 16h + h² + 36 − 12k + k² = r²
49 − 14h + h² + 1 + 2k + k² = r²
Simplifying:
50 − 2h + h² − 14k + k² = r²
100 − 16h + h² − 12k + k² = r²
50 − 14h + h² + 2k + k² = r²
Subtracting the first equation from the second and third equations:
50 − 14h + 2k = 0
-12h + 16k = 0
Solving the system of equations, first reduce:
25 − 7h + k = 0
-3h + 4k = 0
Solve with substitution or elimination. Using substitution, solve for k in the first equation and substitute into the second.
k = 7h − 25
-3h + 4(7h − 25) = 0
-3h + 28h − 100 = 0
25h = 100
h = 4
k = 7h −25
k = 7(4) − 25
k = 3
Now plug these into any of the original three equations to find r.
(1 − h)² + (7 − k)² = r²
(1 − 4)² + (7 − 3)² = r²
9 + 16 = r²
25 = r²
The equation of the circle is:
(x − 4)² + (y − 3)² = 25
Graph: desmos.com/calculator/ctoljeqhnp
Answer:
$0.60
Step-by-step explanation:
If you purchase 6 rolls, you pay $3.60
Each roll is $0.60.
If you purchase 13 individual rolls, you pay
13 x 0.6 = $7.80
But if you purchase the Baker's dozen, you pay only $7.20, so you save $0.60
7.80 - 7.20 = 0.60
Hope this helps! :)
The answer is x = 2 because 8(2) is 16 and 16 - 6 = 10
<span>A quarter is equivalent to 25 cents or $0.25 and a nickel is equal to 5 cents or $0.05. In the given in this item, if there are x nickels then, there are x + 7 quarters. With these and the total amount known, we can now compute for the value of x.
(x)(0.05) + (x + 7)(0.25) = 2.65
Simplifying,
0.05x + 0.25x + 1.75 = 2.65
Simplifying further,
0.3x = 0.9
The value of x from the equation is 3. Hence, there are 10 quarters.</span>
