Step-by-step explanation:
x² + y² − 8x + 10y − 8 = 0
Rearrange:
x² − 8x + y² + 10y = 8
To complete the square, take half of the x and y coefficients, square it, then add the result to both sides.
(-8/2)² = 16
(10/2)² = 25
x² − 8x + 16 + y² + 10y + 25 = 8 + 16 + 25
x² − 8x + 16 + y² + 10y + 25 = 49
Factor the squares:
(x − 4)² + (y + 5)² = 49
The center is (4, -5) and the radius is 7.
Answer:
The umbrella will fit in, but there will be a lot of extra room.
Step-by-step explanation:
Remember the Pythagorean theorem:
x^(2) + y^(2) = n^(2)
where "x" and "y" are the legs of the right triangle and "n" is the hypotenuse
In this problem it is given that the sides (legs) are:
38in, and 24in
and diagonally across is 29in
so the hypotenuse is 29in
therefore we can form the equation:
38^(2) + 24^(2) = 29^(2)
without solving it is clear that
38^(2) + 24^(2) > 29^(2)
because 38 is a leg, but it is greater than 29, which means that 38 - 24 - 29 is not a Pythagorean triple,
but because 38 > 29, then the 29 in umbrella will fit into the suitcase, but it will not be a snug fit, there will be a lot of extra room
Answer:
h(0) = 7
Step-by-step explanation:
by saying h(0) it is asking you to plug in 0 as the x value
3(0)^2 = 0
0 + 7 = 7
Answer:
all work is pictured and shown
