Answer:
C
Step-by-step explanation:
Since these lines have the same slope and different y-intercepts, they are parallel lines. As such lines do not intersect, we can say that :
The system has no solutions.
His plane traveled 2,250 miles because if you multiply 375 * 6 = 2,250
Answer:
67
Step-by-step explanation: Given the quadratic equation $z^2 + bz + c = 0$, Vieta's formulas tell us the sum of the roots is $-b$, and the product of the roots is $c$. Thus,
\[-b = (-7 + 2i) + (-7 - 2i) = -14,\]so $b = 14.$
Also,
\[c = (-7 + 2i)(-7 - 2i) = (-7)^2 - (2i)^2 = 49 + 4 = 53.\]Therefore, we have $b+c = \boxed{67}$.
There are many other solutions to this problem. You might have started with the factored form $(z - (-7 + 2i))(z - (-7 - 2i)),$ or even thought about the quadratic formula.
This is the aops answer :)
Answer:
x = 17
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
15^2 + x^2 = (sqrt(514))^2
225 + x^2 = 514
Subtract 225 from each side
225-225 + x^2 = 514-225
x^2 =289
Take the square root of each side
sqrt(x^2) = sqrt(289)
x = 17
Answer:
8 ft
Step-by-step explanation:
The side length of the base is the square root of the area of the square, so is 12 ft. Then the distance from the center of one side to the center of the square base is 6 ft, The height of the pyramid completes a right triangle with side 6 ft and hypotenuse 10 ft. Then the height is given by the Pythagorean theorem as ...
height = √((10 ft)^2 - (6 ft)^2) = √(64 ft^2)
height = 8 ft
