There are two ways to do this but the way I prefer is to make one of the equations in terms of one variable and then 'plug this in' to the second equation. I will demonstrate
Look at equation 1,
this can quite easily be manipulated to show
.
Then because there is a y in the second equation (and both equations are simultaneous) we can 'plug in' our new equation where y is in the second one
which can then be solved for x since there is only one variable
and then with our x solution we can work out our y solution by using the equation we manipulated
.
So the solution to these equations is x=-2 when y=6
Answer:
12π in³
Step-by-step explanation:
The right triangle formed by the radius (r), height (x), and slant height (y) is a 3-4-5 right triangle, with the dimension 4 inches being the perpendicular height from the base to the apex. That is, the Pythagorean theorem tells us ...
r² + x² = y²
x = √(y² -r²) = √(25 -9) = 4 . . . inches
The formula for the volume of a cone is ...
V = (1/3)πr²h . . . . . . . . h is the height, what you call x
Your cone has r = 3 in, h = 4 in. Filling in these numbers and simplifying, we get ...
V = (1/3)π(3 in)²(4 in) = 12π in³
The volume of the cone is 12π cubic inches.
Answer:
i. 9
ii. 14
iii. 405
iv. 
Step-by-step explanation:
The number of diagonals in a polygon of n sides can be determined by:
where n is the number of its sides.
i. For a hexagon which has 6 sides,
number of diagonals = 
= 
= 9
The number of diagonals in a hexagon is 9.
ii. For a heptagon which has 7 sides,
number of diagonals = 
= 
= 14
The number of diagonals in a heptagon is 14.
iii. For a 30-gon;
number of diagonals = 
= 
= 405
The number of diagonals in a 30-gon is 405.
iv. For a n-gon,
number of diagonals =
The number of diagonals in a n-gon is
Step-by-step explanation:
percentage of green marbles=
(total green marbles÷ total marbles )×100
Answer:
Pedro and paola don't seem so happy together
