Answer:
64.
Step-by-step explanation:
By proportion to number of orange marbles = (40 / 5) * 8
= 320 / 5
= 64 .
Part A:
We need to divide
5 ÷ 2/3
5/1 ÷ 2/3
5/1 * 3/2
15/2 or 7 1/2 plates of nachos.
Part B:
If Rachel can make 7 1/2 plates of nachos with 5 cups of cheese we need to multiply and subtract.
ma2/3 * 9 = 18/3 or 6 cups of cheese to make 9 plates
6 - 5 = 1 more cup of cheese she needs to make 9 plates
Best of Luck!
Answer:
(4,12)
(-1,-3)
Step-by-step explanation:
x^2 - y = 4
y = 3x
Use substitution. Substitute 3x for y in the first equation
x^2 - (3x) = 4
x^2 -3x =4
Subtract 4 from each side
x^2 -3x -4 = 4-4
x^2 -3x-4 =0
Factor
(x-4) (x+1) =0
Using the zero product property
x-4 =0 x+1 =0
x=4 x=-1
Now to find y for each x solution
x=4
y =3x = 3(4) =12
(4,12)
x=-1
y =3x = 3(-1) =-3
(-1,-3)
We are given with the equation y"+ 9 y = t^2 * e^3 t + 6 and asked to determine the general solution to this equation. we convert the equation into r^2 + 9 = 0. The solution to this equation is r = +/- 3i. This solution converted to trigonometric function is equivalent to <span>y</span>= <span>C1 </span>cos3t + <span>C2 </span>sin<span>3t. </span>
