The solution of the system of equation is the intersection point of the two quadratic equations, so we need to equate both equations, that is,

So, by moving the term -3x^3+20 to the left hand side, we have

Then, in order to solve this equation, we can apply the quadratic formula

In our case, a=5, b=-3 and c=-30. So we get

which gives

By substituting these points into one of the functions, we have

and

Then, by rounding these numbers to the nearest tenth, we have the following points:

Therefore, the answer is the last option
Answer:
$16,666.67
Step-by-step explanation:
PMT= PV*i Where PMT is the withdrawals ,PV is present value and i is the dicounting rate
PMT = $1,000.00
PV= ?
i = 6%
hence $1,000 = PV*6%
PV=1,000/6%
PV = 16,666.67
Answer:
41⁰
Step-by-step explanation:
180 - 98 = 82⁰
2x = 82⁰
x = 82/2
= 41⁰
Answer: No her plates will not fit in the box
Step-by-step explanation: Each plate is 0.5 inches tall; therefore, the stack of 8 plates will have a height of .
Also, the diameter of the largest plate is 10 inches or has a radius of 5 inches, which matches the radius of the cylindrical box; therefore, we know that the stack of plates can fit into the base area of the cylindrical box.
What we want to figure out now is the height of the cylindrical box to see if it is greater than or equal to 4 inches—the height of the stack of plates.
The volume of a cylinder is , and since for our cylindrical box the volume is 150 cubic inches; therefore,
putting in and solving for height we get
,
which is not greater than 4 inches, which means the plates will not fit into the box since the height of the stack is greater than the height of the box.
For the first one, the two in the middle apply. for the second one, they all apply