Answer:
r = 3.7 cm
Step-by-step explanation:
19.02 = 1/2π(2radius) + diameter
expanding:
19.02 = 1/2(3.14)(2r) + 2r
19.02 = 3.14r + 2r = 5.14r
r = 19.02/5.14 = 3.7 cm
If i = √-1 ,
then ...
i² = (√-1)² = -1
i³ = - √-1 = -i <== the answer to the question
i⁴ = (i²) · (i²) = (-1) · (-1) = 1
and then the whole thing starts over again, for higher powers of i .
Answer:
siblings. Each cupcake costs $2, and each piece of fudge costs $1.
This system of inequalities models the scenario:
2x + y = <8
x + y > 4
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part
Answer:
<u>The equations system is:</u>
<u>x + y = 10</u>
<u>0.5x + 0.9y = 6</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Liters of 60% acid solution needed = 10
x = Number of liters of the 50% solution
y = Number of liters of the 90% solution
2. Which equation represents the total liters of acid that are needed?
There are two equations needed:
The first one related to the total liters needed, 10 in this case:
x + y = 10
The second one related to the acid concentration of the 10 liters:
0.5x + 0.9y = 10 * 0.6
0.5x + 0.9y = 6
<u>The equations system is:</u>
<u>x + y = 10</u>
<u>0.5x + 0.9y = 6</u>
Solving for x and y in the 2nd equation, we have:
0.5 (10 - y) + 0.9y = 6
5 - 0.5y + 0.9y = 6
0.4y = 6 - 5
0.4y = 1
y = 1/0.4 = 2.5 ⇒ x = 7.5 (10 - 2.5)
The scientist can mix 7.5 liters of the 50% acid solution and 2.5 liters of the 90% acid solution to get the 10 liters of the 60% acid solution.
Answer:
7 games
Step-by-step explanation:
Ricardo has 2 cases with x number of games in each. This means 2x is the amount of video games in both. He gives away 4. He now has 2x-4 and has 10 left. This is 2x-4=10. Solve for x.
2x - 4 = 10
2x = 14
x=7
