Richards Middle School is collecting canned foods. The school has a goal of collecting at least 2000 cans. We have 872 cans so f
2 answers:
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Answer:
Proof below.
Step-by-step explanation:
<u>Quadratic Formula</u>
<u>Given quadratic equation</u>:
<u>Define the variables</u>:
- a = 5
- b = -6
- c = -2
<u>Substitute</u> the defined variables into the quadratic formula and <u>solve for x</u>:
Therefore, the exact solutions to the given <u>quadratic equation</u> are:
Learn more about the quadratic formula here:
Answer:
(i) 30
(ii) 8
Step-by-step explanation:
Start by drawing 3 rings for the Venn diagram. Each ring represents either Audi, BMW, or Citroën.
Next, add the information provided in the problem statement. We know that 20 choose BMW only. Another 20 choose Citroën only.
We know the number who choose all 3 is the same as the number that choose BMW and Citroën, but not Audi. We'll call this number x.
Similarly, we know that the number who choose all 3 is half of those choose Audi and BMW, but not Citroën. So we'll say that number is 2x.
We know the total number of Audi votes is 48, the total number of BMW votes is 36, and the total number of Citroën votes is 34.
Finally, we know the total number of voters is 100, including those who voted for no favorites (we'll call that number n).
We know that BMW got 36 votes, so:
20 + x + x + 2x = 36
20 + 4x = 36
4x = 16
x = 4
We know that Citroën got 34 votes, so:
20 + x + x + z = 34
20 + 4 + 4 + z = 34
28 + z = 34
z = 6
We know that Audi got 48 votes:
y + 2x + x + z = 48
y + 2(4) + 4 + 6 = 48
y + 18 = 48
y = 30
Finally, we know that the total number of voters is 100.
20 + 20 + x + x + 2x + y + z + n = 100
20 + 20 + 4 + 4 + 2(4) + 30 + 6 + n = 100
92 + n = 100
n = 8
