4c^2-8c-1=0 complete the square round to nearest hundredth
Answers
add 1
4c^2-8c=1
divide by 4 to make leading coeficient 1
c^2-2c=1/4
take 1/2 of linear coeficient and square it
-2/2=-1, (-1)^2=1
add that to both sides
c^2-2c+1=1/4+1
factor perfect squaer and add
(c-1)^2=5/4
square root both sides
c-1=+/-(√5)/2
add 1
c=1+/-(√5)/2
c=2.12 or -0.12
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Answers
Answer:
-3.7, -1.9, -1/2, 1 1/3, 1.6, 2 1/3
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if this answer is wrong.
Answer:
-3.7, -1.9, -1/2, 1 1/3, 1.6, 2 1/3
Step-by-step explanation:
hope this helps! have a great day!
Answers
The answer is 8.25
110/x=100/7.5
(110/x)*x=(100/7.5)*x -
110=13.333333333333*x -
(13.333333333333) to get x
110/13.333333333333=x
8.25=x
x=8.25
8.25 = 8.30
The tax on 110 is 8.30.
Answers
Answer: 9 boys remained in the choir.
Step-by-step explanation:
Let x be the number of of boys and y be the number of girls.
In a school choir, 1/2(half) of the members were girls.
i.e (1)
At the end of the year, 3 boys left the choir, and the ratio of boys to girls became 3:4.
Put y= x from (1), we get
Thus , the number of boys : x= 12
Boys remained in the choir = 12-3=9
Answers
Final answer:
To maximize the donation to charity, a total of 117 tickets need to be sold. The price per ticket that maximizes the donation is $29.0625. The maximum donation is $3,400.3125.
Explanation:
To maximize the donation to charity, we need to determine the number of tickets that need to be sold and the price per ticket that will result in the maximum donation.
a) To find the number of tickets, we can start with the minimum attendance requirement of 104 people. For every 8 extra people that attend, the price decreases by $1.25. So the number of extra people is calculated by dividing the total increase in price ($31.25 - $30) by the decrease per person ($1.25), which is 8. Therefore, the number of extra people is 13. To find the total number of tickets, we add the minimum attendance of 104 people and the number of extra people of 13. So the total number of tickets that need to be sold to maximize the donation to charity is 117.
b) To find the price per ticket, we start with the price of $31.25 and take into account the decrease of $1.25 for every 8 extra people. We can calculate the price decrease per person by dividing $1.25 by 8, which is $0.15625. To find the price per ticket, we subtract the decrease per person from the initial price, multiplied by the number of extra people. So the price per ticket that maximizes the donation is $31.25 - ($0.15625 × 13) = $29.0625.
c) To find the maximum donation, we multiply the price per ticket by the total number of tickets sold. So the maximum donation is $29.0625 × 117 = $3,400.3125.
Learn more about Maximizing donation to charity here:
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Answers
Here, y1 = 2200, x1 = 12, y2 = 3000 and x2 = 10, then
(y - 2200)/(x - 12) = (3000 - 2200)/(10 - 12)
(y - 2200)/(x - 12) = 800/-2 = -400
y - 2200 = -400(x - 12)
y = -400x + 4800 + 2200
y=-400x+7000
4, 7, 12, 19, 28
Please show working out
Answers
1st difference +3 +5 +7 +9
2nd difference +2 +2 +2
This is a geometric sequence
The form is:
an² + bn + c
2a is always = to the second difference
2a = 2
a = 1
3a + b = 2nd term - 1st term
3(1) + b = 3
3 + b = 3
b = 0
a + b + c = 1st term
1 + 0 + c = 4
1 +c = 4
c = 3
nth term of sequence {substitute all we have found}
1n² + 0 + 3
n² + 3