Candies with celias and emmas is 60 and 45 respectively.
<u>Solution:</u>
Given, Getting home from trick or treat celia and emma counted their candies. Half of celias candies is equal to 2/3 of emmas candies.
They had a total of 105 candies altogether.
We have to find how many candies did each of them have.
Let the number of candies with celias be n, then number of candies with emma will be 105 – n.
Now according to given condition.
Hence, candies with celias and emmas is 60 and 45 respectively.
Answer:
x=1/3 or x=−2
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Step-by-step explanation:
Step 1: Add 2 to both sides.
3x^2+5x−2+2=0+2
3x^2+5x=2
Step 2: Since the coefficient of 3x^2 is 3, divide both sides by 3.
3x^2+5x/3=2/3
x^2+5/3x=2/3
Step 3: The coefficient of 5/3x is 5/3. Let b=5/3.
Then we need to add (b/2)^2=25/36 to both sides to complete the square.
Add 25/36 to both sides.
x^2+5/3x+25/36=2/3+25/36
x^2+5/3x+25/36=49/36
Step 4: Factor left side.
(x+5/6)^2=49/36
Step 5: Take square root.
x+5/6=±√49/36
Step 6: Add (-5)/6 to both sides.
x+5/6+ −5/6=
−5/6±√49/36x=−5/6±√49/36x=
1/3 or x=−2
X = the amount of water to add
10 - x = amount of 18% bleach to add
.18(10-x)= .12 x 10
1.8 -.18x =1.2
-.18x = -.6
x = 3 1/3 liters water
therefore 6 2/3 liters bleach
Step-by-step explanation:
2^(2x) - 5(2^x) = -4
(2^x)^2 - 5(2^x) = -4
Substitute 2^x = z --> x = ln(z)/ln(2)
z^2 - 5z = -4
z^2 - 5z + 4 = 0
(z - 1)(z - 4) = 0
z = 1 --> x = ln(1)/ln(2) = 0
z = 4 --> x = ln(4)/ln(2) = 2
The answer is 1/3 divide 12 by 12 and 36 by 12
