Mrs. Thompson wants to buy centerpieces to use at a party. It will cost $49 to have the centerpieces delivered plus $0.89 per ce
1 answer:
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The first step for solving this equation is to determine the defined range.
3㏑(2) + ㏑(8) = 2㏑(4x), x > 0
Write the number 8 in exponential form.
3㏑(2) + ㏑(2³) = 2㏑(4x)
Using ㏑(
) = x × ㏑(a),, transform the expression.
3㏑(2) + 3㏑(2) = 2㏑(4x)
Now collect the like terms on the left side of the equation.
6㏑(2) = 2㏑(4x)
Switch the sides of the equation.
2㏑(4x) = 6㏑(2)
Using x × ㏑(a) = ㏑(),, transform the expression on the left side of the equation.
㏑((4x)²) = 6㏑(2)
Using x × ㏑(a) = ㏑(),, transform the expression on the right side of the equation.
㏑((4x)²) = ㏑(
)
Since the bases of the logarithms are the same,, you need to set the arguments equal.
(4x)² =
Take the square root of both sides of the equation and remember to use both the positive and negative roots.
4x = +/- 8
Now separate the equation into 2 possible cases.
4x = 8
4x = -8
Solve the top equation for x.
x = 2
Solve the bottom equation for x.
x = 2
, x > 0
x = -2
Lastly,, check if the solution is in the defined range to find your final answer.
x = 2
This means that the correct answer to your question is x = 2.
Let me know if you have any further questions
:)
3㏑(2) + ㏑(8) = 2㏑(4x), x > 0
Write the number 8 in exponential form.
3㏑(2) + ㏑(2³) = 2㏑(4x)
Using ㏑(
3㏑(2) + 3㏑(2) = 2㏑(4x)
Now collect the like terms on the left side of the equation.
6㏑(2) = 2㏑(4x)
Switch the sides of the equation.
2㏑(4x) = 6㏑(2)
Using x × ㏑(a) = ㏑(
㏑((4x)²) = 6㏑(2)
Using x × ㏑(a) = ㏑(
㏑((4x)²) = ㏑(
Since the bases of the logarithms are the same,, you need to set the arguments equal.
(4x)² =
Take the square root of both sides of the equation and remember to use both the positive and negative roots.
4x = +/- 8
Now separate the equation into 2 possible cases.
4x = 8
4x = -8
Solve the top equation for x.
x = 2
Solve the bottom equation for x.
x = 2
, x > 0
x = -2
Lastly,, check if the solution is in the defined range to find your final answer.
x = 2
This means that the correct answer to your question is x = 2.
Let me know if you have any further questions
:)
John sold 10 hamburgers and 14 cheeseburgers.
Step-by-step explanation:
Given,
Cost of one hamburger = $3
Cost of one cheeseburger = $3.50
Total burgers sold = 24
Total revenue earned = $79
Let,
Number of hamburgers sold = x
Number of cheeseburgers sold = y
According to given statement;
x+y=24 Eqn 1
3x+3.50y=79 Eqn 2
Multiplying Eqn 1 by 3
Subtracting Eqn 3 from Eqn 2
Dividing both sides by 0.50
Putting y=14 in Eqn 1
John sold 10 hamburgers and 14 cheeseburgers.
Keywords: linear equation, elimination method
Learn more about elimination method at:
#LearnwithBrainly
Answer:
About $0.10 per ounce
Step-by-step explanation:
12 pound costs $18.75. Lets find the cost per pound first:
Cost Per Pound =
We know, there are 16 ounces in 1 pound.
We know 1 pound costs 1.5625
To find cost per ounce, we have to divide this by 16.
So,
Cost Per Ounce =
Rounded to nearest cent, that would be 10 cents per ounce