Answer:
The options doesn't match or the question is wrong but the answer is (1,2.5)
Step-by-step explanation:
At the city museum, child admission is $6.00 and adult admission is $9.20. On Tuesday, twice as many adult tickets as child
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
:)
Answer:
Step-by-step explanation:
Given: The radius of circle O is r, and the radius of circle X is r'.
To prove: Circle O is similar to circle X.
Proof: Move the center of the smaller circle onto the center of the largest circle. Translate the circle X by the vector XA onto circle O. The circles now have the same center.
A dilation is needed to increase the size of circle X to coincide with the circle O. A value which when multiplied by r' will create r.
The scale factor x to increase X:
⇒
A translation followed by a dilation with scale factor will map one circle to the other, thus proving the given both circles similar.
Therefore, circle O is similar to circle X.
Step-by-step explanation:
