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galina1969 [7]
3 years ago
7

Use properties of logarithms to condense the logarithmic expression. write the expression as a single logarithm whose coefficien

t is 1. where​ possible, evaluate logarithmic expressions. log(4x+5)-log(x)
Mathematics
2 answers:
FromTheMoon [43]3 years ago
5 0

We can use the quotient rule [ \text{log}_a\frac{x}{y} = \text{log}_ax-\text{log}_ay ] to simplify

\text{log}(4x + 5) - \text{log}(x)\\\text{log}(\frac{4x+5}{x})\\\text{log}(4+\frac{5}{x})

Best of Luck!

Kitty [74]3 years ago
4 0
\log\left( \frac{4x + 5}{x} \right) = \log(4 + \frac{5}{x})
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A family spent $65 on dinner and left a 20% tip. What was the total cost of their meal?
Oxana [17]

Answer: B, $78

Step-by-step explanation:

If the tip is 20% of the dinner cost, then we have to first find what is 20% of 65.

20% x 65 = 13. So the tip for the dinner is 13 dollars.

Now we have to add it to the original dinner cost.

65 + 13 = 78.

Therefore, the total cost of their meal is 78 dollars. So the answer is B, $78!

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3 years ago
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I really need help with this Triangle problem. ​
julia-pushkina [17]

Answer:

x = 10

y = 20

Step-by-step explanation:

\tan \: 30 \degree =  \frac{x}{10 \sqrt{3} }  \\  \\  \frac{1}{ \sqrt{3} } =  \frac{x}{10 \sqrt{3} }  \\  \\ \sqrt{3} x = 10 \sqrt{3}  \\  \\ x =  \frac{10 \sqrt{3} }{ \sqrt{3} }  \\  \\ x = 10 \\  \\  \cos 30 \degree =  \frac{10 \sqrt{3} }{y}  \\  \\  \frac{ \sqrt{3} }{2}  =  \frac{10 \sqrt{3} }{y}  \\  \\ y =  10 \sqrt{3}  \times  \frac{2}{ \sqrt{3} }  \\  \\ y = 10 \times 2 \\  \\ y = 20

4 0
3 years ago
In how many ways can a president, Vice President, and secretary be randomly selected from a class of 25 students
stiks02 [169]
25•24•23=13,000 ways
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4 0
3 years ago
1 day= ____________ seconds <br> Please show the work!!
Nimfa-mama [501]

Answer:

86400 seconds

Step-by-step explanation:

The unit of measurement "day" (symbol d) is defined as 86,400 SI seconds.

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3 years ago
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Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has
Whitepunk [10]

Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0),  Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8  

The length of segment P'Q' = √2

The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

6 0
3 years ago
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