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1 year ago

Miss Osborne enlarges a 4-inch by 6-inch photograph by 2.5x. What are the dimensions of the enlarged photograph?

Mathematics

1 answer:

Valentin [98]1 year ago

4 0

Answer:

Step-by-step explanation:

enlarging the photograph by 2.5x means multiplying all of the sides of the photograph 2.5 times

Then

the dimensions of the enlarged photograph are:

Width = 4 ×2.5 = 10

Length = 6 ×2.5 = 15

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What is the inverse of y= 10^x +8?

shepuryov [24]

Answer:

$x = \log_{10}(y - 8)$ , where $y > 8$ .

Step-by-step explanation:

The question is asking for an expression for $x$ in terms of $y$ .

The first step is to move as many constants away from the side with $x$ as possible. In this question, that could be done by subtracting $8$ from both sides of the equation.

$y - 8 = 10^{x} + 8 - 8$ .

$y - 8 = 10^{x}$ .

Notice how $x$ is in the position of an exponent. Logarithms could help move $x$ out of that position.

For any base $b > 0$ :

$\log_{b} b^{x} = x\, \log_{b}\, b = x$ .

In this question, $10$ would be the base. That is: $b = 10$ .

Take the logarithm (with $10$ as the base) of both sides of the equation $y - 8 = 10^{x}$ :

Left-hand side: $\log_{10} (y - 8)$ .
Right-hand side: $\log_{10} \left(10^{x}\right) = x\, \log_{10}\left(10\right) = x$ .

Equate both sides to find an expression for $x$ :

$x = \log_{10}(y - 8)$ .

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2 years ago

The radius of the semicircle in the following composite figure is 8.5 millimeters. What is the total area of the composite figur

nydimaria [60]

Answer:

13.35 millimeter. (About)

Step-by-step explanation:

To find the area or circumference of any circle, you need to use pi. So, if we are trying to fine the area of a <em>semicircle, </em>you use the the formula:

πr²/2

So, if the radius is 8.5,

8.5 · 3.14 = 26.69

Now we divide it by 2.

26.69 = 13.345

Since the question is asking to round to the hundredths, the answer will be 13.35 millimeters.

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Mashutka [201]

Inverse variation:

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