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Nat2105 [25]
3 years ago
7

Write a variable expression for each. Tell what the variable represents I NEED HELP!!!

Mathematics
1 answer:
Digiron [165]3 years ago
5 0
1. x - 16
2. x + 5
3. x divided by 48 (I don’t have the division symbol.)
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From Sunday to Friday, Desiree jogged the same number of miles. On
jok3333 [9.3K]

Answer:

I believe she did 4.5 miles each day

Step-by-step explanation: all I did was divide 52 by 12

Tell me if im wrong

5 0
3 years ago
Find x?<br> In 3x - In(x - 4) = ln(2x - 1) +ln3
earnstyle [38]

Answer:

x = \displaystyle \frac{5 + \sqrt{17}}{2}.

Step-by-step explanation:

Because 3\, x is found in the input to a logarithm function in the original equation, it must be true that 3\, x > 0. Therefore, x > 0.

Similarly, because (x - 4) and (2\, x - 1) are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, x > 4.

Let a and b represent two positive numbers (that is: a > 0 and b > 0.) The following are two properties of logarithm:

\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right).

\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right).

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}

Right-hand side of this equation:

\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right).

Equate these two expressions:

\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}.

The natural logarithm function \ln is one-to-one for all positive inputs. Therefore, for the equality \begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned} to hold, the two inputs to the logarithm function have to be equal and positive. That is:

\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1).

Simplify and solve this equation for x:

x^2 - 5\, x + 2 = 0.

There are two real (but not rational) solutions to this quadratic equation: \displaystyle \frac{5 + \sqrt{17}}{2} and \displaystyle \frac{5 - \sqrt{17}}{2}.

However, the second solution, \displaystyle \frac{5 - \sqrt{17}}{2}, is not suitable. The reason is that if x = \displaystyle \frac{5 - \sqrt{17}}{2}, then (x - 4), one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be \displaystyle \frac{5 + \sqrt{17}}{2}.

Therefore, x = \displaystyle \frac{5 + \sqrt{17}}{2}.

7 0
3 years ago
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) + 20?
Veronika [31]
The correct answer is the graph is shifted up by 20 units.

When a number is added to or subtracted from f(x), it translates the graph of f(x) either up or down or we can say it moves the graph of f(x) vertically up or down. Addition of a number moves it vertically up and subtraction moves it vertically down.

In this case 20 is being added to f(x), so this will shift the graph of f(x) 20 units up.
7 0
3 years ago
Find the volume of this rectangular pyramid.
LekaFEV [45]

Answer:

25 ft

Step-by-step explanation:

You need to add 9+7+9.

There are two 9s and just one 7. 9+9 is 18 and 18+7 is 25

5 0
2 years ago
What is 6divided by 2(1+2)
Aloiza [94]

Answer: 1

Step-by-step explanation:

6/2(1+2)

6/2(3)

6/6

1

7 0
2 years ago
Read 2 more answers
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