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mart [117]
2 years ago
8

5 plus square root of 45 divided by 4​

Mathematics
2 answers:
Minchanka [31]2 years ago
8 0

5+ sqrt45/4

5+5/4

6.75

exis [7]2 years ago
4 0
5 + square root of 45 divided by 4
= 5 + 6.7 divide by 4
= 5 + 1.675
= 5.675
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Which describes the location of 2 /3 on the number line? A) between 1/3 and 2 5 B) between 2 /5 and 1 /2 C) between 1 /2 and 3 /
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Answer:

2/3 lies between 1 and 2

Option C

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3 years ago
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The lengths of the diagonals of a rhombus are 18 cm and 24 cm. What is its perimeter and what is the distance between the parall
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Try this option:
note, that distance between the parallel sides is shown via formula of area.
If it is possible, check the arithmetic.

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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
At the bookstore, 40 copies of a popular paperback book fit perfectly on a 5-foot shelf. How many copies of this book would fit
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Answer:

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The first step is to find the number of books that will fit in the shelve per foot

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bixtya [17]

Answer:

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Step-by-step explanation:

4(x+5)= 24

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-20 -20

____________

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___ ____

4 4

x= 1

7 0
3 years ago
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