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3 years ago

A factory can make 120 backpacks in 3 hours.how long will it take to make 600 backpacks?

Mathematics

2 answers:

max2010maxim [7]3 years ago

8 0

It will take 15 hours

kirill115 [55]3 years ago

8 0

the right answer for K12 is 15 h

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iVinArrow [24]

Answer:

13.5

Step-by-step explanation:

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2 years ago

Please Help me with the last three questions! It is urgent!

MrMuchimi

Answers:
1. X= 0
2. X= 0
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You can use this method to solve them step by step, hope it will help!

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2 years ago

Item 16 Solve the equation. −4/9f=−3

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The answer is f= $\frac{4}{27}$

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2 years ago

Read 2 more answers

How to reduce into simpler terms.?

Sveta_85 [38]

Answer:

The simplest form of the fraction $\frac{45}{100}$ is $\frac{9}{20}$ .

i.e.

$\frac{45}{100}=\frac{9}{20}$

Step-by-step explanation:

Here are some simple observations regarding how to reduce a fraction into simpler terms:

A fraction is reduced to lowest or simplest terms by finding an equivalent fraction in which the numerator and denominator are as small as possible.

In order to reduce a fraction to lowest or simplest terms, divide the numerator and denominator by their (GCF). Note that (GCF) is also called Greatest Common Factor .

So, lets take a sample fraction and reduce into simpler terms.

Considering the fraction

$\frac{45}{100}$

$\mathrm{Find\:a\:common\:factor\:of\:}45\mathrm{\:and\:}100\mathrm{\:in\:order\:to\:cancel\:it\:out}$

$\mathrm{Greatest\:Common\:Divisor\:of\:}45,\:100:\quad 5$

$\mathrm{Factor\:out\:}5\mathrm{\:from\:the\:numerator\:and\:the\:denominator}$

$45=5\cdot \:9\mathrm{,\:\quad }100=5\cdot \:20$

$\frac{45}{100}=\frac{5\cdot \:\:9}{5\cdot \:\:20}$

$\mathrm{Cancel\:the\:common\:factor:}\:5$

$=\frac{9}{20}$

Therefore, the simplest form of the fraction $\frac{45}{100}$ is $\frac{9}{20}$ .

i.e.

$\frac{45}{100}=\frac{9}{20}$

4 0

3 years ago

Find x? 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

2 years ago