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3 years ago

It x, y, and z are positive intergers and 3x = 4y = 7z, then the least possible value of x + y + z is???

1 answer:

5 0

$3x = 4y = 7z \\ \Rightarrow \begin{cases}3x - 4y = 0 \\4y - 7z = 0 \\ 7z - 3x = 0\end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{4}{3} y\\4y - 7z = 0 \\ 7z - 3( \frac{4}{3}y) = 0\end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{4}{3} y\\4y - 7z = 0 \\ 7z - 4y= 0\end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{4}{3} y\\ y \\ z = \frac{4}{7}y \end{cases} \\ x,y,z\: are\: intergers\Rightarrow y=LCM(3,7)=21\Rightarrow x = 28,z = 12 \\ \Rightarrow x + y + z = 61$

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Which of the following is true with respect to the following functions:

Mkey [24]

The option that is true with regard to the following functions is Option B. "The domain g(x) and h(x) include all real number while the domain of i(x) and h(x) are restricted"

<h3>What is the explanation for the above?</h3>

Lets examine f(x) = 3x + 14

Note that this function is indicative of a straight-line. See the attached graph for function 1. Note that it doesn't have any end points. That is, it is Asymptote.

Let us examine h(x) = 3ˣ + 1

This represents an exponential graph. Just like the function above it doesn't have any end point. It however has an asymptote:

y = 0

Let us look at F'(x) = Log₃ (x = 1).

This is indicative of logarithm graph. It doesn't have any end but has an asymptote x == 0

Let us take a look at g(x) = X⁴ + 3x² - 14

Notice that in the mid point there is an end point given as (0, -14). Thus, it is correct to state that the function in Option B is the only one that exhibits end behavior and as such is restricted.

Learn more about functions:
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1 year ago

Mrs. Williams is crocheting a blanket for her niece. So far the blanket has a radius of 5 feet. She plans to put one final round

Irina18 [472]

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3 years ago

Explain the differences between adding and multiplying radical expressions using 2 examples you create.

ivann1987 [24]

Answer:

When you multiply radical expressions you multiply the numbers under the radical symbols.3–√×7–√=21−−√

When you add radical expression you CANNOT add the numbers under the radical symbols.

3–√+7–√≠10−−√

Step-by-step explanation:

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2 years ago

When three pipes fill a pool, they can finish in 12 hours. Two of the pipes can finish in 18 hours if they are working together.

ladessa [460]

3 pipes take 12 hours
⇒ In 1 hour, the 3 pipes can fill 1/12 of the pool

2 of the pipes take 18 hours
⇒ in 1 hour, the 2 pipes can fill 1/18 of the pool

In 1 hour, the third pipe alone can fill :

$\dfrac{1}{12} - \dfrac{1}{18} = \dfrac{3}{36} - \dfrac{2}{36} = \dfrac{1}{36} \text { of the pool}$

Time needed :

$1 \div \dfrac{1}{36} = 1 \times 36 = 36 \text { hours}$

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Answer: It will take 36 hours for the third pipe to fill the pool.
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5 0

3 years ago

Read 2 more answers

What is the slope of the line passing through (2,9) and (2,-14)

Brilliant_brown [7]

Answer:

The slope is undefined

Step-by-step explanation:

When graphed, the two points form a vertical line, since we can't divide the slope by zero thw slope is considered as undefined

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3 years ago