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3 years ago

The average rate of change of g(x) between x = 4 and x = 7 is 5/6 . Which statement must be true?

Mathematics

1 answer:

Blizzard [7]3 years ago

6 0

Answer:

$\frac{5}{6}=\:\frac{g\left(7\right)-g\left(4\right)}{7-4}$ would be the correct statement.

Step-by-step explanation:

As we know that

Average rate of change = Change in output / Change in input

= Δy / Δx

$=\frac{y_{2} -y_{1}}{x_{2} -x_{1}}$

$=\frac{g(x_{2})-g(x_{1})}{x_{2}-x_{1}}$

$=\frac{g(7)-g(4)}{7-4}$

As the average rate of change of g(x) between x = 4 and x = 7 is 5/6.

$\:Average\:rate\:of\:change\:=\:\frac{g\left(7\right)-g\left(4\right)}{7-4}$

$\frac{5}{6}=\:\frac{g\left(7\right)-g\left(4\right)}{7-4}$

Therefore, $\frac{5}{6}=\:\frac{g\left(7\right)-g\left(4\right)}{7-4}$ would be the correct statement.

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Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a horizontal line crossing the y axis

Lesechka [4]

Answer:

The limit of the function does not exists.

Step-by-step explanation:

From the graph it is noticed that the value of the function is 6 from all values of x which are less than 2. At x=2, the line y=6 has open circle. It means x=2 is not included.

For x<2

$f(x)=6$

The value of the function is -3 from all values of x which are greater than 2. At x=2, the line y=-3 has open circle. It means x=2 is not included.

For x>2

$f(x)=-3$

The value of y is 1 at x=2, because of he close circles on (2,1).

For x=2

$f(x)=1$

Therefore the graph represents a piecewise function, which is defined as

$f(x)=\begin{cases}6& \text{ if } x2 \end{cases}$

The limit of a function exist at a point a if the left hand limit and right hand limit are equal.

$lim_{x\rightarrow a^-}f(x)=lim_{x\rightarrow a^+}f(x)$

The function is broken at x=2, therefore we have to find the left and right hand limit at x=2.

$lim_{x\rightarrow 2^-}f(x)=6$

$lim_{x\rightarrow 2^+}f(x)=-3$

$6\neq-3$

Since the left hand limit and right hand limit are not equal therefore the limit of the function does not exists.

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2 years ago

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Talja [164]

Answer:

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Step-by-step explanation:

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A tree is 58 inches tall. how tall is it in feet and inches

mart [117]

A foot is 12 inches.
12 can go into 58 evenly 4 times, since 12• 4 equals 48 but 12 • 5 equals 60. This means that the tree is at least 4 feet. Then to find the leftover inches we do 58-48 equals 10, therefore the answer is 58 inches translates to 4 feet and 10 inches.

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3 years ago

You spin the spinner once.<br> What is P(6)?

lyudmila [28]

Answer:

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Step-by-step explanation:

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3 years ago

Kimane and a friend picked apples. Kimane picked 4 2/3 and his friend picked 5 5/6 pounds. About how many pound of apples do the

Gala2k [10]

Answer:

$9\dfrac{1}{2}$

Step-by-step explanation:

To find many more pounds of apples Kimane and his friend needs to get, we first need to find out how many pounds of apples they picked together.

Kimane = $4\dfrac{2}{3}$

Friend = $5\dfrac{5}{6}$

We add them together to find out how many pounds of apples they currently have.

Total Pounds = $4\dfrac{2}{3}+5\dfrac{5}{6}$

Just to make the equation clearer, we separate the whole numbers from the fractions.

$=4+5+\dfrac{2}{3}+\dfrac{5}{6}$

$=9+\dfrac{2}{3}+\dfrac{5}{6}$

Now since we cannot add the 2 fractions directly since they have different denominators, we need to convert the $/dfrac{2}{3}$ into a fraction with the same denominator.

We multiply both the numerator and denominator by 2 to have the same denominator.

$\dfrac{2*2}{3*2}=\dfrac{4}{6}$

So now we have:

$=9+\dfrac{4}{6}+\dfrac{5}{6}$

$=9+\dfrac{9}{6}or1\dfrac{1}{2}$

$Total Pounds = 10\dfrac{1}{2}$

Now that we know how many pounds Kimane and his friend collected, we simply subtract 20 and the total amount Kimane and his friend had already collected.

$20-10\dfrac{1}{2}$

$=9\dfrac{1}{2}$

So Kimane and his friend still need to get $9\dfrac{1}{2}$ more pounds of apples to get 20 pounds of apples.

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