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3 years ago

What is the equation for this graph? A. y=2x + 1 B. y=1/2x + 1 C. y=1/2x D. y=2x

Mathematics

1 answer:

MrRa [10]3 years ago

8 0

B is the answer :)))

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Let f be a differentiable function such that f(0) = -5 and f'(x) is less than or equal to 3 for all x. Of the following, which i

stepladder [879]

E) 2
Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5
Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.

3 0

3 years ago

Sorry about the bad quality :(

dmitriy555 [2]

Answer:

Yes, y varies directly with x, and the equation is $y=1.6x$ .

Step-by-step explanation:

To check where there is a direct relationship between x and y, we need to check whether all the x,y pairs we have fit some rule:

$y=k\times x$ .

For the first pair (x=4, y=6.4),

$6.4=k\times 4$

Therefore $k = 1.6$ .

For the second pair (x=7, y=11.2),

$11.2=k\times 7$

Therefore $k = 1.6$ .

For the third pair (x=10, y=16),

$16=k\times 10$

Therefore $k = 1.6$ .

For the second pair (x=13, y=20.8),

$20.8=k\times 13$

Therefore $k = 1.6$ .

So x does directly vary with y, and we have found out that $k=1.6$ .

4 0

4 years ago

Read 2 more answers

You offer senior citizens a 20% discount on their tune-ups at your gas station. Assuming that an average of 50 senior citizens g

andreyandreev [35.5K]

Percentage of discount given to senior citizens for tune-ups at the gas station = 20%
Average number of senior citizens visiting the gas station per month = 50
Average price of tune-up before discount = $49.95
Total amount that would
have been collected before discount = 49.95 * 50
= 2497.50 dollars
Total amount of discount given = (20/100) * 2497.50
= 499.50 dollars
I hope that the procedure is clear enough for you to understand.

6 0

3 years ago

What is the perimeter of ALMN? O 8 units O 9 units O 6+ V10 units O 8+ V10 units

Ludmilka [50]

- The perimeter for it is 8+V10 Units.

5 0

3 years ago

Need help asap please!

RUDIKE [14]

Answer:

$\textsf{$f(1) = \boxed{1}$ , meaning when a $\boxed{1}$ is rolled on the die, the player is awarded}\\\\ \textsf{ $\boxed{1}$ point. This interpretation $\boxed{\sf makes \; sense}$ in the context of the problem.}$

$\textsf{$f(4.5) = \boxed{8}$ , meaning when a $\boxed{4.5}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{8}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}$

$\textsf{$f(10) = \boxed{19}$ , meaning when a $\boxed{10}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{19}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}$

$\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}$

Step-by-step explanation:

Given function:

$f(x)=2x-1$

where:

x is the value rolled on the six-sided die.
The sides of the die are labelled 1 to 6.

----------------------------------------------------------------------------------------------------

f(1) means the value of the function when x = 1.

Therefore, substitute x = 1 into the given function to find f(1):

$\begin{aligned}x=1 \implies f(1)&=2(1)-1\\&=2-1\\&=1\end{aligned}$

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f(4.5) means the value of the function when x = 4.5.

Therefore, substitute x = 4.5 into the given function to find f(4.5):

$\begin{aligned}x=4.5 \implies f(4.5)&=2(4.5)-1\\&=9-1\\&=8\end{aligned}$

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6. Therefore, rolling a "4.5" does not make sense.

----------------------------------------------------------------------------------------------------

f(10) means the value of the function when x = 10.

Therefore, substitute x = 10 into the given function to find f(10):

$\begin{aligned}x=10 \implies f(1)&=2(10)-1\\&=20-1\\&=19\end{aligned}$

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6. Therefore, rolling a "10" does not make sense.

----------------------------------------------------------------------------------------------------

The domain of a function is the set of all possible x-values.

As the faces of the six-sided die are labelled 1 to 6, the only possible values of x are 1, 2, 3, 4, 5 and 6.

$\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}$

The domain can also be written as:

$\{x \in \mathbb{N} \; | \; 1 \leq x \leq 6 \}$

or $\{x \in \mathbb{Z} \; | \; 1 \leq x \leq 6 \}$

8 0

1 year ago