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2 years ago

Let a and b be real numbers where a=/b=/c=/0 which of the following functions could represent the graph below?

Mathematics

1 answer:

Tresset [83]2 years ago

3 0

Answer: The second option; y = (x - a)^2*(x-b)^4

Step-by-step explanation:

Ok, we have that a and b are real numbers different than zero.

In the graph, we can see that the line touches the x-axis in two values. Now, if we would have an equation like:

y = x*(x - a)^3*(x - b)^3

then when x = 0 we would have:

y = 0*(0-a)^3*(0-b)^3 = 0

But in the graph, we can see that when x = 0, the value of y is different than zero, so we can discard options 1 and 3.

So the remaining options are:

y = (x - a)^2*(x-b)^4

y = (x - a)^5*(x - b)

Now, another thing you can see in the graph is that it is always positive.

Particularly the second option allows negative values for y because it has odd powers, then we can also discard this option.

(For example, if x > a and x < b we would have a negative value for y)

Then the only remaining option is y = (x - a)^2*(x-b)^4

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What two products would you add to find 713x48

umka21 [38]

9514 1404 393

Answer:

40·713 and 8·713

Step-by-step explanation:

When this multiplication is carried out "by hand", the usual sum of partial products is ...

8·713 + 40·713

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1 year ago

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If a(x) = 3x + 1 and b (x) = StartRoot x minus 4 EndRoot, what is the domain of (b circle a) (x)?

kiruha [24]

Answer:

$[1,\infty)$

Step-by-step explanation:

$b(x)=\sqrt{x-4}$

$a(x)=3x+1$

Since we want to know the domain of $(b \circ a)(x)$ , let's first consider the domain of the inside function, that is, that of $a(x)=3x+1$ . Every polynomial function has domain all real numbers.

So we can plug anything for function $a$ and get a number back.

Now the other function is going to be worrisome because it has a square root. You cannot take square root of negative numbers if you are only considering real numbers which that is the case with most texts.

Let's find $(b \circ a)(x)$ and simplify now.

$(b \circ a)(x)$

$b(a(x))$

$b(3x+1)$

$\sqrt{(3x+1)-4}$

$\sqrt{3x+1-4}$

$\sqrt{3x-3}$

Now again we can only square root positive or zero numbers so we want $3x-3 \ge 0$ .

Let's solve this to find the domain of $(b \circ a)(x)$ .

$3x-3 \ge 0$

Add 3 on both sides:

$3x \ge 3$

Divide both sides by 3:

$x \ge 1$

So we want $x$ to be a number greater than or equal to 1.

The option that says this is $[1,\infty)$

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

Give an example why option A fails:

A number in the given set is -2.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(-2)=3(-2)+1=-6+1=-5$ and $b(-5)=\sqrt{-5-4}=\sqrt{-9} \text{ which is not real}$ .

Give an example why option B fails:

A number in the given set is 0.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(0)=3(0)+1=0+1=1$ and $b(1)=\sqrt{1-4}=\sqrt{-3} \text{ which is not real}$ .

Give an example why option D fails:

While all the numbers in set D work, there are more numbers outside that range of numbers that also work.

A number not in the given set that works is 3.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(3)=3(3)+1=9+1=10$ and $b(1)=\sqrt{10-4}=\sqrt{6} \text{ which is real}$ .

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2 years ago

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Devon wants to write an equation for a line that passes through 2 of the data points he has collected. The points are (8, 5) and

ser-zykov [4K]

For this case we have the following equation:
$7x - 10y = 3
$
From here, we must substitute ordered pairs of the form:
(x, y)
If the ordered pair satisfies the equation, then it belongs to the line.
We have then:

For (8, 5):
We substitute the following values:
$x = 8

y = 5

7 (8) - 10 (5) = 3

56 - 50 = 3

6 = 3$
We observe that the equation is not satisfied and therefore, this point does not belong to the line.
Since one of the points does not belong to the line, then the equation is not a good model.

Answer:
It is not a good model. One of the points does not belong to the line.

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1 year ago

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At UF, there are always a few days between the end of classes and the beginning of final exams. These days are meant as a study

Natalija [7]

Answer:

This sample is not representative of all UF students, since those who are not local are not considered.

Step-by-step explanation:

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

However, the sample has to be representative

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected Buffalo residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents. This is not representative of all New York State residents, just Buffalo residents.

In this problem, we have that:

They conduct a phone survey (with local numbers selected at random from the student directory) calling people during "dead week". Will this sample be representative of all UF students?

They only call those students with local numbers.

However, in an university, it is expected that there will be a good percentage of non local students.

So this sample is not representative of all UF students, since those who are not local are not considered.

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2 years ago

If the perimeter of a square is 5 feet, how many inches long is each side of the square?

marysya [2.9K]

Well since we know that the perimeter of a square is four times the length of one of its sides. We just have to divide 5 by 4 to get the length of one side:

5feet /4 sides = 1.25 feet

And to finish off, we have to convert feet to inches:

<u>1 foot </u>= <u>12 inches</u>
1.25 feet x inches

x inches = 12 inches x 1.25 feet ÷ 1 foot
x inches = 15 inches

Therefore, each side is 15 inches long.

Hope this helps!

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2 years ago

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