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2 years ago

Which represents a function? Edge 2020.

Mathematics

1 answer:

neonofarm [45]2 years ago

7 0

The data set {(-8,-2),(-4,1),(0,-2),(2,3),(4,-4)} represents a function because for every distinct input x has only one output y, whereas all the other data sets have at least one point of x in which has two or more outputs of y.

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The quotient of (x^3+3x^2-4x-12)/(x^2+5x+6)

Elis [28]

Answer: The quotient is (x-2).

Step-by-step explanation:

Since we have given that

$f(x)=(x^3+3x^2-4x-12)\\\\and\\\\g(x)=x^2+5x+6\\\\So,\ \frac{\left(x^3+3x^2-4x-12\right)}{\left(x^2+5x+6\right)}$

Now, we have to find the quotient of the above expression.

So, here we go:

$Factorise\ (x^3+3x^2-4x-12)\\\\=\left(x^3+3x^2\right)+\left(-4x-12\right)\\\\=-4\left(x+3\right)+x^2\left(x+3\right)\\\\=\left(x+3\right)\left(x^2-4\right)$

Now, we will divide the above simplest form with g(x):

$\frac{\left(x+3\right)\left(x^2-4\right)}{\left(x+2\right)\left(x+3\right)}\\\\=\frac{x^2-4}{x+2}\\\\=\frac{\left(x+2\right)\left(x-2\right)}{x+2}\ using\ (a^2-b^2)=(a+b)(a-b)\\\\=x-2$

Hence, the quotient is (x-2).

6 0

3 years ago

Read 2 more answers

What is the arc measure, in degrees, of major arc \stackrel{\large{\frown}}{ADC} ADC ⌢ A, D, C, start superscript, \frown, end s

Mrrafil [7]

Answer:

$\stackrel{\large{\frown}}{ADC} = 186^{\circ}$

Step-by-step explanation:

Given

See attachment

Required

Determine the measure of $\stackrel{\large{\frown}}{ADC}$

$The\ sum\ of\ angles\ in\ a\ circle\ is$ $360^{\circ}$ .

So, we have:

$\stackrel{\large{\frown}}{ADC} + \stackrel{\large{\frown}}{APB} + \stackrel{\large{\frown}}{BPC} = 360^{\circ}$

Where:

$\stackrel{\large{\frown}}{APB} = 70^{\circ}$

$\stackrel{\large{\frown}}{BPC} = 104^{\circ}$

Substitute these values in the above equation.

$\stackrel{\large{\frown}}{ADC} + 70^{\circ} +104^{\circ} = 360^{\circ}$

$\stackrel{\large{\frown}}{ADC} + 174^{\circ} = 360^{\circ}$

Collect Like Terms:

$\stackrel{\large{\frown}}{ADC} = 360^{\circ} - 174^{\circ}$

$\stackrel{\large{\frown}}{ADC} = 186^{\circ}$

7 0

3 years ago

Read 2 more answers

To determine whether the inverse of a function is a function you can perform the horizontal line test.

iris [78.8K]

Answer:

$\boxed{\text{TRUE}}$

Step-by-step explanation:

If a horizontal line intersects the graph of a function in all places at exactly one point (the horizontal line test), the inverse of the function is also a function.

For example, the inverse of a hyperbola (like ƒ(x) =1/x) is a function, because every horizontal line intersects with the graph at exactly one point.

However, the inverse of a parabola (like ƒ(x) = x²) is not a function, because a horizontal line intersects with the graph at two points.

7 0

3 years ago

If (x + 1)(x-3) = 5, then which of the following statements is true?

bixtya [17]

Answer:

x=−2 or x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x2−2x−3=5

Step 2: Subtract 5 from both sides.

x2−2x−3−5=5−5

x2−2x−8=0

Step 3: Factor left side of equation.

(x+2)(x−4)=0

Step 4: Set factors equal to 0.

x+2=0 or x−4=0

x=−2 or x=4

5 0

3 years ago

How do you do this ??

svet-max [94.6K]

The purpose of the grid is to help you record possible and impossible combinations. The repeat of the headings 1st, 2nd, 3rd, 4th helps you compare to both shirt color and name.

Each given statement has certain implications. You are expected to be able to determine as many of those as you can, and mark the grid accordingly.

The first statement says two girls slide down before two other girls. This means the first two girls listed cannot be 3rd or 4th in line, and the last two girls listed cannot be 1st or 2nd in line. It also means that none of the named girls is wearing the blue shirt (so Madeline must be wearing it). These implications are marked in the attachment with X and a circled 1, to indicate to you that the first statement was where we got the X. The X is used to signify an impossible combination.

The second statement tells you the purple shirt will not be 3rd or 4th in line, since at least two girls are after it. It tells you that Alexis is not wearing purple or yellow (so must be wearing white), and it tells you that Alexis and the yellow shirt are not first in line. (We alread knew that about Alexis.)

The third statement lets you finish the problem. We just found that Alexis is wearing the white shirt, so it tells you Madeline is 2nd in line and Alexis is 3rd. (Alexis is 3rd or 4th, but so is Lauren. The only way Madeline can be next to Alexis is for Madeline to be 2nd and Alexis 3rd.) The check marks labeled with a circled 3 are the conclusions we drew from statement 3.

Since the yellow shirt is not first, Lauren must be wearing it 4th in line.

The final conclusion is ...

Hanna, purple
Madeline, blue
Alexis, white
Lauren, yellow

Once you have identified a combination, it can help to mark off the others in that row and column (of the group of 4 rows and columns) as being impossible. This can narrow the choices for the others. I didn't do that here because it makes the diagram busier and the sequence of marks less clear.

_____

It is a good idea to check your final answer with the original problem statements to make sure the answer is consistent with them.

7 0

3 years ago