Which set of ordered pairs represents a function?
{(-6,-4), (1, -7), (-4, 3), (-4, 8)}
{(-8, -3), (-8, 9), (9, 6), (1, -4)}
{(4,1), (-6, 6), (5,-2), (-4,1)}
{(-3, 6), (-1,0), (-8, 1), (-8, -3)}

Answer:

B (2nd option)

Step-by-step explanation:

Factor each one.

6x^2+39x-21 is divisible by 3 -> 3(2x^2+13x-7) -> 3(2x-1)(x+7)

6x^2+54x+84 is divisble by 6 -> 6(x^2+9x+14) -> 6(x+2)(x+7)

The greatest common factor is 3(x+7), so taking that out of each polynomial, we have (2x-1) and 2(x+2). The least common multiple is the greatest common factor*(2x-1)*2(x+2) which, simplifying, is 12x^3+102x^2+114x-84, or B.

Based on the random sample of beach lengths taken, the probability of a randomly selected beach having a length of 12 miles is C. 0.

Beach length is considered a continuous variable which takes a numerically positive form because it can have any one of infinite possible values.

As a result, there is no possibility that a beach chosen at random will have a given length of 12 miles which means that the probability is 0.

In conclusion, the probability that a selected beach has a length of 12 miles is 0.

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The limit of f(x) as x goes to 1 will not exist for function III.

A limit is given by the value of function f(x) as x tends to a value. For a function with different lateral limits at a point x = a, the limit will not exist at the point x = a. Additionally, the limit may not exist at a point if there is a non-removeable discontinuity.

Factoring the function 1, the limit will be given as follows:

[tex]\lim_{x \rightarrow 1} \frac{1 - x^2}{x - 1} = \lim_{x \rightarrow 1} \frac{(1 - x)(1 + x)}{x - 1} = \lim_{x \rightarrow 1} -(1 +x) = -2[/tex]

Hence the limit exists.

Factoring the function 2, the limit will be given as follows:

[tex]\lim_{x \rightarrow 1} \frac{x^2 - x^3}{x^2 - 1} = \lim_{x \rightarrow 1} \frac{x^2(1 - x)}{(x - 1)(x + 1)} = \lim_{x \rightarrow 1} -\frac{x^2}{x + 1} = -\frac{1}{2}[/tex]

Hence the limit exists.

Factoring the function 3, the limit will be given as follows:

[tex]\lim_{x \rightarrow 1} \frac{x + 1}{x^2 - 1} = \lim_{x \rightarrow 1} \frac{x + 1}{(x - 1)(x + 1)} = \lim_{x \rightarrow 1} \frac{1}{x - 1}[/tex]

Non-revemoveable discontinuity, as we can't remove x - 1 for the denominator, ence the limit does not exist for function III.

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The function of the S&P Capital IQ Excel plug-in allows users to extract company data directly from CapIQ’s database and calculate the desired financial metrics using the CapIQ formulas is; Formula Builder

S&P Capital IQ Excel plug is a tool that helps to provide access to financial data, news and analytics for real estate investment trusts (REITs) including other industry data on bank & thrifts, financial services, insurance, real estate and other markets.

Now, when the Excel Plug-in has been installed, a new toolbar will be

available in Excel. This toolbar is called formula builder and it is useful for the following use in  S&P Capital;

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Answer:

(2+n)-3

That's how you write if that is what you want.

Answer: 9 units

Step-by-step explanation: R is at -7 and is at 2. Think of how far away -7 is from 2. -7+9=2.

Answer:

9 units

Step-by-step explanation:

Length of a segment RV is a difference of values of V and R. According to the number line, R is -7 and V is 2.

The difference or change in two values is 2 - (-7) = 2 + 7 = 9 units.

Henceforth, the segment RV is 9 units.

The  statement that is not true for​ goodness-of-fit tests is: A. Expected frequencies must be whole numbers.

Goodness-of-fit tests can be defined as the test conducted to help find out whether the observe value work hand in hand with expected value or the observe value is different from the expected value.

The statement is not true because it is not must for expected frequencies  to be whole number  despite the fact that expected  frequencies are whole numbers.

Therefore the  statement that is not true for​ goodness-of-fit tests is: A. Expected frequencies must be whole numbers.

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Answer:

Step-by-step explanation:

3.5805

The length of segment XY is 52 units and the length of segment HD is 26 units

Secant lines (a)

To do this, we make use of the following intersecting secant theorem

VZ * VW = VY * VX

Substitute the known values in the above equation

12 * 40 = VY * 8

Divide by 8

12 * 5 = VY

Evaluate the product

VY = 60

The length VX is

XY = VY - VX

Substitute the known values in the above equation

XY = 60 - 8

Evaluate

XY = 52

Hence, the length of segment XY is 52 units

Secant lines (b)

To do this, we make use of the following intersecting secant theorem

GH^2 = HC * HD

Substitute the known values in the above equation

13^2 = 6.5 * HD

Divide by 6.5

13^2/6.5 = HD

Evaluate the quotient

26 = HD

The length HD is

HD = 26

Hence, the length of segment HD is 26 units

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The number of calories per ounce of soda is 10

The given parameters are:

Calories = 50

Ounces = 5

Let the number of calories be y and the ounces be x.

So, we have:

y = kx

Substitute y = 50 and x = 5

50 = 5k

Divide by 5

k = 10

Substitute k = 10 in y = kx

y = 10x

See attachment for the graph of the relationship between the number of calories and the number of ounces

In (a), we have:

k = 10

This means that the number of calories per ounce of soda is 10

The unit rate and the slope represent the same and they have the same value

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Answer:

2

Step-by-step explanation:

a23

2 is column and 3 is row

subtracting (c ^ 2 - 4c + 7) from (7c ^ 2 - 5c + 3) would give 6c² - 9c -4

Given the expressions as

(c ^ 2 - 4c + 7)

(7c ^ 2 - 5c + 3)

We are to substract expression 2 from expression 1

In doing this, we need to know the BODMAS rule ( bracket, of, division, multiplication, addition and subtraction). This would help in finding the solution

(7c ^ 2 - 5c + 3) -  (c ^ 2 - 4c + 7)

Expand the bracket

7c² - 5c + 3 - c² - 4c + 7

collect like terms

7c²- c² - 5c - 4c + 3 - 7

Add or substract the like terms

6c² - 9c -4

Thus, subtracting (c ^ 2 - 4c + 7) from (7c ^ 2 - 5c + 3) would give 6c² - 9c -4

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Answer:6c^2-c-4

Step-by-step explanation:

(7c^2-5+3)-(c^2-4c+7)

7c^2-5c+3-c^2+4c-7

Rearrange the terms

7c^2-c^2-5c+4c+3-7

Combine like terms

6c^2-c-4

By using the PEMDAS order of operations, we get 3(6+7) = 39.

The equation be 3(6+7) then the correct answer is 34.

The order of operations exists as a law that describes the proper sequence of stages for estimating a math expression. We can recognize the order utilizing PEMDAS: Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right).

Given: 3(6+7)

By using the PEMDAS order of operations, we get

(6+7) = 13

Then we get

3(6+7) = 3 [tex]*[/tex] 13

= 39.

Therefore, the value of 3(6+7) = 39.

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Based on the fact that Steve was originally driving the speed limit and then stopped a few hours and drove slower, the situation models a piecewise defined function.

This is a type of function where there are two or more parts joined together. In other words, there are two equations to represent the different parts of the function.

In this case, Steve was driving at a certain speed. This is one function. Then he stopped for a couple of hours which is another function. Then the last function has him driving slower than the speed limit.

In conclusion, this is a defined piecewise function.

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Answer:

Step-by-step explanation:

Comment and Answer

This is a very well laid out proof. It would good for you to see how carefully this this proof has been set up.

Step Three says

DE = DF ÷ 2

The problem is that at least 2 of the choices will work. I think the best reason is that it is the definition of bisect. The previous statement says in language what  statement three says in algebraic notation. So statement 2 is the given statement. Statement 3 tells us that DE is 1/2 DF because it is bisected.

Answer A

Answer: 4/7

Step-by-step explanation:

Slope = Rise/Run = (7-3)/(9-2) = 4/7

Answer:

4/7

Step-by-step explanation:

The formula to find the slope is: (change in y)/(change in x)

Or also: Rise/Run

The change in y is: 3 --> 7 which is +4

The change in x is: 2 --> 9 which is +7

So the (change in y)/(change in x) will be 4/7.

Since 4/7 cannot be simplified further, that is our final answer.

Answer:

(x-7)/9

Step-by-step explanation:

F(c) = 9x + 7

y = 9x + 7  Now switch the y and the x and solve for y

x = 9y + 7  Subtract 7 from both sides

x - 7 = 9y  Divide both sides by 9

(x-7)/9

Answer:

76 sodas

Step-by-step explanation:

152 divided by 2

Answer: 76 sodas

Step-by-step explanation:

To find the sodas, use the data you see. Bottles of water are twice the sodas. So divided water by 2 to get the sodas.
152 ÷ 2 = 76 ( sodas ) . Hope it helps !

Answer:

[tex]\dfrac{3x+6}{x^2+x-6}[/tex]

Step-by-step explanation:

Notice that we can factor the expression [tex]x^2-x-2[/tex] as [tex](x-2)(x+1)[/tex]. Similarly, we can express [tex]3x+3[/tex] as [tex]3(x+1)[/tex]. Now, we can multiply the fraction together as [tex]\dfrac{(x+2)(3)(x+1)}{(x-2)(x+1)(x+3)} = \dfrac{3(x+2)}{(x-2)(x+3)} = \boxed{\dfrac{3x+6}{x^2+x-6}}[/tex].

Step-by-step explanation:

i know this but i don't have time now

Andrea has one less than she started with , Blake has one more than he started with. Therefore , Blake has two more than he started with. Therefore, the correct answer is option B.

Andrea told that 'Blake and I started out with the same number of marbles, but I gave him one of mine. Now Blake has one more than me. '

Here Andrea is wrong with her conclusion. Let's understand this by taking some values.

Let's consider that Andrea and Blake both have 4 marbles(Since it is given that 'they have equal number of marbles). And Andrea gave one of her marbles to Blake. So number of marbles of Andrea will become 4-1=3. And number of marbles of Blake = 4+1 =5. If we compare them , Blake has 2 more marbles than Andrea.

Therefore, the correct answer is option B.

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"Your question is incomplete, probably the complete question/missing part is:"

Suppose that Andrea told you that “Blake and I started out with the same number of marbles, but I gave him one of mine. Now Blake has one more marble than me.” Is Andrea’s reasoning incorrect? If so, how can you help Andrea identify her misunderstanding?

A. Blake needs to take one of his marbles away first. Then, Andrea can give him one of hers. Thus, Blake will have one more than Andrea.

B. Andrea has one less than she started with Blake has one more than he started with. Therefore, Blake has two more than Andrea.

C. Andrea meant to say that after giving Blake one of her marbles, show would have one less than Blake.

D. Andrea meant to say that she took one of her marbles away and not give it to Blake. Therefore, Blake would only have one more than her.

Step-by-step explanation:

we know from the laws of motion that in the equation

h = 20t - 1.86t²

the gravitational acceleration is in the factor of the t² term.

h = v0t + 1/2 × g × t²

v0 being the initial velocity (20 m/s).

and we can therefore see, that the gravitational acceleration "a" on Mars is 2×1.86 = 3.72 m/s²

(a)

the velocity v after 2 seconds is (first law of motion)

v = v0 + at = 20 - 3.72×2 = 12.56 m/s

gravity pulling down, so negative acceleration.

(b)

first we need the time when the rock is at 25 m.

25 = 20t - 1.86t²

0 = -1.86t² + 20t - 25

the solution to a quadratic equation is always

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = t

a = -1.86

b = 20

c = -25

t = (-20 ± sqrt(400 - 4×-1.86×-25))/(2×-1.86) =

= (-20 ± sqrt(214))/-3.72

t1 = (-20 + 14.62873884...)/-3.72 =

= 1.443887409... s ≈ 1.44 s

t2 = (-20 - 14.62873884...)/-3.72 =

= 9.308800763... s ≈ 9.31 s

that means, on its way up the rock reached 25m after

1.44 s.

on its way down the rock reached 25 m after

9.31 s.

velocity 0 (the rock came to a stop before falling back down) was after

0 = 20 - 3.72t

3.72t = 20

t = 20/3.72 = 5.376344086... s

that means the rock was falling after this point back to the ground and was gaining speed again.

that accelerating phase until the rock was again at 25 m was

9.308800763... - 5.376344086... = 3.932456677... s

long

the velocity at these points was

v-up = 20 - 3.72×1.443887409... = 14.62873884... m/s ≈

≈ 14.63 m/s

v-down = 0 + 3.72×3.932456677... = 14.62873884... m/s ≈

≈ 14.63 m/s

as expected : the rock did a perfectly symmetric flight path between the two 25 m marks.

so time and speed on both sides had to be identical.

but we have proven it.

Answer:

a)  12.56 m/s

b) up:  14.63 m/s (2 d.p.)

   down:  -14.63 m/s (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{The Constant Acceleration Equations (SUVAT)}\\\\s = displacement in m (meters)\\u = initial velocity in m s$^{-1}$ (meters per second)\\v = final velocity in m s$^{-1}$ (meters per second)\\a = acceleration in m s$^{-2}$ (meters per second per second)\\t = time in s (seconds)\\\\When using SUVAT, assume the object is modeled\\ as a particle and that acceleration is constant.\end{minipage}}[/tex]

The average gravitational acceleration on Mars is 3.721 m/s² (about 38% of that of Earth).  The fact that the rock is thrown from the surface of Mars rather than the surface of Earth is of no consequence when using the equations of constant acceleration (SUVAT equations) as long as acceleration is not used in the calculations.

Given:

[tex]s=20t-1.86t^2, \quad u=20, \quad t=2[/tex]

[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies 20(2)-1.86(2)^2 & = \dfrac{1}{2}(20+v)(2)\\\\32.56 & = 20+v\\\\v & = 32.56-20\\\\v & = 12.56\:\: \sf m/s\end{aligned}[/tex]

Therefore, the velocity of the rock after 2 s is 12.56 m/s.

Find the time when the height of the rock is 25 m:

[tex]\begin{aligned}20t-1.86t^2 & = s\\\implies 20t-1.86t^2 & = 25\\1.86t^2-20t+25 & = 0\end{aligned}[/tex]

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore:

[tex]a=1.86, \quad b=-20, \quad c=25[/tex]

[tex]\implies t=\dfrac{-(-20) \pm \sqrt{(-20)^2-4(1.86)(25)} }{2(1.86)}[/tex]

[tex]\implies t=\dfrac{20 \pm \sqrt{214}}{3.72}[/tex]

[tex]\implies t=9.308800763..., 1.443887409...[/tex]

Therefore, the height of the rock is 25 m when:

To find the velocity (v) of the rock at these times, substitute the found values of t into the equation, along with s = 25 and u 20 m/s:

[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies v & = \dfrac{2s}{t}-u\\\\v & = \dfrac{2(25)}{t}-20\\\\v & = \dfrac{50}{t}-20\\\\\end{aligned}[/tex]

When t = 1.443887409...s

[tex]\implies v=\dfrac{50}{1.443887409...}-20=14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]

When t = 9.308800763...s

[tex]\implies v=\dfrac{50}{9.308800763...}-20=-14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]

Therefore, the velocity of the rock when its height is 25 m is:

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Answer: 34.3 megabytes

Step-by-step explanation:

To find how many megabytes have been downloaded you must multiply 13.3% by 258. 13.3% can be written as the decimal 0.133

Now let's multiply

[tex]258[/tex]×[tex]0.133[/tex]=34.314

Rounded to the nearest tenth that is 34.3

If the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1) then the area of the rhombus is 16 square units.

Given the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1).

We are required to find the area of the rhombus when the fourth point Z is plotted.

We have to plot the points of the rhombus in the graph. We know that all the sides of the rhombus should be equal to each other. So by adjusting the blocks in the graph we will be able to plot Z as (-2,3).

In this way the diagonals are ZX and WY.

ZX=[tex]\sqrt{(3-3)^{2} +(6+2)^{2} }[/tex]

=[tex]\sqrt{64}[/tex]

=8 units

WY=[tex]\sqrt{(1-5)^{2} +(2-2)^{2} }[/tex]

=[tex]\sqrt{16}[/tex]

=4 units

Area of rhombus=1/2 *([tex]d_{1} *d_{2}[/tex])

=1/2* (8*4)

=8*2

=16 Square units.

Hence if the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1) then the area of the rhombus is 16 square units.

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Answer:

5

Step-by-step explanation:

You save ⅓ of entry fee, so you save 1.20 and you pay 2.40. We only really care about the 1.20 reduction. 5 / 1.2 = 4.16 so he must go 5 times to get the 5 back

The major requirements for a group of individuals and organisations to be a market as evident from the definition big a market is that; there must be an exchange of goods or services in which case, there are sellers and buyers.

The occurrence of the exchange of goods and services represents the qualifying requirement for a market.

The distinctive property between a consumer market and a business-to-business market is the that former, involves the end user of the good or service while the latter involves the use of the good or service exchanged to facilitate the production of other goods.

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The absolute value equation that satisfies the solution set shown on the number line is given by:

|x| = 1/2

The absolute value function is defined by:

[tex]|x| = x, x \geq 0[/tex]

[tex]|x| = -x, x < 0[/tex]

It measures the distance from a point x to the origin at x = 0. In this problem, the solution set has a distance to the origin of [tex]\frac{1}{2}[/tex], as |-0.5 - 0| = |0.5 - 0| = 0.5, hence the equation is:

|x| = 1/2

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Answer: 28

Step-by-step explanation:

[tex]8+(7+1)2+4\\\\8+(8)2+4\\\\8+16+4\\\\24+4\\\\28[/tex]