Why is y=-2x considered a function?


because there are values of y that correspond to more than one value of x.

because x is bigger than y.


because the value of y corresponds only to one value of x.

because y is bigger than x.

If we evaluate the function at infinity, we can immediately see that:

        [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle L = \lim_{x \to \infty}{\frac{(x^2 + 1)^2 - 3x^2 + 3}{x^3 - 5}} = \frac{\infty}{\infty}} \end{gathered}$}[/tex]

Therefore, we must perform an algebraic manipulation in order to get rid of the indeterminacy.

We can solve this limit in two ways.

By comparison of infinities:

We first expand the binomial squared, so we get

                         [tex]\large\displaystyle\text{$\begin{gathered}\sf \displaystyle L = \lim_{x \to \infty}{\frac{x^4 - x^2 + 4}{x^3 - 5}} = \infty \end{gathered}$}[/tex]

Note that in the numerator we get x⁴ while in the denominator we get x³ as the highest degree terms. Therefore, the degree of the numerator is greater and the limit will be \infty. Recall that when the degree of the numerator is greater, then the limit is \infty if the terms of greater degree have the same sign.

Dividing numerator and denominator by the term of highest degree:

                            [tex]\large\displaystyle\text{$\begin{gathered}\sf L = \lim_{x \to \infty}\frac{x^{4}-x^{2} +4 }{x^{3}-5 } \end{gathered}$}\\[/tex]

                                [tex]\ \ = \lim_{x \to \infty\frac{\frac{x^{4} }{x^{4} }-\frac{x^{2} }{x^{4}}+\frac{4}{x^{4} } }{\frac{x^{3} }{x^{4}}-\frac{5}{x^{4}} } }[/tex]

                                [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=\lim_{x \to \infty}\frac{1-\frac{1}{x^{2} } +\frac{4}{x^{4} } }{\frac{1}{x}-\frac{5}{x^{4} } } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{0}=\infty } \end{gathered}$}[/tex]

Note that, in general, 1/0 is an indeterminate form. However, we are computing a limit when x →∞, and both the numerator and denominator are positive as x grows, so we can conclude that the limit will be ∞.

The exponential regression equation that fits the data is D. y = 8.04.0.98​ˣ.

The quickest way is probably to do direct substitution. First, let's try f(0). The values of y predicted by the four equations are, respectively, 3.14, 5.32, 10.84, and 8.46.

From here, it looks like C and D are the closest to the observed data. Let's try f(4) on C and D.

10.84(1.77)⁴ = 10.84 × 9.815 = 106.4

8.46(3.51)⁴ =  8.46 × 151.4 = 1284

Therefore, the exponential regression equation that fits the data is y = 8.04.0.98​ˣ.

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The radical expressions and their corresponding expression in rational exponent form are

[tex]972^\frac 15 = 3\sqrt[5]{4}[/tex], [tex]448^\frac 13 = 4\sqrt[3]{7}[/tex], [tex]3528^\frac 12 = 42 \sqrt 2[/tex] and [tex]4050^\frac 14 = 3\sqrt[4]{50}[/tex]

We start by evaluating each expression as follows:

[tex]972^\frac 15[/tex]

Expand 972

[tex]972^\frac 15 = (243 * 3)^\frac 15[/tex]

Take the 5th root of 243

[tex]972^\frac 15 = 3* (4)^\frac 15[/tex]

Rewrite as:

[tex]972^\frac 15 = 3\sqrt[5]{4}[/tex]

Next, we have:

[tex]448^\frac 13[/tex]

Expand 448

[tex]448^\frac 13 = (64 * 7)^\frac 13[/tex]

Take the 3rd root of 64

[tex]448^\frac 13 = 4 * (7)^\frac 13[/tex]

Rewrite as:

[tex]448^\frac 13 = 4\sqrt[3]{7}[/tex]

Next, we have:

[tex]3528^\frac 12[/tex]

Expand 3528

[tex]3528^\frac 12 = (1764 * 2)^\frac 12[/tex]

Take the square root of 1764

[tex]3528^\frac 12 = 42 * (2)^\frac 12[/tex]

Rewrite as:

[tex]3528^\frac 12 = 42 \sqrt 2[/tex]

Lastly, we have:

[tex]4050^\frac 14[/tex]

Expand 4050

[tex]4050^\frac 14 = (81 * 50)^\frac 14[/tex]

Take the 4th root of 81

[tex]4050^\frac 14 = 3 (50)^\frac 14[/tex]

Rewrite as:

[tex]4050^\frac 14 = 3\sqrt[4]{50}[/tex]

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The probability of drawing a white marble on the first draw, followed by a black marble on the second is 4/15

The distribution of the marbles is given as:

White = 6

Black = 4

When the white marble is drawn, the probability is:

P(White) = 6/10

Now, there are 9 marbles left.

When the black marble is drawn, the probability is:

P(Black) = 4/9

The required probability is:

P = 6/10 * 4/9

Evaluate

P = 4/15

hence, the probability is 4/15

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The equation of the red graph, g(x) is g(x) = |x| - 5

The graph that completes the question is added as an attachment

The function f(x) is given s:

f(x) = |x|

From the attached graph, we can see that the function f(x) is shifted 5 units down to get to g(x).

This means that:

g(x) = f(x) - 5

Substitute f(x) = |x|

g(x) = |x| - 5

Hence, the equation of the red graph, g(x) is g(x) = |x| - 5

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There are 30240 different ways can he arrange the five posters out of the ten on his closet door

The given parameters are:

The number of ways is calculated as:

Ways =[tex]^nP_r[/tex]

This gives

Ways =[tex]^{10}P_5[/tex]

Apply the permutation formula

Ways = 30240

Hence, there are 30240 different ways can he arrange the five posters out of the ten on his closet door

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Answer:

Select four types of data demographers study to make predictions.

birth rate

death rate

employment

income

marriage

migration

kgf chapter 2

VOLINCE VOLINCE VOLINCE

Answer:

Ur question is wrong..

Step-by-step explanation:

In a survey of 100 people, 60 like farming and 65 like civil service?

60+65=125..?

Answer:

Divide each term in

D

C

G

=

145

°

by

C

G

and simplify.

D

=

145

°

C

G

Step-by-step explanation:

ty

[tex]\stackrel{\textit{Half-Angle Identities}}{cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}}} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos\left( \cfrac{45^o}{2} \right)\implies \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos(22.5^o)[/tex]

Answer:

  -2.71

Step-by-step explanation:

This exponential equation can be solved by rewriting it so there is only one base, then using logarithms.

__

  2^x = 3^(x+1) . . . . . given

  2^x = 3·3^x . . . . . . eliminate the constant in the exponent

  (2/3)^x = 3 . . . . . . . divide by 3^x

  x·log(2/3) = log(3) . . . . take logarithms

  x = log(3)/log(2/3) ≈ -2.7095113

The value of x is about -2.71.

__

Alternate solution

Taking logarithms transforms this exponential equation to a linear equation.

  x·log(2) = (x +1)·log(3) . . . . take logs

  x(log(2) -log(3)) = log(3) . . . . . . subtract x·log(3)

  x = log(3)/(log(2) -log(3)) = log(3)/log(2/3) . . . . . same result as above

_____

Additional comment

In the attached, we have used a graphing calculator to find the x-intercept of the function f(x) = 0, where f(x) = 2^x -3^(x+1). This is the solution to the given equation.

The applicable rules of logarithms are ...

  log(a^b) = b·log(a)

  log(a/b) = log(a) -log(b)

A book store is hosting a special night in which families can enjoy a story and craft time. The ticket have been sold so far would be 75.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have given that 45 children's tickets have been sold, being 60% of the total tickets having been sold.

So, we have to solve for x:

60% × x = 45

60/100 × x = 45

Multiplying both sides by 100 and dividing both sides by 60,

x = 45 × 100/60

x = 75

Thus, the ticket have been sold so far would be 75.

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Answer:

f(-5) = -6  

f(-2.6) = 2.4

f(2.1) = 9.41

Step-by-step explanation:

In the question, we are told to find f(-5), f(-2.6), and f(2.1). The numbers in the parentheses represent x.

First, let's look at f(-5). Which equation should we use because x is -5? We should use the first equation because -5 is less than -3. Plug into the equation and solve:

f(-5) = -6      (We didn't have to do much because anything less than -3 equals -6)

Now, let's look at f(-2.6). We should use the equation in the middle because -2.6 is between -3 and 0. Plug -2.6 in the equation and solve:

f(-2.6) = -2.6 + 5

f(-2.6) = 2.4

Lastly, let's look at f(2.1). We should use the third equation because x is greater than 0. Plug 2.1 in the equation and solve:

f(2.1) = [tex](2.1)^{2} +5[/tex]

f(2.1) = 4.41 + 5

f(2.1) = 9.41

Therefore, the final answers are:

f(-5) = -6  

f(-2.6) = 2.4

f(2.1) = 9.41

Hope this helps!! If you have questions about my work, please let me know in the comments!

Answer: 3/4

Step-by-step explanation:   Find the reciprocal of the divisor

Reciprocal of 20/27: 27/20

Now, multiply it with the dividend So, 5/9 ÷ 20/27 = 5/9 × 27/20=  5 × 27/9 × 20 = 135/180

After reducing the fraction, the answer is

3/4

Answer:

9

Step-by-step explanation:

He had 36 Marbles and he gives all to his four friends. And all friends get the same number of marbles so we will have to do division which will be :

36{marbles} divide by 4{friends}=9 so each friend got 9 marbles.

Each friend will have 9 marbles

Division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing.

The division is an operation inverse of multiplication. If 3 groups of 4 make 12 in multiplication; 12 divided into 3 equal groups give 4 in each group in division.

Given that:

[tex]4x=36[/tex]

[tex]36[/tex] ÷ [tex]4[/tex] [tex]=9[/tex]

Therefore, each friend will have 9 marbles

KEYWORDS:

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n = 3m. Think of it this way: every month, this guy is watching 3 movies. So in 1 month, he's watched 3. In 2 months, he's watched 6. So the total number of movies that he's watched in months is 3 * however many months, which the problem is saying noting as 'm'

A population of aardvarks is growing at a rate of 2% per year, there are 714 aardvarks this year and 700 aardvarks were there last year.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let y represent the amount of aardvarks after x years.

It can be represented by the equation:

y = a(1.02)ˣ

If this year there are 714 aardvarks, the amount in the last year is:

714 = a(1.02¹)

a = 700

A population of aardvarks is growing at a rate of 2% per year, there are 714 aardvarks this year and 700 aardvarks were there last year.

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Answer:

C

Step-by-step explanation:

Answer: 7.62

Step-by-step explanation:

[tex]AB=\sqrt{(-2-1)^{2}+(-3-4)^{2}}=\sqrt{9+49}=\sqrt{58} \approx 7.62[/tex]

The smallest number of terms of the AP that will make the sum of terms positive is 73.

Since we need to know the number for the sum of terms, we find the sum of terms of the AP

The sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where

Since we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.

The common difference, d = a₂ - a

= -52.5 - (-54)

= -52.5 + 54

= 1.5

Since we require the sum of terms , S to be positive for a given number of terms, n.

So, S ≥ 0

n/2[2a + (n - 1)d] ≥ 0

So, substituting the values of the variables into the equation, we have

n/2[2(-54) + (n - 1) × 1.5] ≥ 0

n/2[-108 + 1.5n - 1.5] ≥ 0

n/2[1.5n - 109.5] ≥ 0

n[1.5n - 109.5] ≥ 0

So, n ≥ 0 or 1.5n - 109.5 ≥ 0

n ≥ 0 or 1.5n ≥ 109.5

n ≥ 0 or n ≥ 109.5/1.5

n ≥ 0 or n ≥ 73

Since n > 0, the minimum value of n is 73.

So, the smallest number of terms of the AP that will make the sum of terms positive is 73.

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multiply the height x the length x the width to find the volume of a room (or another 3d object)

Answer:

462

Step-by-step explanation:

Base=π × r²

=> π × 3.5²

=>38.48

Volume:

Base times height

=>38.48 x 12

=>461.81

Answer:

Step-by-step explanation:

Given ;

Volume of cylinder = π2²h

Volume of the cylinder is 426m².

Explanation:

Divide the number of times blue came up (114) over the number of spins total (180). Ignore the 60% given to you. That's a theoretical value that doesn't play any part in determining an experimental probability.

114/180 = 0.633 approximately

The '3's go on forever. Round that however your teacher instructs.

The amount of water that will fill the tank is 11100 cu.ft to the nearest hundredth.

A cylinder is a three dimensional figure with two identical circular faces at each end , and a curved surface.

It does not have an edges or vertices.

It is given in the question that

A cylinder with height 14 feet and radius 25 feet.

The volume of a cylinder.

V = π252(14)

The water than can be filled is equal to the volume of the cylinder

V = 11088 cu.ft

There  the amount of water that will fill the tank is 11100 cu.ft to the nearest hundredth.

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Answer: 27,488.94 cubic feet

Step-by-step explanation:

Answer: x - int : (3,0)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = y2-y1/x2-x1

   = -4-2/-3-6

   =-6/-9

   = 2/3

y1 = 2

x1 =6

y - 2 = 2/3(x-6)  

x -int: when y = 0, what is x?

0-2 = 2/3(x-6)

-2 = 2/3x - 4

2 = 2/3x

x=3

~Hope this helps!~

Answer:

y - 5 = 4(x + 2)

Step-by-step explanation:

Given:

The point-slope form is in the form of [tex]\displaystyle \large{y-y_1=m(x-x_1)}[/tex]. Determine the followings:

Therefore, input these in the formula.

[tex]\displaystyle \large{y-5=4[x-(-2)]}\\\\\displaystyle \large{y-5=4(x+2)}[/tex]

Therefore, the answer to this question is y - 5 = 4(x + 2)

Please let me know if you have any questions regarding my answer or explanation!

A major arc is an arc that is greater than 180 degrees.

A minor arc is an arc less than 180 degrees.

An acute angle is an angle less than 90 degrees.

A central angle is an angle created in the center of a circle with 2 sides being the radius.

Thus, we can see in the figure that we are talking about the angle so we can eliminate the major arc and minor arc.

Now, we clearly see that the angle is greater than 90 degrees so it cannot be an acute angle.

The correct answer is the central angle as it goes with the definition.

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Answer:

x = 129°

Step-by-step explanation:

∠ ABD and ∠ DBC are a linear pair and sum to 180° , then

y + ∠ DBC = 180°

107° + ∠ DBC = 180° ( subtract 107° from both sides )

∠ DBC = 73°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles , then

x = ∠ DBC + z = 73° + 56° = 129°