which of the following functions have graphs that contain vertical asymptotes?
power; y=x^n
reciprocal; y=1/x
exponential; y=b^x
logarithmic;y=logb x
root;y=^n sqrt x

could you please explain? I know that two of these answers are correct but I don't fully understand.
Thank you!

Answers

Answer 1
A vertical asymptotic is a point at which y approaches positive or negative infinite, or both, and y is undefined at that x value.

Of the options, the reciprocal has a vertical asymptote. When approaches zero, y approaches 1÷0, or infinite.
The logarithmic function also has a vertical asymptote at x=0. Let's use f(x) =log base 10 (x) as an example. This function describes the exponent you'd have to put on 10 to get x. When x=0, we have a bit of a problem. What power can you raise 10 to to get 0? The answer is negative infinite, which would be
1/ (10^∞) = 0.


Related Questions

for the geometric sequence with a1=4 and r=5, find a5

Answers

General form of a geometric sequence:

A(n) = A1 × r^(n-1)

A(5) = 4 × 5^(5-1)

A(5) = 4 × 5^(4)

A(5) = 4 × 625

A(5) = 2500

Write (1-i)-(4-5i) as a complex number in standard form. I don't exactly get how to do this.. Can anyone help?

Answers

You just subtract. The standard form of a complex number is a+bi 
1 - 4 = -3
-i - (-5i) = 4i
The answer is -3 + 4i

True or False: Low taxation would lead to slower economic growth because it encourages citizens and businesses to consume more and invest less

Answers

The answer is True because low taxation can lead to low economy and less investment.

Low taxation would lead to slower economic growth because it encourages citizens and businesses to consume more and invest less is false.

We have,

Low taxation can actually lead to faster economic growth if it encourages citizens and businesses to consume and invest more.

With more money in their pockets, consumers may have more disposable income to spend on goods and services, which can stimulate demand and create more jobs.

Additionally, with lower taxes, businesses may have more money to invest in capital equipment, research and development, or expansion, which can lead to increased productivity and economic growth.

It's important to note that the relationship between taxation and economic growth is complex and multifaceted.

While lower taxes can be beneficial for growth, they may also lead to reduced government revenues, which can limit the government's ability to fund important public services and investments.

Moreover, the impact of tax policy on economic growth can vary depending on a range of factors, such as the size and structure of the economy, the nature of the tax system, and broader economic conditions.

Thus,

Low taxation would lead to slower economic growth because it encourages citizens and businesses to consume more and invest less is false.

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Can someone help me with this problem too?

Answers

x equals 8 bu i dont know the slope

50 POINTS!

Which statement best explains whether △ABC is congruent to △DEF?

Answers

Option B makes the most sense, because if you follow the steps, they fit perfectly into each other!

Answer:

The second choice is correct.

Step-by-step explanation:

Reflecting ABC across the y-axis will negate the x-coordinates, which will place it directly above triangle DEF.  Counting down from A to D, B to E and C to F, we see that each is 5 units above the image; this means a translation 5 units down will finish mapping the pre-image to the image.  Since they are mapped on top of each other, they are congruent.

What is 187.023 I word form

Answers

One hundred and eighty seven point zero two three

Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^2, x = 3, and y = 4 about the y-axis.

25 times pi divided by 2
97 times pi divided by 3
173 times pi divided by 3
None of these

Answers

The volume of the solid formed by revolving the region bounded by the graphs of the given functions is (25π) / 2.

What is integration?

Integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.

The region bound by all three functions is in the first quadrant. If this region were rotated about the y-axis, the solid formed would have washer-shaped cross-sections.

Therefore, we can use the Washer method: V = π∫ (ROuter)² - (RInner)² dy

R(outer) = 3 and R(inner) = √y  (Note: the inner radius is formed by the function y = x2 which we solve in terms of y since we are rotating about the y-axis).

V = π∫ (3)2 - (√y)2 dy

(the limits of integration are from y = 4 to y = 9, so a = 4 and b = 9)

= π∫  9 - y dy where a = 4 and b = 9

Integrate this definite integral to find the volume,

=  (25π) / 2.

Hence, the volume of the solid formed by revolving the region bounded by the graphs of the given functions is (25π) / 2.

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Answer:

[tex]\textsf{A)} \quad \dfrac{25\pi}{2}[/tex]

Step-by-step explanation:

To find the volume of the solid of revolution created by rotating the region bounded by the curve y = x², x = 3, and y = 4 about the y-axis, we can use the method of cylindrical shells.

As the region of revolution is bounded by the graphs of two functions, y = x² and y = 4, the volume of a solid of revolution using cylindrical shells is given by the integral:

[tex]\displaystyle V=2\pi\int^b_ax\left(f(x)-g(x)\right)\;\text{d}x[/tex]

where:

a and b are the lower and upper bounds along the x-axis.f(x) is the upper function.g(x) is the lower function.

The height of the shell, f(x) - g(x), is determined by the vertical distance between the curve y = x² and the line y = 4. Therefore, the height is:

[tex]f(x)-g(x)=x^2-4[/tex]

The upper bound of the integral is b = 3, since the region is bounded by x = 3.

The lower bound is the x-value of the point of intersection of the two functions y = x² and y = 4. These two functions intersect when x = 2. Therefore, the lower bound of the integral is a = 2.

Substitute these values into the integral:

[tex]\displaystyle V=2\pi\int^3_2x\left(x^2-4\right)\;\text{d}x[/tex]

Expand the brackets:

[tex]\displaystyle V=2\pi\int^3_2\left(x^3-4x\right)\;\text{d}x[/tex]

Evaluate the integral by using the power rule:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Therefore:

[tex]V=2\pi\left[\dfrac{x^4}{4}-\dfrac{4x^2}{2}\right]^3_2[/tex]

[tex]V=2\pi\left[\dfrac{x^4}{4}-2x^2\right]^3_2[/tex]

[tex]V=2\pi\left[\left(\dfrac{(3)^4}{4}-2(3)^2\right)-\left(\dfrac{(2)^4}{4}-2(2)^2\right)\right][/tex]

[tex]V=2\pi\left[\left(\dfrac{81}{4}-18\right)-\left(4-8\right)\right][/tex]

[tex]V=2\pi\left[\left(\dfrac{9}{4}\right)-\left(-4\right)\right][/tex]

[tex]V=2\pi\left(\dfrac{25}{4}\right)[/tex]

[tex]V=\dfrac{25\pi}{2}[/tex]

Therefore, the volume of the solid formed by revolving the region bounded by the graphs of y = x², x = 3, and y = 4 about the y-axis is:

[tex]\Large\boxed{\boxed{\dfrac{25\pi}{2}}}[/tex]

Which statements are true about the ordered pair (5, −6) and the system of equations?

{x+y=−1
3x−y=21

Select each correct answer.

The ordered pair (5, −6) is a solution to the first equation because it makes the first equation true.

The ordered pair (5, −6) is a solution to the second equation because it makes the second equation true.

The ordered pair (5, −6) is not a solution to the system because it makes at least one of the equations false.

The ordered pair (5, −6) is a solution to the system because it makes both equations true.

Answers

The first, second, and last answer is true. The pair is a solution to the whole system, and is also the solution to each the first and second equation. 

Hope this helps! =)

May
The ordered pair (5, −6) is a solution to the system because it makes both equations true.

The ordered pair (5, −6) is a solution to the first equation because it makes the first equation true.

The ordered pair (5, −6) is a solution to the second equation because it makes the second equation true.

Given ƒ(x) = 2x2 − 3x + 7, find ƒ(2.5)

Answers

assuming 2x2 is [tex] 2x^{2} [/tex] you would get 2(2.5)(2.5) - 3(2.5) +7, which is 2(6.25) - 7.5 + 7, 12.5 - 0.5, [12]

Answer:

i need helppp

Step-by-step explanation:

this same problems but where is everyone getting the 6.25 from.

Points J and K lie in plane H.
How many lines can be drawn through points J and K?

0
1
2
3

Answers

1 is the answer bruvy

Answer: 1

Step-by-step explanation:

From the given picture, it can be seen that there is a plane H on which two pints J and K are located.

One of the Axiom in Euclid's geometry says that "Through any given two points X and Y, only one and only one  line can be drawn "

Therefore by Axiom in Euclid's geometry , for the given points J and K in plane H , only one line can be drawn  through points J and K.

Which of the following is NOT prime number? A 1057 B 3163 C 157 D263

Answers

1057 we can divide by 7 
A prime number is a number that is only divisible by 1 and itself, no other number can divide a prime number completely, there will always be some numbers remaining. In the question given above, the correct option is A. This is because 7 will completely divide 7 to give 151.

Point R is between points S and T and SR = 29 and ST = 47

What is RT?

a.) 18
b.) 22
c.) 66
d.) 76

Answers

The answer is:  [A]:  " 18 " .
____________________________________
47 - 29 = 18 .
____________________________________

The closed form sum of $$12 \left[ 1^2 \cdot 2 + 2^2 \cdot 3 + \ldots + n^2 (n+1) \right]$$ for $n \geq 1$ is $n(n+1)(n+2)(an+b).$ find $an +
b.$

Answers

Final answer:

The closed form sum of the given expression is obtained by expanding and simplifying it. Comparing this with the given expression, we can find the values of a and b.

Explanation:

The closed form sum of $$12 \left[ 1² \cdot 2 + 2²\cdot 3 + \ldots + n² (n+1) \right]$$ for $n \geq 1$ is $n(n+1)(n+2)(an+b).$ To find $an + b$, we can simplify the expression by expanding it:

Expanding the sum, we have:

$$\begin{align*} 12 &\left[ 1² \cdot 2 + 2² \cdot 3 + \ldots + n² (n+1) \right] \\ &= 2[1 + (n-1) + 3 + \ldots + (2n-3) + (2n-1)-(n-1)] \\ &= 2[n + 3 + \ldots + (2n-3) + n] \\ &= 2n² \end{align*}$$

Comparing this with the given expression $n(n+1)(n+2)(an+b)$, we can see that $2n² = n(n+1)(n+2)(an+b)$. So, $an+b = \boxed{2}$.

Solve for y.



23+y−19=79



Enter your answer in the box.
y = ____

Answers

y = 75.

(step by step)

23 + 75 = 98

98 - 19 = 79

Hope this helps! ☺♥

Answer:

y = 75

Step-by-step explanation:

23 + y - 19 = 79

We are to solve for y.

To solve for y, we are to follow the step below

23 + y - 19 = 79

subtract nineteen from twenty three

y + 4 = 79

Subtract four(4) from both-side of the equation

y + 4 - 4 = 79 - 4

On the left hand-side of the equation, 4-4=0 leaving us with just y

y = 79 - 4

y =75

Therefore y = 75

What is the property that justifies the illustrated step in solving the equation?
3x + 4 - 2x + 5 = 6x + 2
3x - 2x + 4 + 5 = 6x + 2

Multiplication Property of Equality
Addition Property of Equality
Commutative Property of Addition
Distributive Property of Addition

Answers

It is commutative property of addition.

This means that you can move around where the numbers are in the equation, and you will still get the same solution.

Hope this helps!
Final answer:

The property that justifies the step is the Commutative Property of Addition, which states that the order of addition does not affect the result.

Explanation:

The property that justifies the illustrated step in solving the equation 3x + 4 - 2x + 5 = 6x + 2 as 3x - 2x + 4 + 5 = 6x + 2 is the Commutative Property of Addition.

This property states that the order in which numbers are added does not affect the result. So, we can rearrange the terms in any order without changing their sum.

In this step, we are rearranging the terms -2x and 5 so that like terms, namely 3x and -2x, and 4 and 5, are grouped together.

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Susan's property is assessed at $97,500. The property tax rate in her city is 3.05%. Find her property tax.

Answers

Should be about $2,973.75

solve 5x=5/3 using multiplication property of equality

Answers

 On using multiplication property of equality:
5x=5/3
5 in left hand side is in multiplication, it comes in denominator on right hand side,
we get,

[tex] x = \frac{5}{3\times5} [/tex]

or [tex] x=\frac{1}{3} [/tex]


is 37% bigger than 0.37

Answers

No, they are equivalent

Which of the following has the steepest graph?

Answers

I would say the choice A  it's so steep
Answer:

The equation which has the steepest graph is:

             Option: A

     A.   [tex]y=11x-144[/tex]

Step-by-step explanation:

We know that the slope-intercept form of a line is given by:

                 [tex]y=mx+c[/tex]

where m is the slope of the line and c is the y-intercept of a line.

If the absolute value of the slope is greatest then that line is most steep.

A)

[tex]y=11x-144[/tex]

The slope is: 11

B)

[tex]y=\dfrac{1}{2}x+3[/tex]

The slope is: [tex]\dfrac{1}{2}[/tex]

C)

[tex]y=7x+16[/tex]

The slope is: 7

D)

[tex]y=3x+144[/tex]

The slope of this line is: 3

The line which has the largest absolute value of slope is:

               [tex]y=11x-144[/tex]

Hence, the graph of this equation will be steepest.

Write a word problem that can be solved using 1 3/4 divided by 1/2

Answers

Micheal has 1 3/4 bowls of cereal. Micheal wants to give half to his sister, Mary, how much should he give her?

(3xy^3)^2 (xy)^6 simplify the expression

Answers

9x8y12 it a lot of work to do so I don't want to type how to do the problem

What are 2 equivalent ratios for 9:20?

Answers

Two equivalent ratios for 9:20 would be 18:40 or 27:60

Final answer:

Two equivalent ratios for 9:20 are 18:40 and 27:60, found by multiplying both the numerator and denominator of the ratio by 2 and 3, respectively.

Explanation:

To find two equivalent ratios for 9:20, you can multiply or divide both terms of the ratio by the same non-zero number. Remember, an equivalent ratio has the same proportional relationship as the original one.

Here's how we can calculate two equivalent ratios:

Multiply both terms by 2: 9 × 2 = 18 and 20 × 2 = 40, so one equivalent ratio is 18:40.

Multiply both terms by 3: 9 × 3 = 27 and 20 × 3 = 60, so another equivalent ratio is 27:60.

These both represent the same ratio as 9:20 when simplified.

what is the product? 6(x^2-1)*6x-1/6(x+1)

6(x – 1)2
6(x2 – 1)
(x + 1)(6x – 1)
(x – 1)(6x – 1)

Answers

Answer:

the answer is (x - 1)(6 x-1) on edge, option D.



The product is (x - 1) (6x - 1).

What is Multiplication?

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

The given expression is [6(x² - 1) (6x - 1)] / [6 (x + 1)]

6 is in the numerator as well as denominator. Cancel it.

[6(x² - 1) (6x - 1)] / [6 (x + 1)] =  [(x² - 1) (6x - 1)] / [(x + 1)]

We have to use one of the algebraic identity here.

a² - b² = (a + b) (a - b)

Using this,

x² - 1 = x² - 1² = (x - 1)(x + 1)

[6(x² - 1) (6x - 1)] / [6 (x + 1)] =  [(x² - 1) (6x - 1)] / [(x + 1)]

                                            = [(x - 1)(x + 1)(6x - 1)] / [(x + 1)]

Again, x + 1 is both in the numerator as well as denominator. Cancel it.

[6(x² - 1) (6x - 1)] / [6 (x + 1)] = (x – 1)(6x – 1)

Hence the product is (x – 1)(6x – 1).

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Timothy explains to his brother that the model y=4mt has a constant of variation of 4 and is an example of _____ variation.

Answers

Do you have any Answer choices??

To fence in 2 cows, josie used 64 feet of fence. for 3 cows, she used 96 feet of fence, and for 4 cows, she used 128 feet of fence. how many feet of fence will she use for 6 cows?

Answers

The answer is 192 feet

Answer:

192 feet fence would be used for 6 cows.

Step-by-step explanation:

Given,

64 feet of fence is used for 2 cows,

Ratio in fence and cows = [tex]\frac{64}{2}[/tex] = 32,

96 feet of fence is used for 3 cows,

Ratio in fence and cows = [tex]\frac{96}{3}[/tex] = 32,

128 feet of fence is used for 4 cows,

Ratio in fence and cows = [tex]\frac{128}{4}[/tex] = 32,

Thus, by the above explanation it is clear that in every case the ratio of the length of fence and number of cows is 32,

Let x be the length of cows that is used for x cows,

[tex]\implies \frac{x}{6}=32[/tex]

[tex]\implies x = 192[/tex]

Hence, 192 feet fence would be used for 6 cows.

find the resultant of two forces, one of 72 pounds and the other of 56 pounds if they act at and angle of 37°

Answers

I think the answer is R² = P² + Q² - 2PQ Cos θ ; where P = 72 lbs, Q = 56 lbs and θ = 37° 
R² = 72² + 56² - 2*72*56*Cos 37 
R² = 72² + 56² - 2*72*56*Cos 37 
R² = 14,760.196 
R = 121.49 lb ----- So Answer should be (C) 

A snack stand sold hot dogs and chips at a recent game. The hot dogs cost $2.50 and the snacks cost $0.75. After the game, they tallied 175 transactions totaling $262.50.
Represent the linear system in an augmented matrix:

Answers

x = hot dogs

y = snacks

x +y = 175

x = 175-y

2.50x + 0.75y = 262.50

2.50(175-y) +0.75y = 262.50

437.50-2.50y + 0.75y = 262.50

-1.75y = -175

y = -175 / -1.75 = 100


100 snacks & 75 hot dogs

The number of hot dogs sold is 75 while the number of snacks sold is 100.

Let the number of hot dogs be represented by xLet the number of snacks sold be represented by y.

Based on the information, the equation to solve the question will be:

x + y = 175 ....... i

2.50x + 0.75y = 262.50 ....... ii

From equation i, x = 175 - y.

We'll put the value of x into 2.50x + 0.75y = 262.50 and this will be:

2.50x + 0.75y = 262.50

2.50(175 - y) + 0.75y = 262.50

437.50 - 2.50y + 0.75y = 262.50

Collect like terms

-2.50y + 0.75y = 262.50 - 437.50

-1.75y = -175

y = 175/1.75

y = 100

The number of snacks sold is 100.

Since x + y = 175

x = 175 - 100

x = 75

The number of hot dogs sold is 75

Therefore, 75 hot dogs and 100 snacks were sold.

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Evaluate the function for an input of 10

Answers

The answer is B. On the graph, the line crosses through 18 and 10. That means after 10 hours the cost is $18.

An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is 24pi inches. The artist plans to fill the inside of each dot with blue colored glass.
What is the area of the blue glass will be needed to fill each butterfly dot?
Give your answer in terms of pi.

Answers

[tex]\bf \textit{"The distance around each dot is 24}\pi \textit{ inches."}\\\\ \textit{circumference of a circle}\\\\ C=2\pi r\quad \begin{cases} r=radius\\ -----\\ C=24\pi \end{cases}\implies 24\pi =2\pi r\implies \cfrac{24\pi }{2\pi }=r \\\\\\ \boxed{12=r}\\\\ -------------------------------\\\\ \textit{area of a circle}\\\\ A=\pi r^2\quad \begin{cases} r=radius\\ -----\\ r=12 \end{cases}\implies A=\pi 12^2\implies A=144\pi [/tex]

The area of the blue glass that will be needed to fill each butterfly dot would be 144π.

What is the circumference of the circle?

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

We have given the distance around each dot is 24pi inches.

So, The circumference of the circle = 2πr

                                                 24π = 2πr

                                                 r = 12

The artist plans to fill the inside of each dot with blue-colored glass.

Now, we know that

The area of the circle = [tex]\pi r^{2}[/tex]

                                    = π x 12 x 12

                                    = 144π

Thus, the area of the blue glass that will be needed to fill each butterfly dot would be 144π.

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This IS SO HARD
NEED HELP

I THINK ITS B.. Confirmation?

Answers

Answer:

22sqrt(3)/3

You are correct.

Step-by-step explanation:

You have a 30-60-90 triangle.

In a 30-60-90 triangle, the hypotenuse is twice the length of the short leg. The long leg is sqrt(3) times the length of the short leg.

You are given the length of the long leg.

1) Find the length of the short leg.

HG = GI/sqrt(3) = 11/sqrt(3)

2) Find the length of the hypotenuse, HI.

HI = 2HG = 2(11/sqrt(3)) = 2(11/sqrt(3))*(sqrt(3))/(sqrt(3)) = 22sqrt(3)/3

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