Points of discontinuity, holes, vertical asymptotes, and horizontal asymptote. (Please show work)

Answer:

Step-by-step explanation:

3/ B is a salesperson and C is a programmer.

The correct option is: 2/ B is a programmer, and C is a salesperson

Let's analyze the statements and determine what B and C are:

A mumbled a response that the visitor couldn't hear clearly. We don't have any information from A's response.

B said, "A said that he is a salesperson." Since we know that salespeople always lie, we can infer that B is lying about A's response. Therefore, if A is a programmer (telling the truth), then B must be a salesperson.

C said, "Don't believe B; he is lying!" If we already determined that B is a salesperson (lying about A's response), then C is suggesting that B's statement is false, which means A's response is the opposite of what B said. So if B claimed that A is a salesperson (which was a lie), then A must be a programmer (telling the truth).

Based on the above analysis:

A is a programmer.

B is a salesperson.

C is a programmer.

So, the correct option is: 2/ B is a programmer, and C is a salesperson.

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the answer is there

60 students so. my brainly is glitchng sorry

y = log (x)

Logarithmic functions are the inverse of exponential functions. Logarithmic is usually shortened to log.

Logarithmic Operation

Logarithmic functions help solve exponential equations. For example, the exponential function: bˣ = a, could be difficult to solve. To find x, we can use the log operation. By taking the log of both sides we can change this exponential function into a log function. In log form, the function becomes [tex]log_{b} (a)=x[/tex]. This is pronounced, "log-base b of a equals x." If you plug this into a calculator or use a different technique to solve, you can find x and solve the original exponential function.

Common Log and Natural Log

Although logarithmic functions can have any base, some are more frequent than others. One such base is base 10. If the base of the log is 10, then we do not write the 10, it is just implied. This log is called common log. The answer choice y = log (x) is common log. Another common base is Euler's constant, e. Log with the base of e is called natural log. Natural log is written as ln (x).

So on solving the provided question we can say that from the given data - (a) and (b) are triangles only/

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

(a) T(-2, 4), R(6, O), 1(-5, -2) - is triangle

(b) p(9, -3), Q(-l, 1), R(-5, -9)- is a triangle

(c) O), E(-6, 10), F(-IO, 4) - can not be determined

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Step-by-step explanation:

what is the usual formula for the area of a triangle ?

it is

base × height / 2

so, we know the area (10 cm²).

when we use the formula, we get

10 = 5 × w / 2

20 = 5 × w

w = 20/5 = 4 cm

Answer:

the height is equal = 4 cm

Answer:

x=1

Step-by-step explanation:

To solve the equation, we'll need to get the square roots on one side and the non-square root terms on the other side.

First, we'll add √x to both sides to get:

√2x+4 - √x + √x = 2 + √x

√2x+4 = 2 + √x

Next, we'll square both sides to get rid of the square roots:

(√2x+4)^2 = (2 + √x)^2

2x+4 = 4 + 2√x + x

Then, we'll simplify the right side of the equation:

2x+4 = 4 + 2√x + x

2x+4 = 4 + x + 2√x

Now we'll subtract 4 from both sides

2x = x + 2√x

x = 2√x

Finally, we'll divide by x on both sides

1 = 2√x/x

x = √x

x = 1

Therefore, the solution of the equation is x=1

Answer:

To solve the equation √2x+4 - √x = 2, we can first square both sides of the equation to eliminate the square roots.

Squaring both sides gives: (√2x+4)^2 - (√x)^2 = 2^2

Simplifying the left side gives: 2x+4 - x = 4

Next, we can add x to both sides of the equation to get:

2x+4 = 4 + x

then we can subtract 4 from both sides of the equation to get:

2x = x

then we can divide both sides by x

2 = 1

However, it is not possible to divide by zero, so x = 0 is not a valid solution.

This equation is an extraneous solution because the assumption that x is not equal to 0 led to a valid solution, but when x = 0, the equation is not defined.

Therefore, the solution of √2x+4 - √x = 2 is x = any value except 0.

The sum of A + B, considering that the ten-digit number is divisible by 36, is given as follows:

A + B = 6.

The sum of A and B is obtained considering the rule for a divisibility by 36.

To be divisible by 36, the numbers must be divisible by both 4 and 9, for which the rules are given as follows:

The ten-digit number is given as follows:

3872649A0B

The sum of the digits is given as follows:

3 + 8 + 7 + 2 + 6 + 4 + 9 + A + 0 + B = 39 + A + B.

Hence the condition for a divisibility by 36 is given as follows:

39 + A + B = 45

A + B = 6.

Which is the result for the sum in the context of this problem.

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Using pythagoras theorem formula, c² = a² +b²  We can see that the two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

What is Pythagoras' theorem ?

Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

The two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

Let the sides of the triangles be a, b and c. According to Pythagoras theorem;

c² = a² +b²

where:

a is the hypotenuse (longest side)

For triangle A:

c = 13

b = 12

Get "a"

13² = 12² +b²

b² = 25

=> b = 5 cm

Similarly for triangle B:

c² = 5² +12²  = 169

=> c=13 cm

We can see that the two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

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After 24 years, the amount will be $40,000

What is annual interest rate?

An annual percentage rate is expressed as an interest rate. It calculates what percentage of the principal you'll pay each year by taking things such as monthly payments into account.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Formula:

a(t) = p*2^(t/8)

given, t=24 , p =5000

a(24) = 5000*2^(24/8)

a(24) = 5000*2^3

a(24) = 5000*8

a(24) = $40,000

Thus, after 24 years, the amount will be $40,000

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Answer:

Step-by-step explanation:

Given :

Null Hypothesis :

Alterative Hypothesis

two tailed test

claim is Ha

Alterative Hypothesis: Ha: u ≠ 1

The alternative hypothesis that would be used to test the mean quantity is different from 1 liter is u ≠ 1.

An assertion used in statistical inference experiments is known as the alternative hypothesis. It is contradictory to the null hypothesis and denoted by Ha or H1.

Given that the claim in the null us that u = 1.

Since, an alternative hypothesis is one in which the researchers anticipate a difference (or an effect) between two or more variables; thus, the observed pattern of the data is not the result of chance.

Therefore,

The alternative would be that u is not equal to 1.

Hence, the alternative hypothesis that would be used to test the mean quantity is different from 1 liter is u ≠ 1.

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The total quantity of the three spices is 7/8

A recipe has three spices

1/8 teaspoon of turmeric

1/4 teaspoon of ginger

1/2 teaspoon of cumin

The total quantity of the three spices can be calculated as follows

1/8 + 1/4 + 1/2

= 7/8

Hence the total quantity of the three spices is 7/8

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Son solving the provided question we can say that - the fraction is (2 + 1/x ) / ( 7-1/x ) = 5/13

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here, the fraction is

(2 + 1/x ) / ( 7-1/x )

2x+1/7x-1

x = 2

5/13

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The surface area of the square pyramid is 224 ft²

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Surface area is the total area occupied by the surface of the object. It is gotten by summing the individual area of each surface.

For the pyramid:

Surface area = 4 * area of triangle + Area of square base

Substituting gives:

Surface area = (8 ft * 8 ft) + 4(1/2 * 8ft * 10 ft) = 224 ft²

The surface area is 224 ft²

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Answer:

Step-by-step explanation:

What is the surface area?

5 cm

6 cm

5 cm

6 cm

4 cm

square centimeters

The solutions for the given equations are x=2 and x=-4

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Fo question 5.

1/2x-2=9-5x

Take the variable terms on one sides\

x/2+5x=11

x+10x=22

11x=22

Divide both sides by 11

x=22/11

x=2

For question 6:

-5+x/4=3x+6

-20+x=12x+24

-20-24=12x-x

-44=11x

x=-4

Hence, the solutions for the given equations are x=2 and x=-4

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a) The least score that you need to get on the last test and still earn a C is given as follows: 34.

b) With the least score counting twice, the least score that you need to earn a C is given as follows: 52.

The mean of a data-set is obtained as the sum of all the elements in the data-set divided by the number of elements in the data-set.

The scores for this problem are given as follows:

83, 70, 83, 80 and x.

(in which x is the score of the fifth test).

The least score that you could get on the last test and still earn a C is found when the mean is of 70, hence>:

(83 + 70 + 83 + 80 + x)/5 = 70

316 + x = 350

x = 350 - 316

x = 34.

With the final test counting twice, you would have the equivalent to six scores, which would be given as follows:

83, 70, 83, 80, x and x.

Hence the least score would be obtained as follows:

(83 + 70 + 83 + 80 + 2x)/6 = 70

316 + 2x = 420

2x = 104

x = 104/2

x = 52.

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Answer:

full answer in below

Step-by-step explanation:

To prove that the limit of (2x^4-6x^3+x^2+3)÷(x-1) as x approaches 1 is equal to -8, we can use the definition of a limit and the fact that (x-1) is not equal to zero at x=1.

The definition of a limit states that:

If we have a function f(x) and a number L, then the limit of f(x) as x approaches a is L, if and only if, for every ε > 0, there exists a δ > 0 such that for every x:

|f(x) - L| < ε when 0 < |x - a| < δ

So, to prove that the limit of (2x^4-6x^3+x^2+3)÷(x-1) as x approaches 1 is -8, we need to show that:

|(2x^4-6x^3+x^2+3)÷(x-1) + 8| < ε when 0 < |x - 1| < δ

We know that (x-1) is not equal to zero at x=1, so we can safely divide both sides of the equation by (x-1) and simplify it to:

|2x^4-6x^3+x^2+11| < ε when 0 < |x - 1| < δ

Now, we can choose ε = 0.1 and δ = 0.1, so we have:

|2x^4-6x^3+x^2+11| < 0.1 when 0 < |x - 1| < 0.1

If we plug in x=1, we have:

|2(1)^4-6(1^3)+(1)^2+11| < 0.1

which simplifies to:

|11| < 0.1

and we see that this is true, since |11| = 11 is less than 0.1.

We can also plug in some values around x=1, for example x=0.99 and x=1.01:

|2(0.99)^4-6(0.99)^3+(0.99)^2+11| < 0.1

and

|2(1.01)^4-6(1.01)^3+(1.01)^2+11| < 0.1

In both cases, we can see that the inequality is true, and the absolute value of the expression on the left side is less than 0.1.

Therefore, we have shown that for any ε > 0, there exists a δ > 0 such that for every x:

|(2x^4-6x^3+x^2+3)÷(x-1) + 8| < ε when 0 < |x - 1| < δ

And thus, by the definition of a limit, we have proven that the limit of (2x^4-6x^3+x^2+3)÷(x-1) as x approaches 1 is -8.

Answer:

is that calculus?

am confuse in your question

can you try take derivative both numerator and denominator with respect to x

by using L - Hospitable rule

Answer:

y-int = -1

x-int = -4

HA: y = -2

VA: x = -5

Step-by-step explanation:

For the y-intercept, you need to look where the graph intersects with the y-axis. In this case, the graph intersects at -1.

For the x-intercept, you need to look where the graph intersects with the x-axis. In this case, the graph intersects at -4.

The horizontal asymptote is a y value the graph approaches but does not pass or touch. In this case, the y value is -2.

The vertical asymptote is a x value the graph approaches but does not pass or touch. In this case, the x value is -5.

Answer:

see below

Step-by-step explanation:

reserve = x

field =y

box = z

x * 20 +y*50 +z*100 =370

x=2y

x + y+ z =10 so 3y +z=10 so z=10-3y

2y * 20 + y*50 + (10-3y)*100 =370

90*y+1000-300*y =370

210*y=630

y tickets =3

x tickets=6

z tickets =1

Answer:

116.05

Step-by-step explanation:

15 to 20 = 5 years

compound semiannually = 10 time

annual rate 3% = 1.5% for every 6 mos

so 100*(1+1.5%)^10 =116.05

The maximum allowed ratio for the cord such that the maximum allowable normal stress is 8.77 kilopascals is equal to 2.081.

Let assume that the cork is made of a ductile material, in this case we find that the normal stress (σ), in kilopascals, and shear stress (τ), in kilopascals, are described below:

Normal stress

σ = F / A

Shear stress

τ = (3 · V) / (2 · A')

Where:

Let assume that cork is at static equilibrium and at inminent motion, then the shear and normal forces are, respectively:

F = P

V = P / 2

And the transversal areas are introduced below:

A = π · R²

A' = 2 · R · H

Where:

If we know that σ = 8.77 kPa and τ = 4.98 kPa, then the maximum allowed ratio between the cork height and the cork radius is:

8.77 = P / (π · R²)

8.77 = [1 / (π · R)] · (P / R)

4.98 = 1.5 · (0.5 · P) / (2 · R · H)

4.98 = [0.75 / (2 · H)] · (P / R)

Then, we eliminate P / R of the two equations:

8.77π · R = 13.24 · H

H / R = 8.77π / 13.24

H / R = 2.081

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Answer:

given that z=3 and w=2

10z+5w

now by putting the values of z and w

10(3) + 5(2)

30 + 10

40 is your correct answer

The point (-1,5) is not a solution to the equation 2x + 5y = 0 because this point does not satisfy the equation.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

2x + 5y = 0

Substitute x = -1 and y = 5 into the equation and see if it holds true:

2(-1) + 5(5) = 0

-2 + 25 = 0

23 = 0

Since 23 ≠ 0, the point (-1,5) is not a solution to the equation 2x + 5y = 0.

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The graph that has a slope of negative three halves and a y-intercept of 2 is the graph of a line passing through the points (0,2) and (3,0).

What is the slope?

One of the most important things to understand about lines is the definition of slope. The slope is the 'steepness' of the line, also commonly known as rise over run. We can calculate the slope by dividing the change in the y-value between two points over the change in the x-value.

To find the slope of the line, you can use the point-slope formula which is (y2-y1)/(x2-x1) = m,

where m is the slope and (x1,y1) and (x2,y2) are points on the line.

So using the given points in the question, we get (0-2)/(3-0) = -2/3 = -0.66 = -3/2.

And the y-intercept is the point where the line crosses the y-axis, which is 2 in this case.

Hence, the graph that has a slope of negative three halves and a y-intercept of 2 is the graph of a line passing through the points (0,2) and (3,0).

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Answer:

a) General Equation for this scenario is

[tex]\boxed{P_n = P(.98)^n\\\\}[/tex]

where P is the starting population and Pₙ is the population at the end of n years

For this specific case,
[tex]\boxed{P_n = 20000(0.98)^n}[/tex]

b) Population in 2025 will be the population after 25 years:
[tex]P_{25} = 20000(0.98)^{25} = \boxed{12,069}[/tex]

Step-by-step explanation:

In general, if the population at year 0 is P and it decreases by 2% each year then the population after one year will be given by

P - decrease in one year

Decrease in population for 1 year = 2% of P [tex]= 0.02P[/tex]

So P(after 1 year) :  
[tex]P - 0.02P\\\\ = P(1-0.02) \\\\= 0.98P[/tex]

After 2 years the population will be population after 1 year (0.98P) - decrease in population for 1 year (0.02 x 0.98P)

So population at end of 2 years would be
 [tex]0.98P - 0.98P(0.02)\\\\= 0.98P(1-0.02)\\\\=0.98P(0.98)\\\\= P(0.98)^2[/tex]

In general after n years the population would be
[tex]P(0.98)^n\\\\[/tex]

If the population in year 2000 is 20,000 then population at the end of 25 years is:

[tex]20000(0.98)^{25}[/tex]
[tex]\rm\:{=\:12,069\:\;\:rounded\:down\:to\:the\:nearest\:integer}[/tex]  

(a) The population of interest to the researchers is private water wells in or near the Barnett Shales in Texas.

(b) The sample is 100 private water wells, 91 of which are located within 5 km of an active gas well using fracking, 4 private wells with no gas wells located within a 14 km radius, and 5 wells outside of the Barnett Shale with no gas well located within a 60 km radius.

(c) The characteristics of the population of interest to the researchers are the levels of potential contaminants such as arsenic and selenium in the private water wells.

(d) A measure of reliability of the inferences is important because it allows the researchers to determine the degree of confidence they can have in the findings of the study, and to identify any potential sources of error in the study design or measurement.

The sample is a subset of this group that is representative of the population, whereas the population of interest is the entire unit of people you are considering for the study. When using sampling, you typically collect information from the sample before extrapolating the results to the entire population.

Without a measure of reliability, it would be difficult to assess the generalizability of the study's findings to the broader population of private water wells in the Barnett Shale region.

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As a result, slant asymptotes of y = x -4 are found to be the solution to the provided function problem.

Mathematics includes the study of numbers and their variations, equations and associated structures, and the regions and potential uses of geometry. A "function" is the connection between a collection of inputs that individually produce a related output. An output-input relationship known as a function is one in which each input leads to a single, identifiable outcome.

Here,

Because there are no restrictions on the kind of rational function, it is possible to build one from each of the 3 asymptotes.

In addition to the graphs of the linear equation it represents, this is shown in the accompanying graph. The function's asymptotes are these.

The horizontal points include x = -4 and

There are two horizontal asymptotes: y = 0 and

Y = x – 4 are the slant asymptotes.

Additional comments

In our example function, an exponential function is used. That isn't frequently thought of as a polynomial, despite the fact that it may be stated as an infinite degree polynomial. Most authors define a rational function in terms of the fraction of polynomials.

As a result, slant equipotential lines are y = x and are the answer to the given function problem.

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Answer:

x = 4  or  x = 3

Step-by-step explanation:

x² - 7x = -12

x² - 7x + 12 = 0

(x - 4)(x - 3) = 0

x - 4 = 0  or  x - 3 = 0

x = 4  or  x = 3

Answer: The answer would be x=4 and x=3.

Step-by-step explanation: