#24Graph the function and tell wether or not it has a point of discontinuity at x = 0. If there is a discontinuity, tell wether it is removable or non removable.

#24Graph The Function And Tell Wether Or Not It Has A Point Of Discontinuity At X = 0. If There Is A

Answers

Answer 1

We have the function:

g(x) = x/(x - 2)

Notice that if x = 2 the denominator equals zero and then we have a vertical asymptote at x = 2. Furthermore, if x = 0, g(0) = 0.

The graph of g(x) is shown below:

As you can notice, there is no a discontinuity at x = 0.

#24Graph The Function And Tell Wether Or Not It Has A Point Of Discontinuity At X = 0. If There Is A

Related Questions

2x 5x+6 please simplify ​

Answers

Answer:

Step-by-step explanation:

Maybe

2x times 11x

Find the values of sin 0, cos 0, and tan e for the given right triangle. Give the exact values.sin 0=cos 0=tan 0=87

Answers

We can use the definition:

[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{hypotenuse}} \\ \\ \cos \theta=\frac{\text{adjcent}}{\text{hypotenuse}} \\ \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}[/tex]

Looking at the figure we can see the values:

But we don't have the hypotenuse value, we must use the Pythagorean theorem to find it

[tex]\begin{gathered} \text{hypotenuse = }\sqrt[]{7^2+8^2} \\ \\ \text{hypotenuse = }\sqrt[]{113} \end{gathered}[/tex]

Now we have the hypotenuse we can find all values

[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{hypotenuse}}=\frac{8}{\sqrt[]{113}} \\ \\ \cos \theta=\frac{\text{adjcent}}{\text{hypotenuse}}=\frac{7}{\sqrt[]{113}} \\ \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{8}{7} \end{gathered}[/tex]

Bentley has 32 biscuits left in his treat jar. If this represents 4/5 of what he orginally had in the jar, how may treats did he have in the beginning

Answers

he had 40 biscuits in the beginning

Explanation

to solve this we can use a rule of three

so

Step 1

let x represents the total treats he had in the beginning , so

[tex]\begin{gathered} if \\ 32\text{ biscuits}\rightarrow\frac{4}{5}of\text{ total } \\ then \\ x\text{ biscuits}\rightarrow total\text{ \lparen1\rparen} \end{gathered}[/tex]

so, the proportion is

[tex]\begin{gathered} \frac{32}{\frac{4}{5}\text{ }}=\frac{x}{1} \\ \frac{160}{4}=x \\ x=40 \end{gathered}[/tex]

therefore,

he had 40 biscuits in the beginning

I hope this helps you

Mr. Garcia gave his students a biology test last week.Here are the test scores for each of the fifteen students.Test scores938398899791838692908884858291(b) Construct a histogram for the data.(a) Complete the grouped frequency distribution forthe data. (Note that the class width is 5.)FrequencyTest scores7-6+79 to 835+84 to 88Frequency0.0043+89 to 932+1194 to 980-79 1083941 98844 to 58 89 to 93Test scoresx5?

Answers

Test scores: 93 83 98 89 97 91 83 86 92 90 88 84 85 82 91

organizing the data: 82,83,83,84,85,86,88,89,90,91,91,92,93,97,98

(a) Complete the grouped frequency distribution for the data.

79 to 83 -> 3

84 to 88 -> 4

89 to 93 -> 6

94 to 98 -> 2

(b) Construct a histogram for the data.

the histogram can be constructed using the information obtained in point (a)

use the above diagram to answer the following questions.

Answers

Remember that the sum of the interior angles is 180. Then, we have the following equation:

[tex]55^{\circ}+65^{\circ}\text{ + }\angle M\text{ = 180}[/tex]

This is equivalent to:

[tex]120^{\circ}\text{ + }\angle M=180^{\circ}[/tex]

solve for M-angle:

[tex]\text{ }\angle M=180^{\circ}-\text{ 120}^{\circ}=60^{\circ}[/tex]

Then, te correct answer is :

[tex]\text{ }\angle M^{}=60^{\circ}[/tex]

1. Which of the following would be considered a statistical question? (1) Who was the highest paid athlete in 2020? (2) How much does a gallon of gasoline cost? (3) How many people voted for president in 2016?(4) What are the different types of maple trees?

Answers

Looking at the sentences, we have that (1), (2) and (3) are questions that require just one specific answer (For (1) it's a name of a person, for (2) it's a value and for (3) it's also a single value).

But in sentence (4), there are more than one type of maple tree, so we can answer with each type of maple tree, stating the percentage of each type for example.

So the sentence that would be considered a statistical question is (4).

What is the y-intercept of the line that passes through the point (4,-9) with a slope of -1/2

Answers

Answer:

The y-intercept b for the derived equation is;

[tex]b=-7[/tex]

Explanation:

Given that the line passes through the point (4,-9) and has a slope of -1/2;

[tex]\begin{gathered} \text{slope m=-}\frac{1}{2} \\ \text{ point (4,-9)} \end{gathered}[/tex]

Applying the point-slope form of linear equation;

[tex]y-y_1=m(x-x_1)[/tex]

substituting the slope and the given point;

[tex]\begin{gathered} y-(-9)=-\frac{1}{2}(x-4) \\ y+9=-\frac{1}{2}x+\frac{4}{2} \\ y+9=-\frac{x}{2}+2 \\ y=-\frac{x}{2}+2-9 \\ y=-\frac{x}{2}-7 \end{gathered}[/tex]

Comparing it to the slope intercept form of linear equation;

[tex]y=mx+b[/tex]

where;

m = slope

and b = y-intercept

Therefore, the y-intercept b for the derived equation is;

[tex]b=-7[/tex]

How many fourteenths are there in 3/ 7 ?

Answers

The answer is 6.

This question is asking you to divide 3/7 by 1/14 (because that’s how you calculate how “many” of one number is in another number).

To divide fractions, we keep the first one the same, flip the second one upside down, and multiply them:

3/7 ÷ 1/14 -> 3/7 ÷ 14/1 -> 3/7 * 14/1

When you multiply 3/7 by 14, you get 42/7 = 6.

Tony will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $60and costs an additional $0.50per mile driven
The second plan has noinitial fee and costs an additional $0.70per mile driven
E
For what amount of driving do the two plans cost the
Same

Answers

Plan 1:

Initial (fixed) fee: $60

Variable fee: $0.50 per mile

Plan 2:

Initial (fixed) fee: $0

Variable fee: $0.70 per mile

If we call x to the number of miles driven by Tony, then the cost of Plan 1 is:

P1 = 60 + 0.5x

The cost of Plan 2 is:

P2 = 0.7x

It's required to find the number of miles Tony should drive for both plans to cost the same, that is:

60 + 0.5x = 0.7x

Subtracting 0.5x:

60 = 0.7x - 0.5x

Operating:

60 = 0.2x

Dividing by 0.2:

x = 60 / 0.2

x = 300

Tony should drive 300 miles for both plans to cost the same.

Under that condition, both plans cost the same. Plan 1 cost:

P1 = 60 + 0.5*300

P1 = 60 + 150

P1 = $210

Plan 2 cost:

P2 = 0.7*300

P2 = $210

Both costs are equal

how do I convert the rectangular equation: x=15 to a polar equation that expresses r in terms on theta?I got r=15 sectheta but wanted to double check

Answers

In polar coordinates, the x variable is given as

[tex]x=r\cos \theta[/tex]

So, we have the equation

[tex]r\cos \theta=15[/tex]

By dividing both sides by cosine of thetat, we get

[tex]r=\frac{15}{\cos \theta}[/tex]

since

[tex]\sec \theta=\frac{1}{\cos \theta}[/tex]

The above result is equivalent to:

[tex]r=15\sec \theta[/tex]

Juan earned 60% of the possible points on his first math test. His teacher offered to let him take another test to earn extra credit. Juan earned 80% of the possible points on the second test. Each test had the same number of possible points. If Juan earned 30 points on the first test, how many points did he earn on the second test?

Answers

Let:

x = Number of points Juan earned on the second text

n = Total number of points of each test

First, let's find the total number of points of each test using the information provided:

[tex]\begin{gathered} 0.6\cdot n=30 \\ so\colon \\ n=\frac{30}{0.6} \\ n=50 \end{gathered}[/tex]

Now, we can find how many points Juan earned on the second test:

[tex]\begin{gathered} x=0.8\cdot n \\ x=0.8\cdot50 \\ x=40 \end{gathered}[/tex]

Answer:

40 points

A swim team consists of 5 boys and 5 girls. A relay team of 4 swimmers is chosen at random from the team members. What is the probability that 3 boys are selected for the relay team given that the first selection was a girl? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answers

In order to find the probability start the construction of the possible relay team, if the team is made by any 4 swimmers then

[tex]10\cdot9\cdot8\cdot7=5040[/tex]

if the first member is a girl and the other three needs to be boys, the number of possibilities are

[tex]1\cdot5\cdot4\cdot3=60[/tex]

then, divide in order to find the probability

[tex]\frac{60}{5040}=\frac{1}{84}[/tex]

Find the restricted values of x for the following rational expression. If there are no restricted values of x, Indicate "No Restrictions".
−5r – 8/x² + 4

Answers

The restricted values of x for the following rational expression.

x = 0

x = -3/4

What are restriction value?

Restricted values are those values in a rational expression that bring the denominator to zero. When referring to "Market Value," the term "restricted value" denotes the property's value under the assumption that it is subject to a temporary governmental or private limit on rentals and tenant income levels. The denominator's real numbers that have a value of 0 are not included in the domain. The word "restrictions" refers to these values. Similar to how fractions are simplified, rational expressions can be too. Cancel the common factors after factoring the numerator and denominator. Place a zero as the denominator. Put the equation to rest. The restricted values are the answer or answers.

Rational expressions should first be multiplied, and then the numerator and denominator should be factored. Next, common factors should be cancelled. Notify yourself of the domain's limitations.

−5x– 8/x² + 4 = 0

- 5x - 8/[tex]x^{2}[/tex] = -4

x = 0

x = -3/4

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Sx-3y =-3
(2x + 3y = -6
a. by graphing,
What are
y =

Y2=

Answers

Given,

x-3y=-3

2x+3y=-6

Plotting it in graph we have,

Since we have only one point of intersection so that would be only one solution.

The point of intersection is (-3,0)

Thus x=-3 and y=0

I can't solve them 15 here and 15 on another post

Answers

6. Measure of angle 1 is 60 degrees because it congruent to angle 4 because they are opposed by the vertex

7. Measure of angle 3 is equal to 180 - angle 1 - angle 2 = 180 - 60 - 40 = 80 because these three angles sum 180 degrees

8. Measure of angle 5 is 40 degrees because it congruent to angle 2 because they are opposed by the vertex

9. Measure of angle 6 is equal to angle 3, because they are congruent, so it measures 80 degrees

10. Mesure of angle 7 is equal to the sum of angles 1 and 2 because they are congruent, so measure of angle 7 is 100

11. 80

12. 60

13. 120

14. 60

15. 120

Find the distance and the midpoint for each set of points given

Answers

Given,

The coordinates of the points are (2,6) and (7, 2).

Required:

The distance between the points and the midpoint of the points.

The distance between two points is calculated as,

[tex]\begin{gathered} Distance\text{ =}\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt{(7-2)^2+(2-6)^2} \\ =\sqrt{5^2+4^2} \\ =\sqrt{25+16} \\ =\sqrt{41} \\ =6.4 \end{gathered}[/tex]

Hence, the distance between the points is 6.4

The midpoint is calculated as,

[tex]\begin{gathered} Midpoint=(\frac{2+7}{2},\frac{6+2}{2}) \\ =\frac{9}{2},\frac{8}{2} \\ =(4.5,4) \end{gathered}[/tex]

Hence, the midpoint is (4.5,4).

Are the triangles congruent using AAS?
True
False

Answers

True!!

AAS= Angle Angle Side

The singular lines show one pair of congruent angles.

The double lines show another pair of congruent angles.

So, we know that there are 2 angles.

The triangles both share of their sides, the one going down the middle.

So, we know that there is a side as well!

hope this helped!!! <33

please help this is very difficult

Answers

Answer:

x=-6. y=6. xy=-36

x=-2. y=-3. xy=6

x=1. y=2. xy=2

Sara’s dogsMorning: 39, 21, 12, 27, 23, 19, 31, 36, 25Afternoon: 15, 51, 8, 16, 43, 34, 27, 11, 8, 39Comparing the morning and afternoon groups Create frequency tables to represent the morning and afternoon dogs as two sets of data. Group the weights into classes that range 10 pounds.

Answers

Answer;

Medain for morning is 25

Median for evening is 21.5

Explanation;

Here, we want to create frequency tables for each of the given groups

We start with the morning group

The frequency table for it is as follows;

Now, we proceed to the afternoon group

We have this as follows;

Lastly, we will want to get the median value of both groups

To do this, we need to re-arrange the values in the data set in ascending or descending order

For the purpose of this solution, we shall be using the ascending order mode. Then from here, we pick out the middle value

For the morning group, we have;

12, 19,21, 23,25,27,31,36,39

Since the numbers are 9, the middle number will be the 5th number since it leaves equal spread of values on the left and right

Thus, we have the median value as 25

The afternoon set, we have it as;

8,8,11,15,16,27,34,39,43,51

We proceed to choose the mid 5th values comig from both ends

We have this as;

We have these values as; 16 and 27

We add these and divide by 2

We have this as;

[tex]\frac{16+27}{2}\text{ = 21.5}[/tex]

Which expression represents the area of the rectangle below in square units

Answers

Area of rectangle is given by:-

[tex]\begin{gathered} l\times b \\ =(3x+2)\times2x \\ =6x^2+4x \end{gathered}[/tex]

So the correct answer is

[tex]6x^2+4x[/tex]

Benjamin invested an amount of $12,000.00 in a mutual fund. After 4 years and 6 months the accumulated value of his investment was $13,407.58. What is the nominal interest rate of the investment if interest is compounded semi-annually?__________%Round to two decimal places

Answers

Given:

The accumulated value of investment is A = 13,407.58.

The invested amount is P = 12,000.00.

The time period is 4 years and 6 months.

Explanation:

The formula for the accumulated value at r rate of interest is compounded semi-annually.

[tex]A=P(1+\frac{r}{200})^{2\cdot t}[/tex]

Substitute the values in the formula to determine the value of r.

[tex]\begin{gathered} 13407.58=12000(1+\frac{r}{200})^{2\cdot4.5} \\ \frac{13407.58}{12000}=(1+\frac{r}{200})^9 \\ 1+\frac{r}{200}=(\frac{13407.58}{12000})^{\frac{1}{9}} \\ \frac{r}{200}=1.01239-1 \\ r=0.01239\cdot200 \\ =2.478 \\ \approx2.48 \end{gathered}[/tex]

So the rate of interest is 2.48%.

The length of a rectangle is 9 inches more than the width. The perimeter is 34 inches. Find the length I need both length and the width of the rectangle

Answers

Explanation

The perimeter is the sum of the side lengths of a polygon. Now, let it be:

• l,: the length of the rectangle

,

• w,: the width of the rectangle

Considering the information given and the previous definition, we can write and solve the following system of equations.

[tex]\begin{cases}l=9+w\Rightarrow\text{ Equation 1} \\ l+w+l+w=34\Rightarrow\text{ Equation 2}\end{cases}[/tex]

We can use the substitution method to solve the system of equations.

Step 1: We combine like terms in Equation 2.

[tex]\begin{cases}l=9+w\Rightarrow\text{ Equation 1} \\ 2l+2w=34\Rightarrow\text{ Equation 2}\end{cases}[/tex]

Step 2: We substitute the value of l from Equation 1 into Equation 2.

[tex]\begin{gathered} 2l+2w=34 \\ 2(9+w)+2w=34 \end{gathered}[/tex]

Step 3: We solve for w the resulting equation.

[tex]\begin{gathered} \text{ Apply the distributive property on the left side} \\ 2\cdot9+2\cdot w+2w=34 \\ 18+2w+2w=34 \\ \text{ Add similar terms} \\ 18+4w=34 \\ \text{ Subtract 18 from both sides} \\ 18+4w-18=34-18 \\ 4w=16 \\ \text{ Divide by 4 from both sides} \\ \frac{4w}{4}=\frac{16}{4} \\ w=4 \end{gathered}[/tex]

Step 4: We replace the value of w in Equation 1.

[tex]\begin{gathered} \begin{equation*} l=9+w \end{equation*} \\ l=9+4 \\ l=13 \end{gathered}[/tex]

Thus, the solution of the system of equations is:

[tex]\begin{gathered} l=13 \\ w=4 \end{gathered}[/tex]Answer

The length of the rectangle is 13 inches, and the width of the rectangle is 4 inches.

72bz +96b2h + 90xbz + 120xbh +

Answers

Factoring

Factor the expression:

[tex]72b^2z+96b^2h+90xbz+120xbh[/tex]

Divide the expression into two halves:

[tex](72b^2z+96b^2h)+(90xbz+120xbh)[/tex]

Factor b^2 from the first group and xb from the second group:

[tex]b^2(72z+96h)+xb(90z+120h)[/tex]

Now find the greatest common multiple of 72 and 96:

72= 2*2*2*3*3

96=2*2*2*2*2*2*3

Now we take the common factors with their least number of repetitions:

GCF=2*2*2*3=24

Now we find the GCF of 90 and 120:

90=2*3*3*5

120=2*2*2*3*5

GCF=2*3*5=30

Taking the GCF of each group:

[tex]\begin{gathered} b^224(3z+4h)+xb30(3z+4h) \\ =24b^2(3z+4h)+30xb(3z+4h) \end{gathered}[/tex]

Now we finally take out 3z+4h from both groups:

[tex]\mleft(3z+4h\mright)(24b^2+30xb)[/tex]

This last expression can be further factored by taking out 6b from both terms:

[tex]6b(3z+4h)(4b+5x)[/tex]

This is the final expression factored as much as possible

The chart below shows how many newspapers each person stacked. Which operation would be used to find the total number of newspapers Diane stacked?

Answers

Answer:

Where's the chart?

Step-by-step explanation:

Two rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded) if AB = BE = 2 and AD = ED = 4.

Answers

The area of the overlapping region is of: 6.25 units squared.

Area of a rectangle

The area of a rectangle of length l and width w is given by the multiplication of the dimensions, as follows:

A = lw.

The dimensions of the right triangle as follows:

Leg x.Leg 2.

Hence the remaining leg on the overlapping region is:

4 - x, as AD = 4.

By symmetry, the other dimension of the overlapping region is also of:

4 - x.

Being also the hypotenuse of the right triangles.

The value of x can be found applying the Pythagorean Theorem as follows:

x² + 2² = (4 - x)²

x² + 4 = 16 - 8x + x²

8x = 12

x = 1.5.

Then the two dimensions of the shaded region are:

4 - 1.5 = 2.5.

Meaning that the area is of:

A = 2.5 x 2.5 = 6.25 units squared.

Missing information


The figure is missing and is given by the image at the end of the answer.

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A truck rental is $25 plus $.35/mi. Find out how many miles Ken traveled if his bill was $51.95.

Answers

So,

We could write the following equation, where "x" is the number of miles travelled.

[tex]0.35x+25=51.95[/tex]

If we solve this equation, the first thing we're going to do is to let all "x terms" in a side of the equation and all the numbers in the other side. If "25" is summing in a side, it will change its sign when we pass it to the other side. Like this:

[tex]0.35x=51.95-25[/tex]

Now, we substract the numbers above and get:

[tex]0.35x=26.95[/tex]

Now, if 0.35 is multiplying "x", we are going to pass this number to divide the amount in the other side:

[tex]x=\frac{26.95}{0.35}=77[/tex]

Therefore, Ken travelled 77 miles.

How do the graphs of transformations compared to the graph of the parent function. Need the answer to this

Answers

• A ,Reflection

,

• A ,Vertical Shift 4 units down

1) Considering the parent function, i.e. the simplest form of a family of functions, in this case, to be:

[tex]f(x)=x^4[/tex]

2) Then we can state that this transformed function:

[tex]g(x)=-x^4-8[/tex]

We can see the following transformations:

• A ,Reflection,, pointed out by the negative coefficient

,

• A ,Vertical Shift 4 units down

As we can see below, to better grasp it:

A salaried employee receives an annual salary of $40000. there are 26 pay periods during the year. during the current pay period, She receives a bonus of $200 what is her gross pay for this pay period ?A. $1,938.46B. $1,738.46C. $1,538.46D. $1,338.46

Answers

ANSWER:

C. $1,538.46

STEP-BY-STEP EXPLANATION:

To understand the question we must take into account that it is the gross payment, which is the payment received by the employee agreed with the company, without taking into account deductions or bonuses.

Therefore, we calculate it with the total payment divided by the amount of payments, like this:

[tex]\begin{gathered} p=\frac{40000}{26} \\ \\ p=\text{ \$}1538.46 \end{gathered}[/tex]

So the correct answer is C. $1,538.46

Write an equation of a line in slope-intercept form that has a slope of -3 and goes through the point (0, 3) O y = 3x - 1 O y = 3x + 2 O y = 3x O y = -3x + 3

Answers

ANSWER

y = -3x + 3

EXPLANATION

We want to write the equation in slope-intercept form, which is the form:

y = mx + c

where m = slope; c = intercept

To do that, we have to use the point-slope method:

y - y1 = m(x - x1)

where (x1, y1) = point the line goes through

From the question:

m = -3

(x1, y1) = (0, 3)

So, we have that:

y - 3 = -3(x - 0)

y - 3 = -3x

=> y = -3x + 3

That is the equation of the line in slope-intercept form.

tim wants to order pizza for 22 employees.Each employee should get 1/4 of a pizza.How many pizzas should tim order ?

Answers

Tim should order approximately 6 pizza.

Define division.

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on. One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction. Mathematicians use addition, subtraction, multiplication, and division as their four fundamental arithmetic operations. The division is one of these four operations that we employ most frequently in our daily work. It involves dividing a huge group into equally sized smaller units. Divide 25, for instance, by 5.

Given Data

Number of employees = 22

Slice of pizza one should get = 1/4

Dividing 22 by 1/4

[tex]\frac{22}{4}[/tex]

5 and [tex]\frac{1}{2}[/tex]

Tim should order approximately 6 pizza.

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