The units digit of any integer that is the sum of two fourth powers must be 0, 1, 2, 5, 6, or 7.
Let n be an integer that can be written as a sum of two fourth powers. Then, n = a4 + b4, for some integers a and b. We can write n as n = 10k + c, where k is an integer and c is the units digit of n.
We want to show that the units digit of n must be either 0, 1, 2, 5, 6, or 7. To do this, we will look at the possible values of c when a and b are each 0, 1, 2, 3, and 4.
When a = 0 and b = 0, c = 0. When a = 0 and b = 1, c = 1. When a = 0 and b = 2, c = 4. When a = 0 and b = 3, c = 9. When a = 0 and b = 4, c = 6.
When a = 1 and b = 0, c = 1. When a = 1 and b = 1, c = 0. When a = 1 and b = 2, c = 7. When a = 1 and b = 3, c = 6. When a = 1 and b = 4, c = 5.
When a = 2 and b = 0, c = 4. When a = 2 and b = 1, c = 7. When a = 2 and b = 2, c = 0. When a = 2 and b = 3, c = 3. When a = 2 and b = 4, c = 2.
When a = 3 and b = 0, c = 9. When a = 3 and b = 1, c = 6. When a = 3 and b = 2, c = 3. When a = 3 and b = 3, c = 0. When a = 3 and b = 4, c = 7.
When a = 4 and b = 0, c = 6. When a = 4 and b = 1, c = 5. When a = 4 and b = 2, c = 2. When a = 4 and b = 3, c = 7. When a = 4 and b = 4, c = 0.
Thus, when a and b are each 0, 1, 2, 3, and 4, c can only be 0, 1, 2, 5, 6, or 7. Therefore, the units digit of any integer that is the sum of two fourth powers must be 0, 1, 2, 5, 6, or 7.
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What is the correct answer
C = 45 + 0.25t. The 45 represents the baseline amount that she is charged per month. The t represents each additional text, and the 0.25 represents how much she is charged for each additional text.
Given the diagram find the measurement of AED
A.110°
B.116°
C.118°
D.123°
Note that the measure of ∠AED is 123°. (Option D) This is arrived at using the properties of a 4 sided polygon and angles on a straight light postulate.
What is a polygon?A polygon is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.
We know that the sum of angles in a polygon is 360°
Since ∠ABD = 46°
That is Sum of Angles in ΔBDC Less (79+57) =
180 - (101)
= 46°
And ∠EDB = 180-79 (angles on a straight line)
⇒ ∠EDB = 101°
And ∠BAE = 90° (Given)
Thus,
∠AED = 360 - 90-46-101; Thus
∠AED = 123°
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Let f be a function defined and continuous on the closed interval [a,b]. If f has a relative maximum at c and a < c < b, which of the following statements must be true? f(c) exists. If f'(c) exists, then f'(c) = 0. If f"(c) exists, then f"(c) LE 0. II only III only I and II only I and III only II and III only
Given that function f is defined and continuous on the closed interval [a,b], the correct statements are:
f(c) existsif f'(c) exists, then f'(c) = 0 (C. I and II only)From the case we know that:
function f is on the closed interval [a,b]
c = relative maximum
A function reach its relative maximum when its first derivative function is equal to zero (0). Since c is the relative maximum of function f, then:
f'(c) = 0
The third statement is wrong because when c is the relative maximum point, then its second derivative function must be lower than zero (0), or:
f''(c) < 0
When the second derivative function is greater than zero (0), it indicates that the given critical point is the relative minimum.
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CAN SOMEONE HELP ME WITH THIS
The values for the variables a and b in the parallelogram are 2 and 3 respectively.
How to evaluate for the variables in the parallelogramThe parallelogram STVW have two pairs of parallel sides hence VW = TS and TV = SW.
We shall evaluate for variables a and b as follows:
3a + 11 = a + 15
3a - a = 15 - 11 {collect like terms}
2a = 4
a = 4/2 {divide through by 2}
a = 2
3b + 5 = b + 11
3b - b = 11 - 5 {collect like terms}
2b = 6
b = 6/2 {divide through by 2}
b = 3
Therefore, the values for the variables a and b in the parallelogram are 2 and 3 respectively.
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A
D
In parallelogram
m
(2x +12)
5x°
B
C
ABCD, m
Find the value of X
and of
Answer:
x = 24
Step-by-step explanation:
In a parallelogram, adjacent angles are supplementary.
∠B + ∠C = 180°
5x + 2x + 12 = 180
7x + 12 = 180
Subtract 12 from both sides,
7x = 180 - 12
7x = 168
Divide both sides by 7,
x = 168 ÷7
[tex]\boxed{x = 24^\circ}[/tex]
A group of students was asked about the number of flights they have taken. The data is shown in the line plot. 9 10 11 12 Flights Taken 13 14 ● 15 17 18 Which of the following best describes the spread of the data? Explain its meaning in this situation. The data has a range of 5, which is a wide spread. This means the greatest number of flights was 5. The data has a range of 15, which is a narrow spread. This means that there is not a large difference in the number of flights taken by the students. The data has a range of 5, which is a narrow spread. This means that most of the students have taken a similar number of flights. The data has a range of 15, which is a wide spread. This means that there is a difference of 15 flights between each of the students.
the question is mistake
Find the solution to the system of equations.
-2x+2y=-4
3z + 3y = -18
The solution to the system of equations is x = -1 and y = -3
How to determine the solutionFrom the question, we have the following parameters that can be used in our computation:
-2x+2y=-4
3x + 3y = -18
Multiply (1) by 1.5
So, we have the following representation
-3x + 3y = -6
3x + 3y = -18
Add the equations
6y = -24
So, we have
y = -3
This means that
-2x + 2(-3) = -4
Evaluate
2x = -2
Divide
x = -1
Hence, the value of x is -1
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Student Question Bank chapter 6: Textbook Clinical Chemistry Principles, Techniques, and Correlations 7th ed. Bishop True or Flase? In chromatography, the stationary phase is always of a solid matrix.
Clinical Chemistry Principles, Techniques, and Correlations 7th ed. Bishop is False.
A typical analytical technique (the method used to determine a chemical or physical property of a chemical substance, chemical element, or mixture.) for dissolving a chemical combination into its constituent parts so that each part may be carefully examined is called "chromatography."
The liquid or gaseous medium that moves the items to be separated over the stationary phase of a chromatography device at varying speeds is called as mobile phase.
In chromatography, the stationary phase can be either a solid or a liquid matrix. The mobile phase, which moves through the stationary phase, typically occurs in a liquid or a gas.
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Monroe is tracking the circular path of a satellite in the sky using his telescope. He determined that the satellite has formed an arc of 32° in one hour. The satellite is 36,000 km above the earth's surface. How far did the satellite travel in the one-hour period to the nearest kilometer?
Answer Choices:
1) 1,400 km
2) 10,053 km
3)20,106 km
4)72,382 km
To calculate the distance traveled by the satellite, we need to find the circumference of the circle it traces in the sky. The circumference can be found using the formula:
C = 2 * π * r
where r is the radius of the circle (i.e., the distance from the center of the earth to the satellite), and π is pi, approximately equal to 3.14.
r = 36,000 km
C = 2 * π * 36,000 km
C = 72,000 * π km
Next, we need to find what fraction of the circumference the satellite has traveled in one hour. This is given by the fraction of the total circle the satellite has traced, which is equal to the angle it has formed divided by 360°.
fraction = 32° / 360°
Finally, we can multiply the circumference by the fraction to find the distance traveled by the satellite:
distance = C * fraction
distance = 72,000 * π * 32° / 360° km
Rounding the result to the nearest kilometer, the satellite has traveled approximately:
distance = 73,382 km
So, the satellite traveled approximately 73,382 km in one hour.
Please help me answer #5 and #6
5) The equation of population after year 2000 is expressed as;
P = 65x + 622
6) Population in the year 2012 is; P = 1402 students
How to find the equation of population?The parameters given are;
Population in 2003 = 817
Population in 2006 = 1012
Thus;
Average population growth per year = (1012 - 817)/3
Average population growth per year = 65 people
Now, we see that the population of people in the year 2000 was 622.
Thus;
5) Equation of population is;
P = 65x + 622
where x is number of years after year 2000
6) Population in the year 2012 which is 12 years after year 2000 is;
P = 65(12) + 622
P = 1402
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Please help me,this is proportionality theorems
Answer:
Below
Step-by-step explanation:
Line DE grows to 5 as you move to the midpoints of BC and AC....
go the the other half of the way to the end AB and it grows another 5 for a total of 10
The Triangle Inequality
Feb 08, 6:54:25 PM
Which of the following sets of numbers could not represent the three sides of a
triangle?
O {12, 17, 30}
O {15, 21, 33}
O {4, 6, 7)
O {12, 27, 37)
The sets of numbers could not represent the three sides of a triangle is
{12, 17, 30}.
What is Triangle Inequality?The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side.
Given:
a) {12, 17, 30}
Using Triangle Inequality
12 + 17 < 30 This, measurement cannot give Triangle.
b) {15, 21, 33}
Using Triangle Inequality
15+ 21 > 33
21+33>15
33+15>21
This measurement give Triangle.
c) {4, 6, 7}
Using Triangle Inequality
4 + 6 > 7
6+7>4
7+4 > 6
This measurement give Triangle.
d) {12, 27, 37}
Using Triangle Inequality
12+ 27 > 37
27+ 37 > 12
12 + 37 > 27
This measurement give Triangle.
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A man walks at 50km per hour.What distance would he cover in 2 and a half hours
Answer:
50+50=100
50/2=25
125km in 2 and a half hours
Step-by-step explanation:
Umm I'm assuming this isn't a trick question and saying just add 50+50 for 2 hours and then divide 50 by 2 to get 25. so 125 I hope i'm right :')
Answer:
Step-by-step explanation:
The man would walk 125km.
Explanation: The man would walk 125km, because if every hour he is walking 50km then if he walks for 2.5 hours, then all you have to do is multiply 50km by 2.5 hours.
Write the expression -13y+7-11-4y as a um
-13y + 7 - 11 - 4y can be written as -17y - 11.
What is expression?Expression is a way of conveying emotions, thoughts, or ideas through verbal or nonverbal means. It is often used to communicate an individual's feelings, beliefs, or opinions, and can be expressed through language, art, music, dance, and other forms of communication. Expression can be used to convey a wide range of emotions, from joy and excitement to anger and sorrow. Expression is an essential part of communication, and without it, we would not be able to effectively convey our thoughts, feelings, and desires. The way we express ourselves can also be a reflection of our personality and can give people an insight into who we are. Expression is also important for self-expression, as it allows us to explore our own thoughts and emotions, and express them in a way that may be more comfortable for us.
This can further be written as -17y × (-1) - 11. Therefore, the expression can be written as a multiplication as -17y × (-1) - 11.
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Let X be a random variable with the following probability mass function: P(X = -1) = 1/3, P(X = 0) = 1/3, P(X = 1) = 1/3 Let Y be the random variable defined by Y = 1 when X = 0 Y = 0 when X notequalto 0 That is, Y takes on only two values 0 and 1, and Y is zero whenever X is not, and F is 1 whenever X is zero. Calculate the probability distribution of X, P(X = x), and the probability distribution of Y, P(Y = y). Calculate the joint distributions of X and Y, and determine whether or not X and Y are independent. Calculate the covariance of X and Y. In a previous exercise, you showed that if two random variables were independent, they were uncorrelated. Based on your answer in this problem, is it true that if two random variables are uncorrelated, they are independent?
If two random variables are uncorrelated, they are independent and the covariance of X and Y is 0.
Probability is a measure of the likelihood of an event occurring.
In this case, we are given that P(X = -1) = 1/3, P(X = 0) = 1/3, and P(X = 1) = 1/3.
We are also given a second random variable Y, which is defined in terms of X. Y takes on the value of 1 when X = 0, and 0 otherwise. The probability distribution of Y is the set of probabilities associated with each possible value of Y. In this case, Y can only take on the values 0 or 1, so
=> P(Y = 0) = P(X = -1) + P(X = 1) = 2/3 and P(Y = 1) = P(X = 0) = 1/3.
The joint distribution of X and Y is the set of probabilities associated with each possible combination of X and Y. In this case, there are three possible combinations: (X = -1, Y = 0), (X = 0, Y = 1), and (X = 1, Y = 0). The joint probabilities are simply the products of the marginal probabilities of X and Y.
=> P(X = 0, Y = 1) = P(X = 0) * P(Y = 1) = (1/3) * (1/3) = 1/9.
Finally, we can calculate the covariance of X and Y, which is a measure of how much the two variables vary together. The formula for covariance is:
=> Cov(X,Y) = E[XY] - E[X]E[Y].
Using the joint distribution we calculated earlier, we can find
=> E[XY] = (-1)(2/9) + (0)(1/3) + (1)(2/9) = 0
and
=> E[X] = (-1)(1/3) + (0)(1/3) + (1)(1/3) = 0.
We can also find
=> E[Y] = (0)(2/3) + (1)(1/3) = 1/3.
Therefore,
=> Cov(X,Y) = 0 - (0)*(1/3) = 0.
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frank invests $2,500 in an account that has an annual interest rate of 5.4% compounded continuously. hannah invests $3,000 in an account that has an annual interest rate of 3.2% compounded quarterly. which of the following statements is true when comparing the amount of money in the two accounts after 10 years?
The statement that is true when comparing the two accounts after 10 years is: A: "Hannah's account has more money than Frank's account".
To compare the amount of money in the two accounts after 10 years, we can use the formula for continuous compound interest:
A = Pe^(rt)
where A is the amount of money in the account after t years, P is the principal (initial amount), r is the annual interest rate (expressed as a decimal), and e is the mathematical constant approximately equal to 2.71828.
For Frank's account, we have:
A = 2500e^(0.05410) = 4244.96 dollars (rounded to the nearest cent)
For Hannah's account, we have to take into account the quarterly compounding. The formula for quarterly compound interest is:
A = P(1 + r/n)^(nt)
where n is the number of compounding periods per year (4 for quarterly compounding), and t is the time in years. Thus, we have:
A = 3000*(1 + 0.032/4)^(4*10) = 4412.09 dollars (rounded to the nearest cent)
Therefore, the amount of money in Hannah's account after 10 years is greater than the amount in Frank's account.
"
Complete question
frank invests $2,500 in an account that has an annual interest rate of 5.4% compounded continuously. hannah invests $3,000 in an account that has an annual interest rate of 3.2% compounded quarterly. which of the following statements is true when comparing the amount of money in the two accounts after 10 years?
A: Hannah's account has more money than Frank's account
B: : Frank's account has more money than Hannah's account
"
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Use point-slope form to write the equation of a line that passes through the point ( 12 , 11 ) (12,11) with slope 3 2 2 3 .
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
Substituting the given values, we get:
y - 11 = (3/2)(x - 12)
Expanding and simplifying, we get:
y - 11 = (3/2)x - 18
y = (3/2)x - 7
Therefore, the equation of the line that passes through the point (12, 11) with slope 3/2 is y = (3/2)x - 7 in slope-intercept form or y - 11 = (3/2)(x - 12) in point-slope form.
Select the correct answer.
Select the largest decimal.
1,238.308
1,238.83
1,283.083
1,233.38
1,283.803
Answer:1,283.803
Step-by-step explanation:
everybody help i just need to pass today mwa
Answer:
20
Step-by-step explanation:
Easiest way to solve is to consider the formula for the area of the trapezoid, which is 0.5h(a+b), where h is the altitude and a and b are the two bases.
Here we know the area, the altitude and one base so let's sub these in to find the other base:
92=0.5*8*(3+b)
92=4(3+b)
23=4+b
b=20
state the domain and range of the following function. describe the transformations to the basic function. then, write the equations of each of the function.
The equation for line 1 is y = x+6 and equation for line 2 is y= -x-4. The domain and range is as follows,
y = x+6 {(x,y)| x≤ -5 , y≤ 1}
y= -x-4 {(x,y) x≥-5, y≤1}
The line 1 passes through points (-6,0) and (-5,1).
Equation for a line is y= Ax+B
Using two points we can formulate the following equations
-6A+B =0
-5A+B =1
Subtracting the two equations,
-A = -1, so A= 1
-6A+B = 0
-6 ×1 + B = 0
B= 6
So the equation for the line by substituting values of A and B is
y= x+6
The domain is all values ≤-5 and range is all values ≤1
The line 2 passes through (0,-4) and ( -5,1)
Formulating equations using points
B= -4
-5A+B =1
A = -1
Substituting in equation for line 2
y = -x-4
The domain is all values ≥ 5 and range is all values ≤1.
So the equation, domain and range of line 1 is y = x+6 {(x,y)| x≤ -5 , y≤ 1} and for line 2 is y= -x-4 {(x,y) x≥-5, y≤1}
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The complete question is included as image
If MNOP is a parallelogram,
find the measure of P.:
(5x – 11)°
(11x - 33)
please help! :)
Answer:
[tex]59^{\circ}[/tex]
Step-by-step explanation:
Adjacent angles of a parallelogram are supplementary.
[tex]5x-11+11x-33=180 \\ \\ 16x-44=180 \\ \\ 16x=224 \\ \\ x=14[/tex]
Opposite angles of a parallelogram are congruent.
[tex]m\angle N =m\angle P \implies m\angle P=5(14)-11=59^{\circ}[/tex]
PLEASE HELP DUE ASAP!
The graph of the function f(x) = 3√(3 - x) is at the end of the answer.
How to graph the function?We want to graph the function f(x) = 3√(3 - x)
To do so, we need to find some points on that line, to find the points we need to evaluate the function in some values of x
if x = -1
f(-1) = 3√(3 + 1) = 3*2 = 6
if x = 3
f(3) = 3√(3 - 3) = 3*0 = 0
if x = -6
f(-6) = 3*√(3 + 6) = 3*3 = 9
if x = -13
f(-13) = 3*√(3 + 13) = 3*4 = 12
Then the points are (-1, 6), (3, 0), (-6, 9), (-13, 12)
Now we can just graph these 4 points and connect them with a curve, the graph of the function is below.
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one of your customers wants you to build a personal server that he can use in his home. one of his concerns is making sure that he has at least one data backup stored on the server in the event that a disk fails. you have decided to back up his data using raid.
RAID, which stands for Redundant Array of Inexpensive Disks, is a data storage technology that combines multiple physical disks into a single logical unit to provide data redundancy, improved performance, and increased storage capacity.
RAID accomplishes this by distributing data across multiple disks, so that if one disk fails, the data can be rebuilt from the remaining disks.
There are several different RAID levels to choose from, each with its own benefits and trade-offs. For a personal server with the goal of data backup and redundancy, RAID 1 would be a good choice.
Setting up RAID 1 is relatively straightforward. You'll need two identical hard drives of sufficient size, and a RAID controller (which may be built into the motherboard). You can then configure the RAID controller to mirror the data between the two drives, so that they appear as a single logical drive to the operating system.
It's worth noting that RAID is not a substitute for regular backups. While it can provide protection against disk failures, it won't protect against other types of data loss, such as accidental deletion or corruption. It's still important to have a regular backup schedule, and to store backups offsite or in the cloud to protect against physical damage or theft.
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In which table does y vary directly with x?
Answer:
C
Step-by-step explanation:
In table C, each time x increases by one, y increases by 26 correspondingly. This suggests that y = 26x. The other 3 tables do not show a consistent pattern or relationship between x and y.
Table A can be disproved because, though it seems at first to be a multiple of -2 for every x value, the third data value (3, -16) disproves this. It would have to be (3, -6) for this relationship.
Table B has no clear pattern; the difference from the y values corresponding to x=1 and x=2 is 23, while the difference between x=2 and x=3 is also 23. However, there is no x & y relationship that can be defined to find x or y when given the other.
Table D has no clear pattern; the difference between x=1 and x=2 is 6, but the difference between x=2 and x=3 is 7.
Set up the integral that uses the method of disks/washers to find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified lines. y = 3 root x, y = 3x A) About the y-axisB) About the line y=3
Answer:
See below for answers
Step-by-step explanation:
Part A
[tex]\displaystyle V=\pi\int\limits^d_c {(R^2-r^2)} \, dy\\=\pi\int\limits^3_0 {\biggr(\biggr(\frac{y^2}{9}\biggr)^2-\biggr(\frac{y}{3}\biggr)^2\biggr)} \, dy\\=\pi\int\limits^b_a {\biggr(\frac{y^4}{81}-\frac{y^2}{9}\biggr)} \, dy[/tex]
Make sure to write the functions in terms of y since you rotate on a vertical axis.
Part B
[tex]\displaystyle V=\pi\int\limits^b_a {(R^2-r^2)} \, dx\\=\pi\int\limits^1_0 {((3-3\sqrt{x})^2-(3-3x)^2)} \, dx\\=\pi\int\limits^1_0 {((9-18\sqrt{x}+9x)-(9-18x+9x^2))} \, dx\\=\pi\int\limits^1_0 {(-18\sqrt{x}-9x-9x^2)} \, dx[/tex]
Make sure to fix the radii so they start at y=3.
1.3 Find the center of mass of a right-circular cone with a base radius R, heighth, and a nonuniform mass density varies as the square of the distance from apex (tip of the cone).
1.4Find the center of gravity of a very thin right-circular conical shell of a base radius R, and heighth. The mass density is a constant.
1) The center of mass of a right-circular cone with a base radius r, height h, and a non-uniform mass density varies as the square of the distance from apex (tip of the cone) is:
ρ(x, y, z) = k × ([tex]\sqrt{(x^2 + y^2 + z^2)}[/tex])²
where k is a constant of proportionality.
2) The center of gravity of a very thin right-circular conical shell of a base radius R, and height h is: 2h/3
1) Let us assume that m represents the total mass of the right-circular cone.
The center of mass for the x, y, and z-coordinates would be:
x-coordinate:
[tex]x_{cm}[/tex] = (1/m) × ∫∫∫_V x × ρ(x, y, z) × dV
y-coordinate:
[tex]y_{cm}[/tex] = (1/m) × ∫∫∫_V y × ρ(x, y, z) × dV
z-coordinate:
[tex]z_{cm}[/tex] = (1/m) × ∫∫∫_V z × ρ(x, y, z) * dV
where V - the volume of the cone,
ρ(x, y, z) - the mass density function,
Since the mass density varies as the square of the distance from the apex, we have:
ρ(x, y, z) = k × ([tex]\sqrt{(x^2 + y^2 + z^2)}[/tex])²
where k is a constant of proportionality.
Substituting this into the above equations, we find the center of mass of the cone.
2) Let us assume that x’ be the distance from the vertex of the cone to any point on the axis of the right-circular conical shell.
Also R be the radius of the base of the right-circular conical shell and ‘h’ is the height of the right-circular conical shell.
Let r be the distance of any point on the cone from the axis of the right-circular conical shell , the distance being measured perpendicular to this axis.
And l is the distance of any point on the right-circular conical shell directly from the vertex.
r/R = z/h = l / L
Let us assume that σ be the surface density of mass of the cone.
The formule for center of mass of a system is given by,
x=∫z.σ dA / ∫σdA
but dA = 2πr.dl which is an infinitesimal area around the circle.
After solving this expression we get x = 2h/3
Therefore, the center of gravity of a very thin right-circular conical shell of a base radius R, and height h is given by 2h/3
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What is the slope of the line that passes through the points ( 8 , − 6 ) (8,−6) and ( 5 , − 1 ) (5,−1)? Write your answer in simplest form.
Answer: The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Plugging in the given points, we get:
m = (-1 - (-6)) / (5 - 8)
m = 5 / -3
m = -5/3
So the slope of the line that passes through the points (8, -6) and (5, -1) is -5/3.
Step-by-step explanation:
Which dotted line segment correctly represents the perpendicular bisector of line segment XY?
AB
CD
GF
TW
AB line segment correctly represents the perpendicular bisector of line segment XY.
What is Line segment?Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.
Given that;
There are 4 doted lines are shown.
Now, From all dotted line;
Line segment AB divides the line segment XY into two equal parts.
Hence, AB line segment correctly represents the perpendicular bisector of line segment XY.
Thus, ''AB line segment'' correctly represents the perpendicular bisector of line segment XY.
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Determine the point(s), if any, at which the function is discontinuous. Classify any discontinuity as jump, removable, infinite, or other. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x) = 3 / x2 + 4
jump discontinuitiesx=
removable discontinuitiesx=
infinite discontinuitiesx=
other discontinuitiesx=
jump discontinuities x= DNE
removable discontinuities x= DNE
infinite discontinuities x= -2, 2
other discontinuities x= DNE
The function has an infinite discontinuity at x=-2 and x=2 because the denominator of the fraction, x^2 + 4, approaches 0 as x approaches -2 or 2.
Stefan wants to graph a system of two linear equations to find the solution. Which
statement about the graph of the system is true?
A. If the graph of the system shows parallel lines, then there are infinite
solutions.
B. If the graph of the system shows only one line, then there are infinite
solutions.
C. If the graph of the system shows perpendicular lines, then there are no
solutions.
O
D. If the graph of the system shows lines that cross through the origin, then
there are no solutions.
Answer: The correct answer is A. If the graph of the system shows parallel lines, then there are infinite solutions.
When two linear equations in the system have the same slope and different y-intercepts, the lines will be parallel and will never intersect. This means that there is no solution to the system.
On the other hand, when two linear equations in the system have different slopes, the lines will intersect at exactly one point, which is the unique solution to the system.
So, in summary:
Parallel lines: no solution
Intersecting lines: one solution
Infinite solutions: lines are the same.
Step-by-step explanation: