Answers
Answer:
\(y=-\frac{1}{4} x-1\)
Step-by-step explanation:
find the slope of the line using the two points (0,-1) and (4,-2)
\(\frac{(-2+1)}{(4-0)} =-\frac{1}{4}\)
since we already know that the y-intercept is -1 then you plug the numbers into the slope-intercept form y=mx+b and you get \(y=-\frac{1}{4}x-1\)
Related Questions
Determine if each statement below is true or false. If the statement is true, simply write the word True for your answer; no other justification is needed. If the statement is false, you should write the word False and also give a counter- example to the statement to justify your answer. For example, if the statement is "For all sets A and B, A CAN B", a cor- rect answer would be: False. If A {1, 2} and B = {2,3},then An B = 2, and A & ANB Assume in all cases that that the domain of the given sets is N. In other words, A, B and C are subsets of the natural numbers. (4 pts each) (a) For all sets A and B, B C (AUB). (b) For all sets A and B, (AUB) C A. (c) For all sets A and B, (AUB) - B = A. (d) For all sets A and B, A - (B - A) = A. (e) For all sets A, B and C, if A + B and B + C then A #C.
Answers
All of the statements are false except statement d. Counter-examples are given for each false statement each and explained below.
How to Write a Counter-example?a) The statement is incorrect because there may exist elements in set B that are not included in the union of sets A and B.
Counter-example: if we take A as {1} and B as {2}, we can see that B is not part of the union of A and B, denoted as A ∪ B.
(b) The statement is incorrect because the union of sets A and B can include elements that are not in set A.
Counterexample: Let A = {1} and B = {2}. Then (A ∪ B) = {1, 2}, and {1, 2} is not a subset of A since it contains an element (2) that is not in A.
(c) The statement is false because removing set B from the union of sets A and B may result in elements that are not present in set A.
Counterexample: Let A = {1} and B = {2}. Then (A ∪ B) - B = {1} - {2} = {1}, which is not equal to A.
(d) The statement is true because removing the set A from the set B minus A will result in set A itself.
(e) The statement is false because there can be cases where sets A, B, and C have overlapping elements, indicating that A is not disjoint from C.
Counterexample: Let A = {1}, B = {2}, and C = {1, 2}. Then A + B = {1, 2} and B + C = {1, 2}, but A ∩ C = {1} is not an empty set, so A and C are not disjoint.
Learn more about Counterexample on:
https://brainly.com/question/12955211
#SPJ4
Please help! I'm timed.
Answers
Answer:
M=-10/4
M=-5/2
-5/4+m=-15/4
Step-by-step explanation:
Original equation:
3/4+m=-7/4
=-5/2
the other answers mentioned above is also -5/2
Hope that helps!
Malae a detailed graph of the function f(x)=x 4
+2x 3
−2 defined on the closid interval [-2, ? by anompleting the following stepe. (a) Compate f ′
(x). f ′
(x)− (b) (Show your work.) Deternine those paints for which f ′
(x)=0, that is, compute the eritionl points of f(x). Remember that redpoints are not critical points. critical pocnts: (c) (Show your work.) Determiae the intervals on which f ′
(x)>0 and the intervals on whict f ′
(x)<0. Display your abswer in the form of a sign chart for f ′
(z) that resembles the obes we ereated in class. Yot well fose credit if yots ariswer is not in the form of a suitable sign chart. (d) Using your sunswer in (c), which of the points are local maxima and food minema of f(x). Do not forget the endpoints! Docal maxima: Jocrl minima: (e) Write down the point whicts is the globol marimure and the point that is the gobolo minimum. global maximura: global minimum: 5 (f) Compute f ′′
(x) - f ′′
(x)= (g) (Show your work.) Determine thoee points for which f N
(x)=0, that is, compute the critical points of f ′
(x). critical pooknts of f ′
(x) : (h) (Show your work-) Determine the intervals on which f ′′
(x)>0 and the intervals on which f ′′
(x)<0. Display your answee in the form of a sign chart for f ′′
(x) that resembles the obes we created in class. You will lose eredit if your ansuer is not in the form of a suifelle signt chart. (i) Ueing your answer in (b), which of the points are inglestion points of f(x)
Answers
(a) Taking the derivative of the function f(x) = x^4 + 2x^3 - 2, we get:
f'(x) = 4x^3 + 6x^2
(b) To find the critical points, we need to solve for f'(x) = 0:
4x^3 + 6x^2 = 0
2x^2(2x + 3) = 0
Solving for x, we get x = 0 (multiplicity 2) and x = -3/2.
Therefore, the critical points are (-3/2, f(-3/2)) and (0, f(0)).
(c) We can use the critical points to determine the intervals where f'(x) is positive or negative. We can use a sign chart as follows:
-3/2 0 +inf
f'(x) - + +
Therefore, f'(x) is negative on the interval (-3/2, 0) and positive on (-inf, -3/2) and (0, inf).
(d) To determine the local maxima and minima, we need to examine the sign of f'(x) on the intervals determined in part (c). We also need to check the endpoints of the interval [-2, ?].
f'(-2) = -16, f'(2) = 52
Therefore, the local minimum occurs at x = -2 and the local maximum occurs at x = 2.
(e) To find the global maximum and minimum, we need to compare the values of f(x) at the critical points and the endpoints of the interval [-2, ?]:
f(-2) = 2, f(-3/2) = -49/16, f(0) = -2, f(2) = 18
Therefore, the global maximum is f(2) = 18 and the global minimum is f(-3/2) = -49/16.
(f) Taking the second derivative of the function f(x), we get:
f''(x) = 12x^2 + 12x
(g) To find the inflection points, we need to solve for f''(x) = 0:
12x^2 + 12x = 0
12x(x + 1) = 0
Solving for x, we get x = 0 and x = -1.
Therefore, the inflection points are (-1, f(-1)) and (0, f(0)).
(h) We can use the inflection points to determine the intervals where f''(x) is positive or negative. We can use a sign chart as follows:
-1 0 +inf
f''(x) - + +
Therefore, f''(x) is negative on the interval (-1, 0) and positive on (-inf, -1) and (0, inf).
(i) The inflection points (-1, f(-1)) and (0, f(0)) are inflection points of f(x).
Learn more about "critical points of function" : https://brainly.com/question/7805334
#SPJ11
divide 150 toys amongst two groups of children in the ratio 6:9
Answers
Answer:
60 and 90
Step-by-step explanation:
150/15 = 10
6 x 10 = 60
9 x 10 = 90
The required number of toys that can be divided among two groups is 60 and 90.
Given that,
To divide 150 toys amongst two groups of children in a ratio of 6:9.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Ratio = 6 / 9
Total of ratio = 15
Now,
For 1 group toys = 150 [6 / 15] = 60
For group 2 toys = 150 [9 / 15] = 90
Thus, the required number of toys that can be divided among two groups is 60 and 90.
Learn more about ratios here:
brainly.com/question/13419413
#SPJ2
Jayden had $43 in his bank account. He wanted to buy a game at GameStop. The game cost $15. He made the purchase.
a) Write an expression to show his purchase activity.
b) How much did he have, after the purchase of the game?
Answers
Answer:
a) 43 - 15
b) 28
2 lines intersect. Lines D E and A B intersect at point C.
Angle ACD is supplementary to angles ACE and BCD and congruent to angle BCE.
Which statements are true about the angles in the diagram? Select three options.
Angle ACE is supplementary to angle BCD.
Angle BCE is supplementary to angle ACE.
Angle BCD is supplementary to angle BCE.
Angle ACE is congruent to angle BCE.
Angle BCD is congruent to angle ACE.
Answers
Answer:
The answer is B, C, and E
Step-by-step explanation:
I did this
Answer:
b,c, and e on edge
Step-by-step explanation:
for a standard normal distribution, the probability of obtaining a z value between –2.4 and –2.0 is _____.a. .0146b. .0400c. .5000d. .4000
Answers
The answer is option A (.0146).
To find the probability of obtaining a z value between -2.4 and -2.0, we need to find the area under the standard normal distribution curve between these two values.
Using a standard normal distribution table or calculator, we can find that the area to the left of -2.0 is .0228 and the area to the left of -2.4 is .0082.
To find the area between -2.4 and -2.0, we subtract the smaller area from the larger area:
.0228 - .0082 = .0146
Therefore, the probability of obtaining a z value between -2.4 and -2.0 is .0146.
In a standard normal distribution, the probability of obtaining a z value between -2.4 and -2.0 can be found by looking at the area under the curve between these two points. To calculate this, you need to find the cumulative probability for each z value and then subtract them.
For a z value of -2.4, the cumulative probability is 0.0082.
For a z value of -2.0, the cumulative probability is 0.0228.
Now, subtract the two probabilities:
0.0228 - 0.0082 = 0.0146
So, the probability of obtaining a z value between -2.4 and -2.0 is 0.0146 (option a).
Learn more about normal distribution here: brainly.com/question/15603885
#SPJ11
23.f(s) = Vs - 1 ÷Vs + 1 .Find the derivatives.
Answers
Answer:The derivative of f(s)
Step-by-step explanation:
The derivative of f(s) = (Vs - 1)/(Vs + 1) with respect to s is
df/ds = (V(Vs + 1) - (Vs - 1)V)/(Vs + 1)^2
= (V^2 -1)/(Vs + 1)^2
which answer is an example of volunteer sampling? responses asking every fifth person their age asking every fifth person their age counting everyone who attends a game counting everyone who attends a game submitting an online survey submitting an online survey asking your neighbors if they approve of the mayor
Answers
Submitting an online survey is one example of volunteer sampling.
What exactly does volunteer sampling imply?When researchers look for volunteers to participate in studies, they use voluntary sampling. Volunteers can be recruited in person, online, through public postings, and through a variety of other means. When using voluntary sampling, a researcher usually makes little effort to control the sample composition.
The customer satisfaction survey is a common form of voluntary sampling. When a company provides a service or a product, it frequently asks customers to rate their satisfaction. The sample is voluntary and biased because the company asks all customers to volunteer their opinions.
Researchers in academia frequently seek volunteer samples by asking students to participate in research or by looking for people in the community. Volunteer samples are used for a variety of different types of research because they are inexpensive.
To know more about volunteer sampling, visit:
https://brainly.com/question/2648569
#SPJ4
What is the circumference of the circle
A. 18.84
B. 17.6
C. 21.79
D. 15.65
Answers
Answer:
18.84
Step-by-step explanation:
The formula for circumference is 2(pi)r, I think. The radius is 3. 3 times 2 is 6. 6 times 3.14 is around 18, I think.
hope this helps
Answer:
A
Step-by-step explanation:
Use the information in the picture.
Is it a parallelogram? YES
NO
If yes, give the theorem:
Answers
Match the term with the definition. (5 points) Column A 1. Line : Line 2. Line Segment : Line Segment 3. Ray : Ray 4. Point : Point 5. Vertex : Vertex Column B a. a location, has no dimension b. the common endpoint of two segments or rays that form the "corner" of an angle c. an infinite number of points extending in opposite directions that has only one dimension d. part of a line that has two endpoints e. part of a line that has one endpoint and continues in one direction infinitely
Answers
Answer:
a. Point.
b. Vertex.
c. Line.
d. Line segment.
e. Ray.
Step-by-step explanation:
a. Point: a location, has no dimension. Also, a point doesn't have a size i.e no length, depth, breadth or height.
b. Vertex: is the common endpoint of two segments or rays that form the "corner" of an angle.
c. Line: is an infinite number of points extending in opposite directions that has only one dimension.
d. Line segment: is part of a line that has two endpoints.
e. Ray: is part of a line that has one endpoint and continues in one direction infinitely.
Which angle measure is equivalent to 14π/9 radians?a. 70°b. 280°c. 140°d. 20°
Answers
Answer:
b. 280°
Step-by-step explanation:
((14π)/9)= 4. 8869(((180)/π))= 280°
How do you put fractions in order from least to greatest?
Answers
To put fractions in order from least to greatest, you need to compare their values by finding the common denominator.
Here are the steps to follow:Step 1: Find a common denominator for all the fractions.
Step 2: Convert each fraction to an equivalent fraction with the common denominator.
Step 3: Compare the numerators of the equivalent fractions. The fraction with the smallest numerator is the smallest fraction, and the fraction with the largest numerator is the largest fraction.
Step 4: If two or more fractions have the same numerator, compare their denominators. The fraction with the smallest denominator is the smallest fraction, and the fraction with the largest denominator is the largest fraction.
Step 5: Write the fractions in order from least to greatest.
For example, let's say you need to put the fractions 1/3, 2/5, and 3/8 in order from least to greatest.
Step 1: The common denominator for 3, 5, and 8 is 120.
Step 2: Convert each fraction to an equivalent fraction with a denominator of 120.
1/3 = 40/120
2/5 = 48/120
3/8 = 45/120
Step 3: Compare the numerators of the equivalent fractions: 40 < 45 < 48
Step 4: Since 40 is not equal to 45 or 48, we don't need to compare the denominators.
Step 5: Write the fractions in order from least to greatest: 1/3 < 3/8 < 2/5.
To learn more about fractions click on,
https://brainly.com/question/29158062
#SPJ4
Given a full subtractor with inputs X and Y , what is X "minus" Y, given that X = 1, Y = 0 and Yout = 1 ? O a. 0 Ob. 1 O c. 2
Answers
Given a full subtractor with inputs X and Y , what is X "minus" Y, given that X = 1, Y = 0 and Yout = 1. The correct answer is indeed: b. 1
In a full subtractor circuit, the inputs X and Y represent the minuend and subtrahend, respectively, and the output Yout represents the borrow. The operation "X minus Y" is performed by subtracting the subtrahend (Y) from the minuend (X), taking into account any borrow (Yout) from the previous subtractor stage.
In the given truth table, when X = 1, Y = 0, and Yout = 1, we can see that the result of "X minus Y" is 1. This means that when subtracting 0 from 1, the result is 1.
The borrow (Yout) being 1 indicates that there was a borrow from the previous subtractor stage, which is important when performing subtraction with multiple bits. However, in this case, since we are only considering a single subtractor, we can focus on the X and Y inputs and the resulting output, which is 1.
Therefore, the correct answer is indeed:
b. 1
Learn more about inputs from
https://brainly.com/question/31510469
#SPJ11
in a group of 42 students, 22 take history, 17 take biology and 8 take both history and biology. how many students take neither biology nor history?
Answers
Out of the 42 students, 22 take history, 17 take biology, and 8 take both history and biology. Therefore, there are 11 students who take neither biology nor history.
To find the number of students who take neither biology nor history, we need to subtract the number of students who take at least one of these subjects from the total number of students in the group.
Let's break down the information given:
Total number of students (n) = 42
Number of students taking history (H) = 22
Number of students taking biology (B) = 17
Number of students taking both history and biology (H ∩ B) = 8
To find the number of students who take at least one of these subjects, we can use the principle of inclusion-exclusion. The formula for the principle of inclusion-exclusion is:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
In this case, A represents the set of students taking history, and B represents the set of students taking biology.
Using the formula, we can calculate the number of students taking at least one of these subjects:
n(H ∪ B) = n(H) + n(B) - n(H ∩ B)
= 22 + 17 - 8
= 31
Therefore, there are 31 students who take either history or biology or both.
To find the number of students who take neither biology nor history, we subtract this value from the total number of students:
Number of students taking neither biology nor history = Total number of students - Number of students taking at least one of the subjects
= 42 - 31
= 11
Hence, there are 11 students who take neither biology nor history.
In summary, out of the 42 students, 22 take history, 17 take biology, and 8 take both history and biology. Therefore, there are 11 students who take neither biology nor history.
Learn more about biology here
https://brainly.com/question/20659064
#SPJ11
I know it's easy but, I'm thinking of different ways of doing it.
Answers
Answer:
9 students
Explanation:
Every 8th person that entered the cinema received a free ticket.
The number of students who entered in the first hour = 76.
The first person given a ticket was the 8th person.
To calculate the number of persons who received a free ticket, we can view this problem as an arithmetic sequence in which:
• The first term = 8
,• The last term = 76.
,• The common difference (every 8th person) = 8.
Using the formula for the last term of an arithmetic sequence, we have:
\(\begin{gathered} l=a+(n-1)d_{} \\ 76=8+8(n-1) \end{gathered}\)Our goal is to find n, the number of students.
\(\begin{gathered} 76=8+8n-8 \\ 76=8n \\ n=\frac{76}{8} \\ n=9.5 \end{gathered}\)Since the number of students that entered in the first hour is not more than 76, we have that:
\(\begin{gathered} n\le9.5 \\ \implies n=9 \end{gathered}\)9 students received a free ticket.
A person who was listening to a siren noticed that the frequency fluctuated with time, measured in seconds. The minimum frequency was 500 Hz and the maximum frequency was 1000 Hz. The maximum frequency occurred at t = 0 and again every 3 seconds. What is the equation of the cosine function that describes the frequency of this siren?
Answers
f(t) = 250cos(2π/3t) + 750 is the equation of the cosine function that describes the frequency of this siren
The generic cosine function is f(x) = Acos(B(x - C)) + D where:
A is the amplitude
B is 2π/period
C is the horizontal shift
D is the vertical shift (midline location)
In given problem,
we can calculate D = 750 Hz (since that is halfway between the max and min)
We can calculate that A = 250 Hz (since the max or min is 250 from the midline)
We can deduce that C = 0 (since the function maximum is at t = 0 and that's what the basic cosine function does)
We can calculate B as 2π/3 (since the period is 3 seconds)
Then we can put these all together:
f(t) = 250cos(2π/3t) + 750
Hence , f(t) = 250cos(2π/3t) + 750 is the equation of the cosine function that describes the frequency of this siren
Learn more about Cosine equation at:
https://brainly.com/question/26993851
#SPJ4
i need help with this please
Answers
Step by step:
:)
It takes Mark 45 minutes to ride his bike 5 miles. At this rate, how long will it take him to ride 8 miles?
Answers
Answer:
1 hour and 12 mins
Step-by-step explanation:
how many solutions are there to the equation 7x+12=5x-8
Answers
Which polynomial represents the area of the rectangle?
a. 3x2+2x−5
b. 3x2−5
c. 3x2−2x−5
d. 3x2−8x−5
Answers
Answer:
Step-by-step explanation:
The correct option is C.
Step-by-step explanation:
The width of the rectangular pen is
The length of the rectangular pen is
The perimeter of a rectangle is
Therefore the correct option is C.
Classify the equation 6x + 4x - 1 = 2(5x + 4) as having one solution, infinitely many solutions, or no solutions
Answers
Answer: no solutions
Step-by-step explanation:
6x+4x-1=2(5x+4)
10x-1=10x+8
+1 +1
10x=10x+9
The equation is not true. It has no solutions.
la relación de dos varillas es 3/4 y la suma de sus longitudes es de 28cm¿cuánto mide cada una de las varillas?
Answers
Answer:
its 6
Step-by-step explanation:
Hi please answer??????
Answers
Answer:
All rational numbers are real,
Answer:
False
Step-by-step explanation:
This is because all non terminating numbers are not rational because they a non terminating number may non repeating which means it may not be able to go in p/q form, hence, NOT ALL NON TERMINATING NUMBERS ARE RATIOANL, BUT FEW ARE.
If my answer helped, kindly mark me as the brainliest !!
Thanks!!
Compare. Use >, <, or =.
123,546,789 >, <, or =, 123,456,789
please help
Answers
Step-by-step explanation:
123,546,789 > 123,456,789
#CMIIWSomeone, please help me with this MATH question.
Show work for full points.
Answers
Answer:
24x^2-36x+60
Step-by-step explanation:
1 2 ( 2 ^ 2 − 3 + 5 )
12 x 2 = 24x^2
12 x -3 = -36x
12 x 5 = 60
Basically multiplying and then putting it like that.
2x - y when x = 0 and y = -5
Answers
Answer:
5
Step-by-step explanation:
2x - y when x = 0 and y = -5
2(0) - (-5) =
= 0 + 5
= 5
Answer:
5
Step-by-step explanation:
2x-y
2(0)-(-5)
0-(-5)
0+5
5
I NEED HELP PLEASE!!!
Answers
Answer:
C (-13,-2)
Step-by-step explanation:
The two shorter sides of a triangle measure 12 cm and 18 cm. which of the following could be the length of the longest side of the triangle?
1. 30 cm
2. 17 cm
3.27 cm
4. 11 cm