How do you determine a relation is function on a GRAPH?
Answers
To Determine: How to determine a relation is function on a GRAPH
In other to achieve this, we will use the vertical test
If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function
Check the image below for a better clarification
With the use of the vertical line test, the graph in OPTION C and OPTION D are functions and the graph in OPTION A and B are not functions
In summary, you determine a relation is a function on a graph by using a vertical line test
Related Questions
Solve the system of two linear inequalities graphically.Sy < -2x + 3y > 6x – 9Step 1 of 3: Graph the solution set of the first linear inequality.
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The red graph represents y < -2x + 3
The blue graph represents y > 6x - 9
The solutions of the system of inequalities lie on the red-blue shaded
The part which has two colors
Since the first inequality is y < -2x + 3, the shaded is under the line
Since the second inequality is y > 6x - 9, the shaded is over the line
The common shaded of the two colors represents the area of the solutions of the 2 inequalities
The type of boundary lines is dashed
The points on the boundary lines are
For the red line (0, 3) and (4, 0)
For the blue line (0, -9) and (1, -3)
There is a common point on the two lines (1.5, 0)
The annual rainfall in a town has a mean of 54.11 inches and a standard deviation of 12.59 inches. Last year there was rainfall of 48 inches. How many standard deviations away from the mean is that? Round your answer to two decimal places.
Answers
SOLUTION
Mean=54.11, standard deviation = 12.59
X=48
Using the z formula
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substituting values gives
[tex]z=\frac{48-54.11}{12.59}[/tex]Solve for z
[tex]z=-0.4853[/tex]This shows that the result shows that the value x=48 is 0.4853 standard deviation to the left of the mean.
(a) How high is the javelin when it was thrown? How do you know?(b) How far from the thrower does the javelin strike the ground?
Answers
The height of the javelin is given by
[tex]h(x)=-\frac{1}{20}x^2+8x+6[/tex]Here, x is the horizontal distance from the point at which the javelin is thrown.
a)
When the javelin is thrown, the horizontal distance from the point at which the javelin is thrown is zero. So, put x = 0 to find the height of the javelin when thrown. So, the distance:
[tex]\begin{gathered} h(0)=-\frac{1}{20}(0)^2+8(0)+6 \\ =0+0+6 \\ =6 \end{gathered}[/tex]Thus, the height of the javelin when it was thrown is 6 ft.
b)
When the javelin strikes the ground the value of h(x) is zero.
Find the value of x when h(x) is zero.
[tex]\begin{gathered} h(x)=0 \\ -\frac{1}{20}x^2+8x+6=0 \\ -x^2+160x+120=0 \\ x^2-160x-120=0 \end{gathered}[/tex]Now, the roots of the equation are x = 160.74 and x = -0.74.
The distance cannot be negative. So, the javelin is 160.74 ft far from the thrower when it strikes the ground.
figure0123456vehicles4122028364452linear ?pattern ?constant?
Answers
Problem
Solution
For this case we need to verify if the pattern is linear so we cna check this doing the following operations:
(12-4)/(1-0) =8
(20-12)/(2-1) =8
(28-20)/(3-2) =8
(36-28)/(4-3) =8
(44-36)/(5-4) =8
(52-44)/(6-5) =8
And as we can see we have the same constant so we can conclude that we have a linear pattern with a constant value of k=8
That means for every increase in the figure the vehicles increase by 8
We can also find the formula for the linear pattern and we have:
4 =8 (0)+b
And solving for b we got
b= 4
And the equation y=mx+b is:
y= 8x +4
Please it’s due todayAre there any limitations on the inputs of the equation?Does the graph have any symmetry?If so, where? When will the graph point upward? When will it point downward?
Answers
We have the following:
1.
There is no limitation on the input values, the domain is all real numbers.
2.
Yes, it has an axis of symmetry at the point (0,0)
3.
The graph point upward in the interval:
[tex](0,\infty)[/tex]The graph point downward in the interval:
[tex](-\infty,0)[/tex]Triangle BCA is similar to Triangle STR . What is the value of x?
Answers
Sin the triangles are similar the ratio 4 to 6 should hold for any side, this means that:
[tex]\frac{4}{6}=\frac{x}{9}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{4}{6}=\frac{x}{9} \\ x=9(\frac{4}{6}) \\ x=\frac{36}{6} \\ x=6 \end{gathered}[/tex]Therefore. x=6.
10 ptsQuestion 3Find the measure of each interior angle. Round to the nearest hundredth.4x(6x - 90)(3x + 31)(7x+19)X=(4x)" =(6x - 90)(7x + 19)° =(3x + 31)º =
Answers
Alexandre, this is the solution:
Let's recall that the interior angles of a rhombus add up to 360 degrees.
Upon saying that, we have:
4x + 3x + 31 + 6x - 90 + 7x + 19 = 360
20x - 40 = 360
Adding 40 at both sides:
20x - 40 + 40 = 360 + 40
20x = 400
Dividing by 20 at both sides:
20x/20 = 400/20
x = 20
Now, we can calculate each of the angles and prove they add up to 360 degrees, as follows:
• 4x = 4 * 20 =, 80
,• 3x + 31 = 3 * 20 + 31 = 60 + 31 =, 91
,• 7x + 19 = 7 * 20 + 19 = 140 + 19 = ,159
,• 6x - 90 = 6 * 20 - 90 = 120 - 90 = ,30
80 + 91 + 159 + 30 = 360
An initial amount of $3500 is invested in an account at an interest rate of 6% per year, compounded continuously. Assuming that no withdrawals aremade, find the amount in the account after two years.Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
For this problem we use the continuously compounded interest formula:
[tex]M=M_0e^{rt}[/tex]where M_0 is the initial amount, r is the interest rate per year and t is the number of years.
Substituting M_0=$3500, r=0.06, and t=2 we get:
[tex]\begin{gathered} M=3500e^{0.06\cdot2}=3500e^{0.12} \\ M=3946.24 \end{gathered}[/tex]multiply mentally to find the product
Answers
8 * 404 = 8(----- + 4)
At first, we will split 404 into two numbers one of them is 4
To find the other number subtract 4 from 404
404 - 4 = 400
8 * 404 = 8(400 + 4)
Now we will multiply 8 by 40 and 8 by 4
8(400 + 4) = 8 * 400 + 8 * 4
It is easy to find the product of 8 and 4
8 * 4 = 32
8 * 400 = 3200
Let us add them
3200 + 32 = 3232
The answer is 3232
is there one solution to the following system of equations by elimination 3x + 2y equals 3 3x + 2y equals 19
Answers
3x+2y= 3 (a)
3x+2y= 19 (b)
Subtract (b) to (a) ; elimination method.
3x+ 2y = 3
-
3x+2y= 19
_________
0 = 19
Since both variables were eliminated, the system has no solutions.
option c.
Below, the two-way table is given for aclass of students.Freshmen Sophomore Juniors Seniors TotalMale 462. .Female 33246TotalIf a student is selected at random, find theprobability the student is a junior. Roundto the nearest whole percent.
Answers
The final answer is: 27%
We are asked to find the probability that a student chosen at random is a junior. This requires that we know the total number of students in each level from Freshmen to Seniors.
Totals:
Freshmen = 4 + 3 = 7
Sophomore = 6 + 4 = 10
Juniors = 2 + 6 = 8
Seniors = 2 + 3 = 5
Thus we can calculate the total number of students considered:
7 + 10 + 8 + 5 = 30 students in total.
Now we can calculate the probability as:
[tex]\begin{gathered} P(\text{choosing juniors) = }\frac{Number\text{ of Juniors}}{\text{Total Number of Students}} \\ \end{gathered}[/tex]The number of Juniors was calculated earlier as: Juniors = 8
We have the total number of students as 30
Therefore, we can solve:
[tex]P(\text{choosing juniors)=}\frac{8}{30}=\frac{4}{15}[/tex]But we were asked to round to the nearest whole percent, which means we are required to put the fraction into percentage.
The way we do this is to multiply the fraction by 100%
[tex]\begin{gathered} \frac{4}{15}\times100=26.6667. \\ \\ \therefore P(\text{choosing juniors)=27\% (to the nearest whole percent)} \end{gathered}[/tex]Therefore the final answer is: 27%
In the right trapezoid ABCD, BC is parallel to AD, and AD is contained in the line whose equation is y=−12x+10 y = − 1 2 x + 10 . What is the slope of the line containing BC? Explain how you got your answer
Answers
JCPenney sells jeans for $49.50 that cost $38.00. What is the percent markup on cost? Check the cost. (Round your answer to the nearest hundredth percent.)
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The percent mark up on the cost is 30.26%.
How to find the percent mark-up on cost?JCPenney sells jeans for $49.50 that cost $38.00.
The percent mark up can be calculated as follows:
Mark up percentage is calculated by dividing the gross profit of a unit by the cost of that unit.
In other words, Mark-up percentage is the difference between a product's selling price and cost as a percentage of the cost.
Hence,
selling price = $49.50
cost price = $38.00
mark up = 49.50 - 38 = 11.5
Therefore,
percent mark up = 11.5 / 38 × 100
percent mark up = 1150 / 38
percent mark up = 30.2631578947
Therefore,
percent mark up = 30.26%
learn more on percent mark up here: brainly.com/question/12284542
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find the volume and total surface area of a right circular cone whose base diameter is 10 cm and whose altitude is 20 cm.
Answers
SOLUTION
Given the question in the question tab, the following are the solution steps to calculate the required measurements.
Step 1: write the given parameters
[tex]\begin{gathered} \text{diameter}=10\operatorname{cm},\text{altitude}=\text{height}=20\operatorname{cm} \\ r=\frac{d}{2}=\frac{10}{2}=5\operatorname{cm} \end{gathered}[/tex]Step 2: Calculate the volume of the right circular cone
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{\pi\times5\times5\times20}{3} \\ V=\frac{500\pi}{3}=523.5987756 \\ V\approx523.5988\operatorname{cm}^3 \end{gathered}[/tex]Step 3: Calculate the total surface area of the right circular cone
[tex]\begin{gathered} \text{TSA}=\pi r(r+\sqrt[]{h^2+r^2)} \\ \text{TSA}=\pi(5)(5+\sqrt[]{20^2+5^2)} \\ \text{TSA}=5\pi(5+\sqrt[]{400+25)} \\ \text{TSA}=5\pi(5+\sqrt[]{425})=5\pi(5+20.61552813) \\ \text{TSA}=5\pi(25.615528134) \\ \text{TSA}=402.3677749 \\ \text{TSA}\approx402.3678cm^2 \end{gathered}[/tex]Hence, the volume and the total surface area of the given right circular cone are approximately 523.5988cm³ and 402.3678cm² respectively
Find the perimeter of the isosceles triangle in simplest form. x2 + 20 units 2x units
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The perimeter of an isosceles triangle is given by:
[tex]P\text{ = 2a + b}[/tex]From the question, b = 2x; a = x^2 + 20
[tex]P\text{ = 2a }+b=2(x^2+20)+2x=2x^2+40\text{ + 2x}[/tex][tex]P=2x^2\text{ + 2x + 40}[/tex]Hello! I think the answer is 398. Would you mind guiding me?
Answers
Given -
Total Personal Videos Players = 400
Video Players with no defects = 398
Number of Video Players sent = 2000
To Find -
The number of Video Players with no defects =?
Step-by-Step Explanation -
Total Personal Videos Players = 400
Video Players with no defects = 398
So,
Two video players in every 400 are defected
So,
2000 = 5 × 400
So,
Total number of Video Players with defects = 5 × 2 = 10
Hence,
The number of Video Players with no defects = 2000 - 10 = 1990
Final Answer -
The number of Video Players with no defects = 1990
What is the slope of this line? :(
Answers
Answer:
y=1/4x+1
Step-by-step explanation:
Answer:
m=1/4
Step-by-step explanation:
Got it correct
I need help with solving this: what is the 8th term to 1,5,25,125,..
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
1,5,25,125,..
Step 02:
[tex]an=5^{n-1}[/tex]if n = 8
[tex]a_8=5^{8-1}=5^7=78125[/tex]The answer is:
8th term is 78125
Solve each equation for the given variable.-2x + 5y = 12 for ySolve each equation for y. Then find the value of y for each value if x.y + 2x = 5; x = -1, 0, 3
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
-2x + 5y = 12
y = ?
Step 02:
We must apply algebraic rules to find the solution.
-2x + 5y = 12
5y = 12 + 2x
y = 12 / 5 + 2x / 5
[tex]y\text{ =}\frac{12}{5}\text{ + }\frac{2x}{5}[/tex]The answer is:
y = 12 / 5 + 2x / 5
0.25(60) + 0.10x = 0.15(60 + x)
Answers
Answer: X = 120
Step-by-step explanation:
lol:
V = (−∞,∞)
X = 120
3x - 4y = 65x + 8y = -1
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Ethan's income is 4500 per month a list of some of his expenses appear below what percent of Ethan's expenses is food?
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Ethan's earns 4500$ per month*
the amount spent on the food is 600 $
so percentage will be'
[tex]=\frac{4500}{600}=\frac{1500}{200}=7.5\text{ \%}[/tex]so the answer is the percentage amount spent on food is, 7.5 %
how to find the width to a pyramid with the volume height and length
Answers
The volume of a pyramid is given by the formula
[tex]V_{\text{pyramid}}=\frac{1}{3}\times base\text{ area}\times height[/tex]Write out the given dimensions
[tex]\begin{gathered} \text{Volume}=80\operatorname{cm}^3 \\ \text{Height}=10\operatorname{cm} \\ \text{length}=6\operatorname{cm} \\ \text{width}=\text{unknown} \end{gathered}[/tex]Since the base of the pyramid is a rectangle, the base area is
[tex]A_{\text{rectangle}}=\text{width }\times length[/tex]Substituting the given dimensions to get the value of the width\
[tex]\begin{gathered} V_{\text{pyramid}}=\frac{1}{3}\times width\times length\times height \\ 80=\frac{1}{3}\times width\times6\operatorname{cm}\times10\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} 80\operatorname{cm}=20\times width \\ \text{width}=\frac{80}{20} \\ \text{width}=4\operatorname{cm} \end{gathered}[/tex]Hence, the width of the pyramid is 4cm
32Lucky Lanes Bowling Alley is putting this design on its roof.4 feet4 feet20 feet4 feet4 feet10 feet
Answers
In order to find the volume of the design, we want to find the volume of the figures that compound it:
Total volume = volume 1 + volume 2
Volume 1The volume of each box is given by the product of its sides:
side 1 x side 2 x side 3.
In this case, we have that
side 1 = 4 ft
side 2 = 4 ft
side 3 = 20 ft - 4 ft = 16 ft
Then,
side 1 x side 2 x side 3.
↓
volume 1 = 4 ft x 4 ft x 16 ft = 256 ft³
volume 1 = 256 ft³
Volume 2For the second part we have that:
side 1 = 4 ft
side 2 = 4 ft
side 3 = 10 ft
Then,
side 1 x side 2 x side 3.
↓
volume 2 = 4 ft x 4 ft x 10 ft = 160 ft³
volume 2 = 160 ft³
Total volumeThe total volume is given by
Total volume = volume 1 + volume 2
↓
Total volume = 256 ft³ + 160 ft³
Total volume = 416 ft³
Answer: 416 ft³
To beA train started from City A to City B at 13:30. The train travelledat an average speed of 180 miles per hour. If the distancebetween City A and City B is 756 miles, at what time did thetrain arrive at City B? Give your answer in a 24-hour clockformat, such as 19:00. DEnter the answer
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Remember that
the speed is equal to divide the distance by the time
speed=d/t
solve for t
t=d/speed
we have
d=756 miles
speed=180 miles per hour
substitute
t=756/180
t=4.2 hours
4.2 hours=4 hours +0.20 hours
Convert 0.20 hours to minutes
Multiply by 60
0.20 h=0.20*60=12 minutes
so
4.2 hours=4 h 12 min
therefore
A train started from City A to City B at 13:30.
13:30+ 4h 12 min=17:42 hrs
This is a non graded practice that I am doing. I don’t under these questions 5-11
Answers
7. The intersection of two intersecting lines is a point.
In the given image, we see that lines NQ and ML intersect at point P.
Therefore, the intersection of NQ and ML is P.
Which of the following represents the translation of R (-3, 4), along the vector <7, -6> <-1, 3>.
Answers
Solution
Step 1:
The translation is a term used in geometry to describe a function that moves an object a certain distance.
Step 2:
Pre-mage R = (-3,4)
Step 3:
When moved along (7, -6) the new coordinates become:
R' = (-3+7 , 4 - 6 ) = (4 , -2)
R' = ( 4 , -2 )
Step 4:
When moved along (-1, 3) the new coordinates become:
R'' = ( 4-1 , -2+3 ) = ( 3 , 1 )
R'' = (3 , 1)
Final answer
[tex]R(-3\text{ , 4\rparen }\rightarrow\text{ R'\lparen4 , -2\rparen }\rightarrow\text{ R''\lparen3 , 1\rparen}[/tex]if sound travels at 335 miles per second through air and a plane is 2680 miles away how long will the sound take to reach the people
Answers
It will take 8 seconds for the sound to reach the people
Here, we want to calculate time
Mathematically;
[tex]\begin{gathered} \text{time = }\frac{dis\tan ce}{\text{speed}} \\ \end{gathered}[/tex]With respect to this question, distance is 2680 miles while speed is 335 miles per second
Substituting these values, we have;
[tex]\text{time = }\frac{2680}{335}\text{ = 8}[/tex]The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 30.8 miles per gallon, with a standard deviation of 4.1 miles per gallon. Assume that a Normal model applies. Find the probability that a randomly selected automobile will average: 1. Less than 28 miles per gallon. Chapter 6 Assignment 2. More than 26 miles per gallon.
I need much help with this normal distribution question.
Answers
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean.
What is meant by normal distribution?The probability density function for a continuous random variable in a system defines the Normal Distribution.
A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean. This shows that data close to the mean occur more frequently than data far from the mean. On a graph, the normal distribution is represented by a "bell curve."
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Factor out the greatest negative common factor for the expression.- 8mºn - 40m?n4Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.OA. - 8mºns - 40mºn4-(Factor completely.)OB. There is no common factor other than 1.
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Solution
- The question tells us to factor out the greatest negative common factor of the expression below:
[tex]-8m^3n^5-40m^3n^4[/tex]- The greatest negative common factor is the negative monomial with the largest magnitude, which divides evenly into each term of the given expression.
- Let us factorize the expression to derive this greatest negative common factor below:
[tex]\begin{gathered} -8m^3n^5-40m^3n^4 \\ -8,m^3,\text{ and }n^4\text{ are all co}mmon\text{ in the expression above.} \\ \text{Thus, we have:} \\ \\ -8m^3n^4(n-5) \end{gathered}[/tex]Final Answer
The answer is
[tex]-8m^3n^4(n-5)[/tex]