A proportional relationship is represented by the equation y = 3x. Identify the constant of proportionality, make a table, and sketch a graph of the relationship. Identify the constant of proportionality.
Answers
a) Proportional relationships have the following form:
\(y=kx\)Where "k" is the Constant of proportionality.
For this case you have this equation that represents a Proportional relationship:
\(y=3x\)So you can identify that the Constant of proportionality is:
\(k=3\)b) To make a table you must use different x-values, substitute them into the equation and evaluate, in order to get their corresponding y-values.
- For:
\(x=-2\)You get:
\(y=3(-2)=-6\)- For:
\(x=-1_{}\)You get that:
\(y=3(-1)=-3\)- For:
\(x=2\)\(y=3(2)=6\)- For:
\(x=4\)\(y=3(4)=12\)Knowing those coordinates, you can make the following table:
c) Use the table the sketch the graph of the relationship.
You can see in the table that you have the following points:
\((-2,-6),(-1,-3),(2,6),(4,12)\)Plot these points on a Coordinate plane. The line must pass through those points (It's important to know that, by definition, the graph of this relationships will always pass through the origin):
The graph of the Proportional relationship is
Related Questions
Solve the following quadratic equation by completing the square: x^2-12x+5=7
PLS HELP ASAP
Answers
Answer:
\( {x}^{2} - 12x + 5 = 7\)
i) move constants to the right-hand side and change its sign
\( {x}^{2} - 12 {x} = 7 - 5\)
ii) subtract the numbers
\( {x}^{2} - 12x = 2\)
iii) add (12/2)² to both sides of the equation
\( {x}^{2} - 12x + ( \frac{12}{2} ) {}^{2} = 2 + ( \frac{12}{2} ) {}^{2} \)
iv) using a²-2ab+b²=(a-b)² , factorize the expression
\((x - \frac{12}{2} ) {}^{2} = 2 + ( \frac{12}{2} ) {}^{2} \)
v) calculate the value
\((x - \frac{12}{2}) {}^{2} = 2 + 36\)
\((x - \frac{12}{2}) {}^{2} = 38\)
vi) reduce the fraction
\((x - 6) {}^{2} = 38\)
vii) solve the equation for x
\(x - 6 = + - \sqrt{38} \)
1) first value of x
\(x - 6 = \sqrt{38} \)
\(x = \sqrt{38} + 6 \: or \: 12.16\)
2) second value of x
\(x - 6 = - \sqrt{38} \)
\(x = - \sqrt{38} + 6 \: or \: - 0.16\)
Fake Question: Should Ujalakhan01 be a moderator? (If you could answer I'd appreciate it haha.)
Real Question: Simplify \((a^5*a^4)+(b^2*b^3)-(c^7*c^6)\)
Answers
Answer:
\(a^9 + b^ 5 + c^{13}\)
Step-by-step explanation:
\((a^5 \times a^4)+(b^2 \times b^3) + (c^7 \times c^6)\)
When bases are same and it is multiplication, then add the exponents.
\((a^{5+4})+(b^{2+3})+(c^{7+6})\)
\((a^9)+(b^ 5) + (c^{13})\)
Apply rule : \((a^b)=a^b\)
\(a^9 + b^ 5 + c^{13}\)
Answer:
\(a^9+b^5-c^{13\)
Step-by-step explanation:
\((a^5*a^4) + (b^2*b^3)-(c^7*c^6)\)
When bases are same, powers are to be added.
=> \((a^{5+4})+(b^{2+3})-(c^{7+6})\)
=> \(a^9+b^5-c^{13\)
whats the value of this expression 1732÷4
Answers
Answer:
433
us that good or did you need explanation because if you do just say you did long division
Factor −5x2 + 10x.
PLS HURRY NEED THIS DUE TODAY
Answers
Answer:
C. 5x(-x + 2)
Step-by-step explanation:
To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.
Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.
Both terms have the common factor of 5x, so we can factor out 5x:
5x(-x + 2)
Therefore, the factored form of -5x² + 10x is -5x(x - 2).
\(\hrulefill\)
Additional notes:
If we expand the expressions in the given answer options, we get:
A. −5x(x + 2) = -5x² - 10x
B. 5(−x² + 10x) = -5x² + 50x
C. 5x(−x + 2) = -5x² + 10x
D. x(5x + 10) = 5x² + 10x
Hence confirming that the correct answer is option C.
To factor \(-5x^2+10x\), we can begin by factoring out the greatest common factor, which is \(-5x\):
\(-5x^2 + 10x = \boxed{-5x(x - 2)}\)We can check our answer by distributing \(-5x\) to the expression inside the parentheses:
\(\begin{aligned}-5x(x - 2)& = (-5x)(x) + (-5x)(-2)\\& = -5x^2 + 10x\end{aligned}\)\(\therefore\) The answer is \(-5x(x-2)\).
\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)
1. What is a function? Give an example of a function and explain why it is a function
2. For the equation y = 7x - 2, what is the rate of change? Explain what that rate of change means.
Answers
Answer:
a function is :a relation from the set of inputs to a set of possible outputs where each input is related o exactly one output
or a function is: a function is an equation that has only one answer for y for every x
solve for x if y = -10 y = 4x - 16
Answers
-10 + 16 = 4x
6/4 = x
1.5 = x
X = 1.5
What is the measure of
Answers
Answer:
C. 35
55 degrees + 35 degrees= 90 degrees
The ratio of teachers to students on a field trip is 2:13. If there are 132 more students than adults on the field trip, how many adults are there and how many students are there?
Answers
There are 284 number of students and 152 number of adults.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The ratio of teachers to students on a field trip is 2:13
Let x be the number of adults
If there are 132 more students than adults on the field trip, then 132+x
To find the number of adults and number of students formulate a equation as below
2/13=(x+132)/x
Apply cross multiplication
2x=13(x+132)
Apply distributive law on RHS
2x=13x+1716
11x=1716
Divide both sides by 11
x=152
x+132=152+132=284
Hence there are 284 number of students and 152 number of adults.
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How do you look for a correlation using data points?
Answers
The Correl function is the easiest way to for calculating correlation between two variables.
What is correlation ?
correlation can be defined as the measure of relation between two variables.
In case you want to measure of degree the power of a dating between two variables, you can accomplish that through using a complicated or on line calculator. you could additionally placed your mathematical abilities to apply and calculate it through hand. while calculating a correlation coefficient via hand.
To find correlation using data points are as follows :
Determine your data sets.
Calculate the standardized value for your x variables.
Calculate the standardized value for your y variables.
Multiply and find the sum.
Divide the sum and determine the correlation coefficient.
Hence, The Correl function is the easiest way to for calculating correlation between two variables.
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15. A new television's regular price is $800. It is on sale with a 15% discount. Ms. Adams buys the
television on sale and pays an 8% sales tax. What was the total cost of the television?
Answers
Answer:
734.4
Step-by-step explanation:
800 * 0.85=680
680 * 1.08=734.4
From a random sample of potential voters in an upcoming election, 47% indicated they intended to vote for Candidate R. A 95 percent confidence interval was constructed from the sample and the margin of error for the estimate of 5%. Which of the following is the best interpretation of the interval?
A) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%
B) We are 95% confident that the proportion who intend to vote for Candidate R from the population is between 42% and 52%
C) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is 47%
D) We are 95% confident that the proportion who intend to vote for Candidate R from the population is 47%
E)We are confident that 95% of the population intended to vote for Candidate R
Answers
The best interpretation is A) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%.
The confidence interval is constructed based on the sample data, not the population. The interval represents the range in which the true proportion of people who intend to vote for Candidate R in the population is likely to fall, given the sample data. The margin of error of 5% indicates that the estimate may be off by up to 5%. So, there is a 95% chance that the true proportion is between 42% (47% - 5%) and 52% (47% + 5%).
Option D) We are 95% confident that the proportion who intend to vote for Candidate R from the population is 47% is not correct because there is always some degree of uncertainty in sample estimates. The confidence interval takes into account this uncertainty by providing a range of possible values.
Option E) We are confident that 95% of the population intended to vote for Candidate R is not correct because the confidence level refers to the level of confidence in the estimate, not the proportion of people who actually intend to vote for the candidate.
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determine the surface area and volume
Answers
The surface area of a cylinder is 284m² and it's volume is 366.9m³
What is the surface area and volume of a cylinder?To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:
Surface Area (A) = 2πr² + 2πrhVolume (V) = πr²hFrom the given question, the data are;
radius = 4mheight = 7.3ma. The surface area of the cylinder is;
SA = 2π(4)² + 2π(4)(7.3)
SA = 283.999≈284m²
b. The volume of the cylinder is
v = πr²h
v = π(4)²(7.3)
v = 366.9m³
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Eric bought 8 pounds of flour for $5. How many pounds of flour did he get per dollar? If necessary, round your answer to the nearest hundredth.
Answers
Answer:
Step-by-step explanation:
8 pounds of flour = 5 dollars
1 pound of flour = x
Cross multiply
8x = 1*5 Divide by 8
8x/8 = 5/8
5/8 = 0.625
Therefore x = 0.625 dollars will buy 1 pound of flour.
Rounded x = 0.63
What is the radius of a circle with a Circumference of 64 pi yards?
Answers
The median weekly income for a student who drops out of high school is 451. Someone with a bachelor's degree from college earns 1053 in that same week. Calculate each person's yearly income and then the difference between them.
Answers
The difference between their yearly incomes is $31,304.
To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:
For the student who drops out of high school:
Yearly Income = Weekly Income x Number of Weeks
= 451 x 52
= 23,452
For someone with a bachelor's degree:
Yearly Income = Weekly Income x Number of Weeks
= 1053 x 52
= 54,756
The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:
Difference = Bachelor's Yearly Income - Student's Yearly Income
= 54,756 - 23,452
= 31,304
Therefore, the difference between their yearly incomes is $31,304.
It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.
Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.
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Sara gave 1/4
of her money to each of her 3 sisters. What fraction of her money
did she give away?
Answers
Answer:
3/4
Step-by-step explanation:
3*(1/4)=3/4
how do you math please help me
Answers
Question 12 of 22
Select the action you would use to solve = 16. Then select the property that
justifies that action.
A. Property: Multiplication property of equality.
B. Action: Add 4 to both sides.
C. Property: Addition property of equality.
D. Action: Divide both sides by 4.
E. Property: Division property of equality.
OF Action: Multiply both sides by 4.
Answers
Answer:
The correct answer is:
D. Action: Divide both sides by 4.
E. Property: Division property of equality.
A.solves routine and non-routine problems involving perceentage using appropriate strategies and tools.M5NS-IIIIb-40
Observe the solution to the given problem below.
christmas season is coming and ana is so excited to do her shopping in her list is a pair of shoes that she will wear for their christmas party.what made her more excited was when she saw that her dream pair of shoes is on sale.
from P 4 295, it is now sold with 20%
Answers
The sale price of the shoe is given as follows:
P3,436.
How to obtain the sale price of the shoe?The sale price of the shoe is obtained applying the proportions in the context of the problem.
The initial price is of:
P 4,295.
The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:
0.8 x 4295 = P3,436.
Missing InformationThe problem asks for the selling price of the shoe.
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Is the relation shown in the table below a function? (type in yes or no)
Answers
Answer:
Yes
Step-by-step explanation:
To know if a table is a function or not, we have to see if 1 input only has 1 output.
Looking at the table each input only has 1 output, so it is a function.
Please help due today
Answers
78.) x= {-4, 9}
79.) x= {5/3, 2}
80.) x= {1/9, 3}
81.) x= {-6, 18}
82.) x= {-3√3 +4, 3√3 +4}
83.) x= {-7, -3}
84.) x= {-√85 +9 /2, √85 -9 /2}
-3w-4+5w=32 what is the solution?
Answers
Answer:
w = 18
Step-by-step explanation:
Step 0: Set up the equation
=> -3w - 4 + 5w = 32
Step 1: Move the same variable together
=> -3w + 5w = 32 + 4
Step 2: Add up and simplify
=> 2w = 36
Step 3: Divide both by 2
=> w = 18
Answer:
W=18
Step-by-step explanation:
-3w-4+5w=32
-3w+5w-4=32
2w-4=32
2w=32+4
2w=36
W=18
The figure is cut into 15 equal pieces. Shade 2/5 of the figure
Answers
Answer: Shade 6 pieces
Step-by-step explanation:
Because 2/5 of 15 is 6
each of the following tables you find a relationship between an input x and an output y which of the relationships represents a function
a table a and table c
b table a and table b
c table b and table c
d table c and table d
Answers
Answer:
B table a table b
Step-by-step explanation:
All of the other tables have one x value mapped to multiple y values.
Drag the correct graph of each equation into the space next to that equation to show
how the output y-values change with changes in the input values, x
Answers
Answer:
see the explanation and the attached figure
Step-by-step explanation:
Part 1) Linear
we have
This is the equation of the line in slope intercept form
The slope is positive and equal to m=1
The y-intercept is b=3
As the value of x increases the value of y increases too
As the value of x decreases the value of y decreases too
therefore
The graph in the attached figure
Part 2) Quadratic function
Answer:
Step-by-step explanation:
solve the triangle for which angle a =30\degree, angle b=45\degree, and a=20
Answers
The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636
Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.
Here, it is given that,
angle a = 30 degrees
angle b = 45 degrees
side a = 20
angle c = 180 - (angle a + angle b)
angle c = 180 - (30 + 45)
angle c = 180 - 75
angle c = 105 degrees
We know that, a/sin(A) = b/sin(B) = c/sin(C)
a/sin(A) = b/sin(B) = c/sin(C)
20/sin(30) = b/sin(45) = c/sin(105)
b/sin(45) = 20/sin(30)
b = (sin(45) * 20) / sin(30)
b ≈ (0.7071 * 20) / 0.5
b ≈ 14.142 / 0.5
b ≈ 28.284
Now,
c/sin(105) = 20/sin(30)
c = (sin(105) * 20) / sin(30)
c ≈ (0.9659 * 20) / 0.5
c ≈ 19.318 / 0.5
c ≈ 38.636
Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.
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Activity
You have also set up a card game in which a player picks a card from a standard deck of 52 cards. The player wins if these two events occur together: E1, in which the card drawn is a black card, and E2, in which the card drawn is a numbered card, 2 through 10.
Question 1
What is the probability of getting a black card and a numbered card? Calculate the probabilities P(E1) and P(E2) as fractions.
Answers
The probability of getting a black card and a numbered card is 9/26.
To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.
There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).
Therefore, the probability of drawing a black card (P(E1)) is:
P(E1) = Number of favorable outcomes / Total number of possible outcomes
P(E1) = 26 / 52
Simplifying this fraction, we get:
P(E1) = 1/2
So the probability of drawing a black card is 1/2.
To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.
Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.
Therefore, the probability of drawing a numbered card (P(E2)) is:
P(E2) = Number of favorable outcomes / Total number of possible outcomes
P(E2) = 36 / 52
Simplifying this fraction, we get:
P(E2) = 9/13
So the probability of drawing a numbered card is 9/13.
To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:
P(E1 ∩ E2) = P(E1) × P(E2)
P(E1 ∩ E2) = (1/2) × (9/13)
Simplifying this fraction, we get:
P(E1 ∩ E2) = 9/26
Therefore, the probability of getting a black card and a numbered card is 9/26.
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Ms. Cody needs 2.65 yards of fabric to make one pillow. How many yards of fabric will she need to make 17 pillows?
Answers
Ms. Cody needs 45.05 yards of fabric to make 17 pillow.
What is referred as the unitary method?The unitary formula is used to measure the value of one unit given a multiple.The unitary method determines the value of a unit and then calculates the value of a necessary number of units.If we need to calculate the ratio with one quantity to another, we must employ the unitary method.The value of a unit quantity is determined by calculating first in the unitary method before calculating the value of other units. It comes in two varieties.Variation in DirectVariation in the inverseFor the given question;
Ms. Cody needs 2.65 yards of fabric to make one pillow.
For finding yards for 17 pillows, simply multiply the given yards by 17.
For 17 pillows = 17×2.65
For 17 pillows = 45.05
Thus, 45.05 yards of fabric is required to Ms.Cody to make 17 pillows.
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Farmer Smith has 160 feet of fencing that she is using to make a rectangular enclosure for her chickens. She will use the side of an existing chicken coop as one side of the enclosure and use the fencing for the other three sides.
Which function gives the area A, in square feet, as a function of the length of one of the sides perpendicular to the existing coop
Answers
Answer:
C
Step-by-step explanation:
4x-3y=24 in slope-intercept form
Answers
Answer:
y=(4/3)x-8
Step-by-step explanation:
Slope-intercept form: y=mx+b
4x-3y=24
3y=4x-24 (isolating the 3y)
y=(4/3)x-8 (dividing both sides by 3)
Hope this helps!