determine weather y varies directly with x. if so, find the constant variation and write the equation
Answers
Answer:
Yes, k = 1/3 and y = 1/3x
Step-by-step explanation:
[tex]\text{The given line passes through the origin, hence it has equation of the form:}\\y=kx[/tex]
[tex]\text{Therefore y varies directly as x.}The line passes through the point (3,1)}[/tex]
[tex]\text{This implies that,}[/tex]
[tex]1=k(3)\\k=\frac{1}{3}[/tex][tex]\text{Hence the constant of variation is}[/tex] ⇒ [tex]\frac{1}{3}[/tex]
The equation would be ⇒ [tex]y=\frac{1}{3} x[/tex]
Related Questions
Solve the equation x³ - 5x²+2x+8 = 0 given that - 1 is a zero of f(x)= x3 - 5x²+2x+8.
The solution set is? (Use a comma to separate answers as needed.)
Answers
Answer:
added in the picture
Step-by-step explanation:
added in the picture
(
Given that a = 7 cm and b = 8 cm,
work out the area of the triangle.
Give your answer rounded to 1 DP.
a
cm²
b
The diagram is not drawn accurately.
Answers
Answer:
28cm²
Step-by-step explanation:
The area of a triangle is given as:
= 1/2 × b × h
= 1/2 × 7 × 8
= 28cm²
What is the value of h?
Answers
Answer:
h=-2
Step-by-step explanation:
the graph was shifted 2 units left
Write the mathematical expression for cost of each item if y items cost a
total of $25.00.
Answers
A major airline is planning to purchase new airplanes. It wants to borrow $800 million by
issuing bonds. The bonds are for a 10-year period with simple interest computed quarterly at
a rate of 2 percent per quarter. Interest is to be paid each quarter to bondholders.
How much (in millions) will the airline have to pay in quarterly interest? $
million
How much interest (in millions) will it pay over the 10-year period? $ million
Answers
Answer:
look at the picture
Step-by-step explanation:
look at the picture
. . . , , ,
help please
Answers
The system of inequalities of the graph is (a) y > x² + 2x - 3 and y > 2x + 3
How to determine the inequalities?The complete question requires that we determine the system of inequalities of the graph (the graph is attached)
Going by the list of options, the equation of the quadratic curve is:
y = x² + 2x - 3
From the graph, we can see that:
The curve uses a dotted lineThe upper part is shadedThe above means that the inequality is greater than i.e. >
So, we have:
y > x² + 2x - 3
The above eliminates options (b) and (c)
From the graph, we can see that the straight line has a positive slope, a dotted line and the upper part is shaded.
The linear inequality in option (a) has the above characteristics.
So, the inequality is:
y > 2x + 3
Hence, the system of inequalities of the graph is (a) y > x² + 2x - 3 and y > 2x + 3
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Find the radius of a circle with area 345 square centimetres
30 pts need in like 10 mins!!
Please say the answer like-
… divided by … = ……
Or
… times … = …..
Answers
Answer:
5.9
Step-by-step explanation:
It's because area is 345
Formula , A=πr2Find the √ of 34518.6=3.14×f2fR = 5.9Step-by-Step Solution:
Radius (r) = ?
Area (A) = πr² = 345 sq. cm
Therefore,
πr² = 345
3.14 * r² = 345
r² = 345/3.14
r² = 109.87
r = √109.87
=> r = 10.48
Radius (r) = 10.48 cm
What amount would u have if u deposited 1800 a year for 30 years at 7% compounded annually
Answers
Answer: $183,731
Step-by-step explanation:
After 30 years, the interest is $183,731
Question 3(Multiple Choice Worth 4 points)
Which expression is equivalent to 73.7-57
0 72
0 77
17
글
Answers
Answer: [tex]\frac{1}{7^{2}}[/tex]
Step-by-step explanation:
Using the exponent rule [tex]a^{b} \cdot a^{c}=a^{b+c}[/tex], we get that
[tex]7^{3} \cdot 7^{-5}=7^{-2}[/tex]
Then, using the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex], we get that
[tex]7^{-2}=\boxed{\frac{1}{7^{2}}}[/tex]
Want to earn 20 points for correct answer CLICK ME
Answers
Answer:
64 is the answer
Step-by-step explanation:
Mark me brainliest answer pls
What is the simplified form of StartRoot 100 x Superscript 36 Baseline EndRoot ?
10x Superscript 18
10x Superscript 6
50x Superscript 18
50
Answers
The simplified form of the expression √(100x³⁶) will be 10x¹⁸. Then the correct option is A.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ √(100x³⁶)
Then the simplified form of the expression will be
⇒ √[(10x¹⁸)²]
⇒ 10x¹⁸
Then the correct option is A.
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Answer:
Step-by-step explanation:
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Ace
13K answers
73.3M people helped
The simplified form of √(400x¹⁰⁰) is;
D; 20x⁵⁰
We want to find the simplified form of √(400x¹⁰⁰)
Now, according to laws of indices;
√ab = √a × √b
Thus;
√(400x¹⁰⁰) = √400 × √(x¹⁰⁰)
⇒ 20√(x¹⁰⁰)
Also according to law of indices;
a⁴ = a² × a²
Thus;
x¹⁰⁰ = x⁵⁰ × x⁵⁰
Thus;
√(x¹⁰⁰) = √(x⁵⁰ × x⁵⁰)
⇒ x⁵⁰
Our final answer is;
20x⁵⁰
There is a 45% chance of snow on Friday. Thereis a 78% chance that I will go sledding if it snows. What is the probability that I will go
sledding?
Answers
Answer:
35.1% chance of going sledding
Step-by-step explanation:
45% chance of snow on Friday
Convert percentage to decimal form (divide by 100)
45% = 0.45
78% chance of sledding if it snows
Convert percentage to decimal form (divide by 100) to multiply
78% = 0.78
Multiply to find the probability of both occurring
0.78 * 0.45 = 0.351
Convert back into a percentage (multiply by 100)
0.351 = 35.1% chance of sledding
Let me know if you have any questions!
Look at the photo and answer it pls
Answers
Answer:
There isn't a photo
Step-by-step explanation:
There is no photo
The number of measles cases increased 36.5% to 193 cases this year. What was the number of cases prior to the increase? The number of measles cases increased 36.5 % to 193 cases this year . What was the number of cases prior to the increase ?
Answers
Answer:
70.445
Step-by-step explanation:
you have to subtract 36.5 by 193.
Which table correctly shows all the sample spaces for tossing a coin to get heads and rolling a number on a six-sided number cube?
Answers
Using it's concept, the sample space for the experiment is given as follows:
{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
What is the sample space of an experiment?The sample space is the set that contains all possible outcomes for an experiment.
In this problem:
For the coin, there are 2 outcomes, H for heads and T for tails.For the number, there are 6 outcomes, which are the 6 numbers.Hence the sample space is given as follows:
{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
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A ship leaves port at 1 pm traveling north at the speed of 30 miles/hour .at 3 pm the ship adjusts its course20° eastward. Sketch a diagram to show the path the ship moved and the distance the ship is from the port. And how far the ship is from the port at 4pm?
Answers
The ship is 88.8 miles far from the port at 4 pm.
Given,
The displacement from 1 to 3 in the afternoon.
D1 = 30 miles/hr × 2 hr
= 60 miles to the north
The displacement from 3 till 4 in the afternoon.The ship changes its course 20 degrees eastward at 3 o'clock.
Therefore, D2 = 30 miles/hr × 1 hr
= 30 miles to the 20° north eastward
By combining two vectors, the resulting displacement:
D = √((D1 ₊ D2 × cos(20°))² ₊ (D2 × sin(20°))²
D = √((60 ₊ 30 × cos (20°))² ₊ (30 × sin(20°))²
D = 88.8 miles
Hence the ship is 88.8 miles far away from the port at 4 pm.
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Factor the polynomial function.
G(v) - 196v² + 100
Answers
Answer:
4(49v²+25)
Step-by-step explanation:
[tex]196 {v}^{2} + 100[/tex]
[tex]4(49 {v}^{2} + 25)[/tex]
the amount of money sue needs to pay (m) equals $30 to go to an apple orchard and pick apples plus $5 for every bushel of apples (b) she takes home
Answers
the elegante is aborto 3
At May 31, Lily Company has net sales of $395,000 and cost of goods available for sale of $268,000.
Compute the estimated cost of the ending inventory, assuming the gross profit rate is 35%.
Answers
The estimated cost of the ending inventory, assuming the gross profit rate is 35% is; $11250
How to find Estimated Cost?Let us first calculate the gross profit;
Gross Profit = Sales * Profit%
Gross Profit = 395000 * 35%
Gross Profit = $138250
Cost of goods sold = Sales - Gross Profit
Cost of goods sold = 395000 - 138250
Cost of goods sold = $256750
Cost of ending inventory = Cost of goods available for sale - Cost of goods sold
Cost of ending inventory = 268000 - 256750
Cost of ending inventory = $11250
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Answer this please, thank you in advance :D
Answers
i) Student A used the property of the power of a power and student B used the definition of power and the property of the product of power with the same base. ii) Both were correct.
How to understand power properties
In this question we must analyze the procedure used by each student to simplify a power into the form rⁿ:
i) The student A used the property of the power of a power which states that [tex](r^{m})^{n} = r^{m\cdot n}[/tex]. In exchange, the student B used the definition of power and the property of the product of powers with the same base.
ii) Based on the description in i), both students used correct methods of simplifying.
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Identifying Proportional Relationships
Which graph represents a proportional relationship?
Answers
Answer:
I can't answer this if you don't have the answer choices
I'm sorry
is the square root of 10 a rational number
Answers
Answer:
No
Step-by-step explanation
The square root of 10 is irrational because it isn't a fraction
Solve for x in the equation 4/x-3=x
Answers
Answer:
jenejebdjdndnr
r
r
r
r
r
r
Answer:
Step-by-step explanation:
Comment
Multiply through by x - 3
Then factor the result
4*(x - 3) / (x - 3) = x*(x - 3)
4 = x * (x - 3 ) Remove the brackets
4 = x^2 - 3x Subtract 4 from both sides
4-4 = x^2 - 3x - 4 Simplify
0 = x^2 - 3x- 4
This factors
0=(x - 4)(x + 1)
Answer
x - 4 = 0
x = 4
x+ 1 = 0
x = - 1
Based on statistics from a worldwide health organization, in there were million people worldwide living with a certain disease, and million deaths from the disease. By , the number of people living with the disease had grown to million, and million deaths were reported. Find the percent change for each statistic, and write any conclusions you can draw.
Answers
Based on the statistics from the worldwide health organization, the percentage change in those living with the disease is 19.7% and the change in those who have died is 70%.
This shows that the disease is getting worse and not being treated effectively.
What do the statistics on the disease show?The number of those living with the disease went from 71 million to 40 million:
= (85 - 71) / 71
= 19.7% increase
The percent change in those who have died is:
= (6.8 - 4) / 4
= 70% increase
This shows that the measures being implemented against the disease are not working because both the number of people who have the disease and have died from it has increased.
Full question is:
Based on statistics from a worldwide health organization, in 1999 there were 71 million people worldwide living with a certain disease, and 4 million deaths from the disease. By 2015, the number of people living with the disease had grown to 85 million, and 6.8 million deaths were reported. Find the percent change for each statistic, and write any conclusions you can draw.
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[tex]\frac{1}{28} + \frac{1}{70} + \frac{1}{130} + \frac{1}{208} + \frac{1}{304} = ?[/tex]
Evaluate this expression.
Answers
Considering the least common multiple of the denominators, it is found that the result of the expression is given by:
[tex]\frac{9100}{138320}[/tex]
How do we add fractions?We place all the terms of the addition in "equivalent" fractions, with the same denominator, found from the last common multiple of all the denominators.
In this problem, the denominators are as follows: 28, 70, 130, 208, 304. Using a calculator, their lcm is of 138,320.
Considering equivalent fractions(the numerators are the division of the lcm by the previous denominator), the expression is:
[tex]\frac{4940}{138320} + \frac{1976}{138320} + \frac{1064}{138320} + \frac{665}{138320} + \frac{455}{138320} = \frac{4940 + 1976 + 1064 + 665 + 455}{138320} = \frac{9100}{138320}[/tex]
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Please create an example using exponential growth and exponential decay
Answers
Answer:
f(x)=4^x exponential growth, -6^x exponential decay Step-by-step explanation:
What are the similarities and differences between these data sets in terms of their centers and their variability?
Data Set A: 14, 21, 24, 28, 28, 35
Data Set B: 18, 19, 21, 25, 29, 32
Select from the drop-down menus to correctly complete the statements.
Comparing the centers of the data sets, the median for Data Set A is
Choose...
the median for Data Set B. The mean for Data Set A is
Choose...
the mean for Data Set B.
Answers
The median for Set A is (24+28)/2 = 26
The median for Set B is (21+25)/2 = 23
The mean for set A is (14+21+24+28+28+35)/6 = 25
The mean for set B is (18+19+21+25+29+32)/6 = 24.
Thus, the mean for Data Set A is greater than the mean for Data Set B.
Leah wants to buy a home for
$380,000, but can only get a loan from the bank for $330,600. What percentage does Leah have to put down in order to pay for the home?
Answers
Leah have to put down 13% of the total money in order to pay for the home.
What is a Home Loan ?The amount of money a person borrows from a bank to buy a house is termed as Home Loan.
It is given that
Leah wants to buy a home for $380,000
The amount of money he can get from bank is $ 330,600
The amount of money Leah needs to have
= $ 380000 - $ 330600 = $49400
The percentage Leah have to put down in order to pay for the home is
=($49400 /$380000 ) * 100%
= 0.13 * 100 %
= 13%
Therefore Leah have to put down 13% of the total money in order to pay for the home.
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A theme park had 1099 visitors in 3 days. There were twice as many visitors on saturday than on Friday. There were 234 more visitors on Sunday than on Saturday. How many visitors were there on Saturday?
Answers
Answer:
346
Step-by-step explanation:
Visitors on Friday(x)+Visitors on Saturday(2x)+Visitors on Suday(2x+234)
x+2x+2x+234=1099
5x+234=1099
5x=1099-234
5x=865
x=865/5
x=173
So, visitors on Saturday = 2x = 346
Assume that t varies jointly as r and q2². If t=320 when r=5 and q = 4, what is the value of q when r= 1 and t= 196?
q=
Answers
Step-by-step explanation:
[tex]t = k(r)( {q}^{2} )[/tex]
[tex]320 = k(5)( {4}^{2} )[/tex]
[tex]320 = 80k[/tex]
[tex]k = 4[/tex]
[tex]196 = 4(1)( {q}^{2} )[/tex]
[tex]49 = {q}^{2} [/tex]
[tex]q = 7[/tex]