determine weather y varies directly with x. if so, find the constant variation and write the equation

Determine Weather Y Varies Directly With X. If So, Find The Constant Variation And Write The Equation

Answers

Answer 1

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

114
4. Line p contains point (6,-5) and is perpendicular to line q. The equation for line gis y = 3x + 5.
Write an equation for line p.
Part I: Find the slope of line q. (1 point)
Part II: Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.) (1 point)
that
Part III: Use the point given for line p and the slope you found in Part II to write an equation for line pin
point-slope form: y - y₁ = m(x-x₁). (1 point)

Answers

Line q has slope 3, as you've found.

Any line perpendicular to q will then have slope -1/3, as you've found.

Line p thus has slope -1/3 and we know it passes through (6, -5), so from the point-slope formula we get the equation

[tex]y - (-5) = -\dfrac13 (x - 6) \implies \boxed{y + 5 = -\dfrac13 (x - 6)}[/tex]

400g is what percent of 80kg?

Answers

.5%,

you take 400/80000, since 80,000g = 80kg

What is the domain of f(x) = 5x – 7?

{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}

Answers

Answer:

all real number {x | x is a real number}

given the following pyramid identify the L, P, and B then find the surface area

Answers

Answer:

slant length (l) = 7.5 m

perimeter of base P = 40 m

area of base B = 100 m^2

Surface Area = 250 m^2

Step-by-step explanation:

Surface area of a pyramid formula

1/2Pl + B

1/2 (40)(7.5) + 100

150 + 100 = 250 square meters


3(x-5)² +14(x-5)-24

Answers

Answer:

3x^{2} -16x-19

Step-by-step explanation:

If we are going to be simplying this problem, then we need to take it step by step.

Start off by using the distributive property, and then combining like terms. Keep in mind the square, and make sure that gets sorted out correctly.

Answer:

(3x - 19) • (x + 1)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((3•((x-5)2))+14•(x-5))-24

STEP

2

:

Equation at the end of step 2

(3 • (x - 5)2 + 14 • (x - 5)) - 24

STEP

3

:

Trying to factor by splitting the middle term

Factoring 3x2-16x-19

The first term is, 3x2 its coefficient is 3 .

The middle term is, -16x its coefficient is -16 .

The last term, "the constant", is -19

Step-1 : Multiply the coefficient of the first term by the constant 3 • -19 = -57

Step-2 : Find two factors of -57 whose sum equals the coefficient of the middle term, which is -16 .

-57 + 1 = -56

-19 + 3 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -19 and 3

3x2 - 19x + 3x - 19

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (3x-19)

Add up the last 2 terms, pulling out common factors :

1 • (3x-19)

Step-5 : Add up the four terms of step 4 :

(x+1) • (3x-19)

Which is the desired factorization

Based on the graph of g (x), on which intervals
are the function's values positive? Select all that
apply.

Answers

Answer:

[tex]\text{A}) \text{ } -\infty < x < 3\\\\\text{C}) \text{ } -1 < x < 2\\\\[/tex]

Step-by-step explanation:

The graph lies above the x-axis for these intervals.

Two buses leave a station at the same time and travel in opposite directions. One bus travels12m/hrslower than the other. If the two buses are 765 miles apart after 6 hours, what is the rate of each bus?

Answers

distance = speed * time

the first bus speed = x

second bus = x - 12

the sum of distance = 765 miles

first distance = 6x

second distance = 6 (x -12)

6x + 6(x-12) = 765

x + x -12 = 127.5

2x = 139.5

x = 69.75 mi/h which is the faster bus

the second bus speed = 57.75 mi/h

50 people sponsor Paula and she raises a total of $180.65 for charity. 28 people sponsor Kate and she raises a total of $135.60 for charity. 45 people sponsor Sam and he raises a total of $169.25 for charity.

How much money is raised altogether by three of them?
$_____________

Answers

Answer:

485.5

Step-by-step explanation:

180.65+135.60+169.25

Plss helppppppppppppppp

Answers

Answer: [tex]-\frac{3}{2} \leq x < 5[/tex]

Step-by-step explanation:

We can split this into two inequalities, namely [tex]2x-3 < x+2[/tex] and [tex]x+2 \leq 3x+5[/tex].

Solving the first inequality,

[tex]2x-3 < x+2\\\\x-3 < 2\\\\x < 5[/tex]

Solving the second inequality,

[tex]x+2 \leq 3x+5\\\\2 \leq 2x+5\\\\-3 \leq 2x\\\\-\frac{3}{2} \leq x[/tex]

So, the solution is [tex]-\frac{3}{2} \leq x < 5[/tex]

Find f(x) and g(x) so that the
function given can be described
as y = f(g(x)).

Answers

Answer:

[tex]g(x) = x^3+1\\f(x) = x^2[/tex]

Step-by-step explanation:

Answer:

f(x)=x^2 and g(x)=x^3+1

Step-by-step explanation:

to find y=f(g(x))

substitute g(x) into f(x)

y= (x^3+1)^2.

Nick volunteers at the library shelving books.
The graph shows how many books Nick shelves one Saturday.

Graph of a diagonal line on a coordinate plane with ALTDCTime in hoursALTDC on x-axis and ALTDCNumber of BooksALTDC on y-axis. The diagonal line is going up and to the right. Line passes through points (0, 0), (2, 60) and (4, 120).

Part A
How many books does Nick shelve in 2 hours? Enter your answer in the box.

Answers

The book does nick shelve in 2 hours is 60.

What is graph?

Given coordinates:

(0, 0), (2, 60) and (4, 120).

If we look at the coordinates (2, 60)

The value corresponds to 2 hours is 60.

Hence, the book nick shelves in 2 hours is 60.

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what is the answer please?

Answers

Answer:

34.562

Step-by-step explanation:

To find the perimeter of a circle, it's 2 * the radius * pi. In this case, we have a semicircle, so it would be the circle's perimeter divided by 2, or just the radius * pi.

The radius, 11, times pi (3.142), is 34.562.

Brainliest, please :)

Math Problem...can you help? (Functions)

Answers

Step-by-step explanation:

[tex]h(x) = \frac{3}{x}\\h(h(x)) = \frac{3}{\frac{3}{x}}\\\\h(h(x)) = \frac{3}{1} * \frac{x}{3}\\h(h(x)) = \frac{3x}{3}\\h(h(x)) = x\\\\\\f(f(x)) = (x^2-3)^2-3\\f(f(x)) = x^4+2(x^2)(-3)+(-3)^2-3\\f(f(x)) =x^4-6x^2+9-3\\f(f(x)) = x^4-6x^2+6\\[/tex]

how to find the side length of x

Answers

Pythagorean theorem
x^2 + 5^2 = 10^2

x^2 + 25 = 100

x^2 = 75

x = +sqrt(75), -sqrt(75) = +5sqrt(3), -5sqrt(3)

Calculate the area of this triangle.
11 cm,
cn
18 cm
14 cm

Answers

Answer:

1/2*b*h

1/2*18*14

1*9*14

126

Step 2 of 2 : Suppose a sample of 782 suspected criminals is drawn. Of these people, 548 were not captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.

Answers

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

(0.6625, 0.7388).

What is confidence interval?

A confidence interval is the mean of your estimate plus and minus the variation in that estimate.

Given sample, n= 782

As, 548 were not captured.

x= 548

So, p= 548/ 782

     p = 0.7007

q= 1- 0.7007 = 0.2993

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

Now,

α = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

For confidence level of 98% , z is 2.33

Now,

(0.70007 - 2.33√ (0.7007(0.2993))/782 , 0.70007 + 2.33 √(0.7007(0.2993))/782

= (0.6625, 0.7388)

Hence, 98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

(0.6625, 0.7388).

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Mountain Climbing Gym has a gym registration fee of $30 and then charges $55 per month for all access climbing.

Susie wanted to model what she has spent in total on the climbing gym at any given month in the future.

Fill in the blanks for the equation if C = total Cost and m = number of months.

Answers

Answer:

C=55m + 30

Step-by-step explanation:

You would multiply 55 by the number of months so you'd get 55m, and since 30 is a one time fee you would just add 30 to your monthly payment.

find X :))))))))))))))

Answers

Answer:

X + 35° = 70° ( this is one of the property of triangle in which the sum of two interior angles of a triangle is equal to its other angle)

X = 70 - 35

X = 35°

A local dry cleaner interviewed 17 candidates for the positions of the cashier, washer, salesperson, and delivery driver. How many ways can they fill the 4 positions?


HELP PLSPLSPLS

Answers

Using the permutation formula, it is found that there are 57,120 ways to fill the 4 positions.

There are different roles, hence the order is important, which means that the permutation formula is used.

What is the permutation formula?

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 4 roles are chosen from a set of 17, hence the number of ways is given by:

[tex]P_{17,4} = \frac{17!}{13!} = 57120[/tex].

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The perimeter of a rectangle is 286 meters. Find the length and width if the length is an integer and the width is 5 times the next consecutive integer.

Answers

Answer:

See below

Step-by-step explanation:

Please answer all of the questions and if u are correct I will give u brainliest ;) xoxo <3

Answers

Answer:

the answer for the 2nd question is 1/4

Step-by-step explanation:

i took the test

ASSIGNMENTS
COURSES
2.(-4)2
3.42
Assignment 5. Solving Equations with Exponents
Attempt 10 of 7
Evaluate each expression. Determine if the final simplified form of the expression is positive or negative
1.-42
NEXT QUESTION
SECTION

Answers

Answer:

-16, 16, 16

Step-by-step explanation:

1) -16

2) 16

3) 16

Write 1 3/4 as a decimal and as a percent

Answers

Answer:

Decimal: 1.75

Percentage: 175%

Hey there!

1 3/4

= 1 * 4 + 3 / 4

= 4 + 3 / 4

= 7 / 4

= 7 ÷ 4

= 1.75

= 1.75 * 100

= 175%

Therefore, your answer should be:

• 1.75 (as your decimal form)
• 175% (as your percentage form)


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

What are the following expressions simplified?

(11 √40) (9 √5)

(2 √6) (10 √8)

5 √6 ÷ √7 - √5 ÷ √6

Answers

The simplified expressions are

1.  990√2

2.  80 √3

3. 30- √35 / √42

What is expression?

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

(11 √40) (9 √5)

= 11*9* √40*√5

= 99*√200

= 99* 10√2

= 990√2

(2 √6) (10 √8)

= 2*10 *  √6 * √8

=20*  √48

= 20* 4 √3

= 80 √3

5 √6 ÷ √7 - √5 ÷ √6

=30- √35 / √42

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It costs $164.34 to rent a standard-size car for 5 days. Find the price per day to rent this car.

Answers

164.34 divided by the amount of days, in this case 5.
164.34 divided by 5 =32.868.

That answer can be rounded to $33 or $32.87. I would go with the first one if asked to round.

In a study of cell phone usage and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 6965 subjects randomly selected from an online group involved with ears. There were 1302 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than​ 20%. Use the​ P-value method and use the normal distribution as an approximation to the binomial distribution

Answers

The hypothesis test shows that we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%

What is the claim that the return rate is less than 20% by using a statistical hypothesis method?

The claim that the return rate is less than 20% is p < 0.2. From the given information, we can compute our null hypothesis and alternative hypothesis as:

[tex]\mathbf{H_o :p =0.2}[/tex]

[tex]\mathbf{H_i:p < 0.2}[/tex]

Given that:
Sample size (n) = 6965

Sample proportion [tex]\mathbf{\hat p = \dfrac{x}{n} = \dfrac{1302}{6965} \sim0.1869}[/tex]

The test statistics for this data can be computed as:

[tex]\mathbf{z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}}[/tex]

[tex]\mathbf{z = \dfrac{0.1869 -0.2}{\sqrt{\dfrac{0.2(1-0.2)}{6965}}}}[/tex]

[tex]\mathbf{z = \dfrac{-0.0131}{0.0047929}}[/tex]

z = -2.73

From the hypothesis testing, since the p < alternative hypothesis, then our test is a left-tailed test(one-tailed.

Hence, the p-value for the test statistics can be computed as:

P-value = P(Z ≤ z)

P-value = P(Z ≤ - 2.73)

By using the Excel function =NORMDIST (-2.73)

P-value = 0.00317

P-value ≅ 0.003

Therefore, we can conclude that since P-value is less than the significance level at ∝ = 0.01, we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%

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A rectangle has a length 10 more than its width. If the width is increased by 8 and the length by 4, the resulting rectangle has an area of 135 square units.
Part A Write an equation to model the above scenario. Use the model to find the length of the original rectangle?
Part B What is the perimeter of the expanded rectangle?

Answers

The equation to model the above scenario is [tex]x^{2}[/tex] +22x - 23 = 0

The perimeter of the expanded rectangle is 48 units

What is a rectangle?

A rectangle is a quadrilateral with its 4 angles 90°

Analysis:

First rectangle:

length = 10 + x

width = x

Second rectangle:

length = x + 14

width = x + 8

Area of expanded rectangle = 135 square unit

(x+8)(x+14) = 135

[tex]x^{2}[/tex] + 8x + 14x + 112 = 135

[tex]x^{2}[/tex] + 8x + 14x -23 = 0

[tex]x^{2}[/tex] + 22x -23 = 0

[tex]x^{2}[/tex] + 23x - x - 23 = 0

(x-1)(x+23) = 0

Therefore x = 1

Expanded length = 1+14 = 15

Expanded width = 1+8 = 9

Perimeter = 2(9+15) = 48 units

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In ΔABC, m < C = 50* , a = 14 and b = 15. Find the length of side c, to the nearest integer.

Answers

The length of the side c, to the nearest integer is 12.

What is a cosine law?

Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.

u² = s² + t² - 2(s)(t)·cos U

In ΔABC, m < C = 50* , a = 14 and b = 15.

We can solve for the length of side a to the nearest whole number using the Laws of Cosines

c² = b² + a²- 2ba CosC

Solving for the value of a, we have:

c² = 15² + 14²- 2(15)(14)cos50°

c² = 225 + 196 - 269.97

c² = 151.029

c = 12.28

Hence, The length of the side c, to the nearest integer is 12.

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Find the truth set of each predicate.

Answers

The truth set for each predicate are:

a) d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}

b) d ∈ {  1, 2, 3, 6}

c) x ∈ { [-2, -1] U [1, 2]}

d) x ∈ {-2, -1, 1, 2}

How to find the truth set of each predicate?

We only need to find the sets of values such that the statements are true.

a)

We want to find vales of d, such that d is an integer, and 6/d is an integer.

Here the possible values of d will be:

d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}

Which are all the factors of 6, so all these integers divide 6.

b) Same as before, but this time the domain is a positive integer, so now the truth set will be:

d ∈ {  1, 2, 3, 6}

c) We want to find real values of x such that:

1 ≤ x² ≤ 4

If we apply the square root to the 3 sides, we get two inequalities:

-√1 ≥ x ≥ -√4

√1 ≤ x ≤ √4

Simplifying:

-1  ≥ x ≥ -2

1  ≤ x ≤ 2

So the truth set is:

x ∈ { [-2, -1] U [1, 2]}

c) Same as before, but now we only have integer solutions, so the truth set is:

x ∈ {-2, -1, 1, 2}

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Can anyone help me solve this? Please and thank you!

Answers

It's the sum of a geometric sequence.

Let's rewrite it a bit:

[tex]\displaystyle\\\sum_{n=1}^{10}8\left(\dfrac{1}{4}\right)^{n-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot \left(\dfrac{1}{4}\right)^{-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot 4=32\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]

And now let's calculate this sum [tex]\displaystyle \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\a=\dfrac{1}{4}\\n=10\\r=\dfrac{1}{4}\\\\S_{10}=\dfrac{\dfrac{1}{4}\cdot\left(1-\left(\dfrac{1}{4}\right)^{10}\right)}{1-\dfrac{1}{4}}=\dfrac{\dfrac{1}{4}\cdot\left(1-\dfrac{1}{1048576}\right)}{\dfrac{3}{4}}=\dfrac{\dfrac{1048575}{1048576}}{3}=\dfrac{1048575}{3145728}=\\=\dfrac{349525}{1048576}[/tex]

Now let's calculate the initial sum:

[tex]\displaystyle 32\cdot \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n=32\cdot \dfrac{349525}{1048576}=\dfrac{349525}{32768}\approx10.67[/tex]

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