if y varies inversely as x, and y=20 as x=3, find y for the x value 4

Answers

Answer 1

[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \begin{cases} y=20\\ x=3 \end{cases}\implies 20=\cfrac{k}{3}\implies 20\cdot 3=k\implies 60=k \\\\\\ thus\qquad \boxed{y=\cfrac{60}{x}}\\\\ -------------------------------\\\\ now\qquad x=4\qquad y=\cfrac{60}{4}[/tex]

Related Questions

What is the square root of 26 in simplest radical form?

Answers

Final answer:

The square root of 26 in simplest radical form is just √26, as 26 has no perfect square factor. It can also be expressed as 26 raised to the power of 0.5 based on the concept of fractional powers corresponding to roots.

Explanation:

The square root of 26 in its simplest radical form cannot be simplified further as a perfect square factor because 26 is not a perfect square. However, if we apply the concept of expressing numbers as fractional powers, we can say that any number 'x' squared, written as x², is equivalent to the square root of 'x'. Thus, the square root of 26 can also be written as 26 to the power of 0.5 or 26⁰.⁵.

Expressing the concept mathematically, we can write the square root of any number 'x' as x to the power of 0.5, which is a helpful way to solve for unknown values in various equations. This idea is useful in scenarios where different roots of a number or expressions involving fractional exponents are to be calculated, and it is essential to remember that the square root is just another form of an exponent.

Suppose that y varies inversely with x, and y=0.2 when x=2. What is an equation for the inverse variation

Answers

[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \begin{cases} y=0.2\\ x=2 \end{cases}\implies 0.2=\cfrac{k}{2}\implies 0.2\cdot 2=k\implies 0.4=k \\\\\\ thus\qquad y=\cfrac{0.4}{x}[/tex]

I just need to know how do I find the domain for this function Y=-4x+2

Answers

Answer: Set of all real numbers

The domain is the set of all real numbers because we can plug in any x value we want to get some y value. There is no worry about dividing by zero. We don't have to worry about taking the square root of a negative number. There are no restrictions for x.

How would I solve this?

Answers

[tex] \sqrt{2k^2+17} =7\\\\
2k^2+17=49\\\\
2k^2=32\\\\
k^2=16\\\\
k=4[/tex]
Final answer: C

If babe ruth averaged 46 home runs per year, how many home runs did he hit in 12 years

Answers

If he averaged 46 per year, you can just multiply that average times the number of years.

46(12)=552 home runs

Answer:

He hit 552 home runs in 12 years

Step-by-step explanation:

To solve this problem, we will follow the steps below;

Using proportion;

Let x be the number of home runs he hits in 12 years

46 home runs = 1 year

x = 12

cross -multiply

x × 1 = 46× 12

x = 552 home runs

Therefore, he hit 552 home runs in 12 years

If you quadruple the input of a function and the resulting output is one-fourth the original output, what may be true of the function? Check all that apply.

A. The function is inversely proportional.
B. The function is directly proportional.
C. More input results in less output.
D. More input results in more output.

Answers

Answer:

More input results in less output.
The function is inversely proportional.

Step-by-step explanation:

those two. other answer is completely wrong

If you quadruple the input of a function and the resulting output is one-fourth the original output, what may be true of the function? The correct options are A. The function is inversely proportional and C. More input results in less output.

In mathematical terms, let's consider the function as f(x), where x is the input, and f(x) is the output.

1. Option A: The function is inversely proportional.

If quadrupling the input (4x) leads to the output being one-fourth of the original output (1/4 f(x)), it implies that f(4x) = 1/4 f(x). Inverse proportionality means that as the input increases, the output decreases, and vice versa. In this case, increasing the input by a factor of 4 (4x) causes the output to reduce to one-fourth of its original value (1/4 f(x)), indicating an inverse relationship.

2. Option C: More input results in less output.

As mentioned earlier, quadrupling the input (4x) and obtaining an output of one-fourth the original (1/4 f(x)) demonstrates that increasing the input leads to a decrease in the output. When x increases, 4x (quadruple of x) will also increase, and as a result, f(4x) will be less than f(x). This aligns with the statement that more input results in less output.

It is important to understand the relationship between the input and output of a function. In this case, the given conditions indicate inverse proportionality and that increasing the input leads to a decrease in the output. Keep in mind that mathematics often deals with relationships between variables, and understanding such relationships can help solve various problems and make predictions about how a system behaves.

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(05.03)The equation shows the relationship between x and y:

y = −7x + 9

What is the slope of the equation?
−7
−2
7
9

Answers

In y = mx + b form, the slope will be in the m position

y = mx + b
y = -7x + 9

notice that in the m position, the number is -7. That means ur slope = -7

Answer:

Option 1) -7

Step-by-step explanation:

Given : The equation shows the relationship between x and y : [tex]y=-7x+9[/tex]

To find : What is the slope of the equation?

Solution :

The general slope form of the equation is [tex]y=mx+b[/tex]

Where, m is the slope and b is the y-intercept.

Now, We compare the given equation with general form of the equation

[tex]y=-7x+9[/tex]

On comparing, m=-7 and b=9

So, The slope of the given equation is -7.

Therefore, Option 1 is correct.

(Solve for v) 2v − 6 = 4

Answers

2v-6=4
[add 6]
2v=10
[divide by 2]
v=5

The polynomial 9x2+3x3y2z is what degree?

Answers

In polynomials, when you are asked for its degree, you are to determine its highest degree of which the variable is raised to. For this example, one might argue that the highest degree is 3 at x³. But there is a rule that for polynomials containing implicit terms in the equation, you add up their exponents. Now, this is not applicable in algebraic operations. When you multiply the terms x³y²z, it does not become (xyz)⁶. This is not valid because they don't have common bases. The rule of adding up exponents is only applicable for classification. Therefore, the polynomial given is in the 6th degree.

The area of a circle is 28.26 square centimeters. What is its diameter (use 3.14 for Pi)?

Answers

6 cm because it is an i know it and you have to trust me and i need 20 characters

area=r×r×pi
r= squareroot of 28.26÷3.14=3
D= r×2
D=3×2=6

D=6

Which of the following lists some of the non-monetary factors that are taken into account when doing cost-benefit analysis

Answers

Time and Effort are the answer because it is the only non-monetary factors that take into account when doing a cost-benefit analysis. Cost Benefit Analysis is a systematic approach to estimate the strength and weakness of alternatives for example in transaction, activities and project requirement.

Answer:

product being used by everyone

the aesthetic value of nature

identifying internal costs

categorizing internal and external costs

Step-by-step explanation:

Which combination of compounds will create a buffer solution? a weak acid and a weak base a weak acid and its conjugate base a strong acid and its conjugate base a strong acid and a strong base

Answers

Either a weak acid and its conjugate base, or a weak base and its conjugate acid.

Answer:

a weak acid and its conjugate base

Step-by-step explanation:

A Buffer solution is a solution that tends to keep the pH almost constant when small amounts of acids (H +) or bases (OH-) are added, therefore, they are very useful to reduce the impact of drastic changes in (H+) and (OH-) in processes that require a specific pH. They can be prepared by dissolving in water adequate amounts of a weak acid and a salt of its conjugate base, or a weak base and a salt of its conjugate acid.

The cross section of a square pyramid taken perpendicular to the base that passes through the top vertex produces which two-dimensional shape?

Note: Use all lowercase letters in your answer to receive credit.

Answers

I don't see a diagram, but it produces a triangle.

Answer:

triangle.

Step-by-step explanation:

given: a square pyramid

to find : shape of cross section made when a plane perpendicular

to base and passes through top vertex.

when a plane cuts the square pyramid perpendicular to base and passes through top vertex we get a cross section made by its two equal slant height and side of the square.

therefore, we get a triangle or more specifically isosceles triangle.

picture is attached.

what is the common difference in the arithmic sequence 30,27,24,21,18

Answers

if you have two terms in a sequence, then a term decreased by the previous term=common difference

so
30 and 27

27 decreased by 30 is -3

the common differce is -3

Answer:

-3

Step-by-step explanation:

Its decresing by -3.

The amount of candy left in a Halloween bucket is given by the function A(t) = 50(0.8)t where t stands for the number of minutes the candy is available and A(t) stands for the amount of candy left at any given time. How much candy is there after five minutes?

50 pieces

40 pieces

16 pieces

200 pieces

Answers

I think that equation is supposed to look like this:
[tex]A(t)=50(.8) ^{t} [/tex]
The reason I say that is because this is an exponential decay problem, with a starting amount of 50 pieces of candy.
If that's the case, then it would look like this with a t value of 5:
[tex]A(5)=50(.8) ^{5} [/tex]
and [tex]A(5)=50(.32768)[/tex]
so the amount of candy left after 5 minutes is 16.384 or 16

A car is purchased for $28,000. After each year, the resale value decreases by
35%. What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.

Answers

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &28000\\ r=rate\to 35\%\to \frac{35}{100}\to &0.35\\ t=\textit{elapsed time}\to &3\\ \end{cases} \\\\\\ A=28000(1-0.35)^3\implies A=28000(0.65)^3\implies A=7689.5 \\\\\\ \textit{which rounds up to }7689[/tex]

Final answer:

Using the formula for decrement, the resale value of a $28,000 car that depreciates at a 35% rate annually for three years would be roughly $10,012.

Explanation:

This question is about calculating the effects of percent decrease over a period of time. Specifically, the student is asked to calculate the value of a $28,000 car, after it undergoes a 35% percent decrease in value each year for three years. This type of problem is typically solved using the formula v = p * ((1 - r)^n), where v is the final value, p is the initial value, r is the rate of decrease, and n is the number of periods. In this case, the initial value (p) is $28,000, the rate of decrease (r) is 35% or 0.35, and the number of periods (n) is 3 years. Substituting these into the formula, we can find that the resale value after 3 years is v = 28000 * ((1 - 0.35)^3) = $10,011.75. Rounding this to the nearest dollar, we get an estimated resale value of $10,012.

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what operation represents a ratio

Answers

The operation that would represent a ratio would be division. A ratio, in mathematics, relates two numbers which indicates how many time is the first value contains the second value. It says how much of something is there as compared to another thing. For example, we have 3 blue circles to 1 red circle, it would be written as 3/1 or 3:1. Ratio and division are closely related. However, ratio is a relationship between things and division is an operation that can be used in this relationship but is not limited to this problem. If you are given 14 dogs, 7 chickens and 21 cows, the ratio would be 2:1:3. Indeed, you have divided the values but this is a ratio problem rather than a division problem.

Evaluate the expression 2(8 - 4)^2 - 10 / 2

Answers

Answer:

Step-by-step explanation:

2(8 - 4)^2 - 10/2

Using the order PEMDAS, or parenthesis, exponents, multiplication, division, addition, subtraction, we will start with the parenthesis, or 8-4.

2(4)^2 - 10/2

Next is exponents.

2(16) - 10/2

And then multiplication.

32 - 10/2

Then division.

32 - 5

Finally, subtraction.

Therefore, the answer is 27.

Consider the equation
(x^m)^3 = (x^13)^5 times (x^-8)^-5.

The value of m is?

A. 15
B. 28
C. 35
D. 70

It's 35, I figured it out

Answers

This is the concept of algebra, the value of m will be calculated as follows;
(x^m)^3=(x^13)^5*(x^-8)^-5
expanding the above we get;
x^(3m)=x^(65)*x^(40)
x^(3m)=x^(65+40)
x^(3m)=x^105
the x will cancel out and we shall remain with:
3m=105
dividing both sides by 3 we get;
m=105/3
m=35
You are right the answer is m=35.
Bravo!!

The area of a rectangular wall of a barn is 300 square feet. its length is 10 feet longer than twice its width. find the length and width of the wall of the barn.

Answers

L * W = 300 sq ft
Length is 10 ft greater than twice the width.
L = 2W + 10
Substituting
(2W+10)*W = 300
2W^2 + 10W = 300
Divide both sides by 2
W^2 + 5W = 150
W^2 + 5W - 150 = 0
Factor
(W +15)(W -10) = 0

Roots are W=-15 and W=10.
A negative width is impossible, so W=10
L = 2W + 10
L = 2(10) + 10
L = 30

length = 30 feet, width = 10 feet

Check: 30*10 = 300

Final answer:

To find the dimensions of the barn wall, we first expressed the given information as an equation using the formula for area. After simplifying and factoring the quadratic equation, we determined the width to be 10 feet and the length to be 30 feet.

Explanation:

The question involves finding the length and width of a rectangular wall when given the area and a relationship between the length and width. We know the area of the wall is 300 square feet and that the length is 10 feet longer than twice the width. Let's denote the width as 'w' and the length as 'l'. The relationship between them can be expressed as l = 2w + 10. Using the formula for the area of a rectangle, which is A = l * w, we substitute the given area and the relationship between length and width to create an equation: 300 = (2w + 10) * w.

Solving this quadratic equation:

Expand the right side: 300 = 2w^2 + 10wMove all terms to one side: 2w^2 + 10w - 300 = 0Divide by 2 to simplify: w^2 + 5w - 150 = 0Factor the quadratic: (w + 15)(w - 10) = 0Find the roots: w = -15 or w = 10 (since width can't be negative, w = 10)Substitute w back into the relationship to find l: l = 2(10) + 10 = 30

Therefore, the width of the wall is 10 feet, and the length is 30 feet.

A car is a vehicle with four wheels.
Rewrite the statement as a true conditional with a converse that is false.
Write a similar true conditional with a converse that is true

Answers

Answer:

If a vehicle does not have 4 wheels, it is not a car.

Dont forget to give brainliest and thanks

What is the slope and the y intercept of the line y=6x-9?

Answers

The slope is: 6 .
The y-intercept is: -9 ; (or, more precisely:  "(-9, 0)" .
_________________________________________________
   Note: The line in written in "point-slope form"; also known as:
"slope-intercept format" ; that is: " y = mx + b" ; in which:
                                              m = slope = coefficient of "x" ;
                                              b = "y-intercept" (or, more precisely; the value
                                                  of "x" in the "x-coordinate" of the point of the
                                                   "y -intercept).
__________________________________________________
    So:   Given: y = 6x - 9 ;   m = slope = 6 ;
                                             b = -9 .
__________________________________________________

Hello there! :)

This equation is written in slope-intercept form. which means we can easily idenify the slope and the y-intercept.

First of all, slope-intercept form looks like this:

y=mx+b

The letter m represents the slope, while the letter b represents the y-intercept.

Now, let's look at the values that we have.

We are given the equation of the line:

y=6x-9

We know that m is the slope; therefore, in this equation, 6 is the slope.

-9 is the y-intercept (the letter b)

Therefore, 6 is the slope and b is the y-intercept.

I hope it helps you. Let me know if you have any queries.

~A smiley teen

[tex]MagicalNature[/tex] here to help

A ball is thrown from 4 feet off the ground with a vertical velocity of 30 feet per second.
Is the ball at its maximum height after 1 second? In two or more complete sentences, explain how you know whether or not the ball is at its maximum height.

Answers

A ball is at it maximum height when its velocity is zero. y = 4+30t - 16t^2 is the formula, where
V = V(0) -32t
0 = 30- 32t
t = 15/16 seconds when its velocity is zero.
It is not at its maximum height but is falling.

PLZ ASAP, I NEED HELP ASAP
When 8668/25+4141/9-5533/25 is computed and written as a mixed number in simplest form, what is the fractional part of the mixed number, plz give the right answer

Thanks

Answers

I won't give you the answer because I am sure you are capable of finding it yourself once given a push, but what I would do is simplify all of the numbers into a mixed fraction (a b/c) and then go from there. Don't subtract the two numbers with the denominator of 25 first because they goes against PEMDAS. Change all of the fractions so they have like denominators, and once you solve it, just write the fraction part of the answer (b/c). If you have any other questions, just ask.

0.9×10-1 in Standard notation

Answers

[tex]0.9*10^{-1}= \cfrac{0.9}{10}=0.09 [/tex]

0.9×1/10
0.9/10 =0.09
when a number has a 0 power then u have to flip over the number and change the power to positive

When the outliers are removed, how does the mean change?
The mean remains the same.

The mean decreases by 2.

The mean increases by 2.

There are no outliers.

Answers

Q1 = (19 + 20)2 = 19.5
Q2 = 26
Q3 = (32 + 33)/2 = 32.5
IQR = 32.5 - 19.5 = 13
13 * 1.5 = 19.5

outliers are : 19.5 - 19.5 = 0...anything below 0
32.5 + 19.5 = 52...anything above 52

there are no outliers <====

evaluate the summation of 2n+5 from n=1 to 12

29
36
216
432

Answers

[tex]\bf \sum\limits_{n=1}^{12}\ 2n+5\implies \sum\limits_{n=1}^{12}\ 2n+\sum\limits_{n=1}^{12}\ 5\implies 2\sum\limits_{n=1}^{12}\ n+\sum\limits_{n=1}^{12}\ 5 \\\\\\ 2\cdot \cfrac{12(12+1)}{2}+(12\cdot 5)\implies 156+60\implies 216[/tex]

Where can the perpendicular bisectors of the sides of a right triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle

A. I only
B. II only
C. I or II only
D. I, II, or II

please show your work

Answers

It is B because, I drew a diagram of 2 right triangles, and used my protractor so I won't get an inaccurate answer.

What is the sum of 12 and the quantity 8 times a number k is equal to 48? It was on my math homework, it hardly makes any sence to me, please help me, whats the answer?

Answers

Final answer:

The question is asking for the solution to the algebraic problem 12 + 8k = 48. By isolating 'k', it is found that the value of 'k' is 4.5.

Explanation:

The problem presented here belongs to the branch of algebra. It is showing a relationship between the sum, multiplication, and is presented in a typical algebraic equation format. Let's break it down:

The sum of 12 and a number (which is 8 times k) is equal to 48. This can be written in equation form as:

12 + 8k = 48

To find the value of k, we need to isolate 'k' in the equation. First, subtract 12 from both sides of the equation:

8k = 48 - 12

Then, simplify the right side:

8k = 36

Finally, divide both sides by 8 to solve for k:

k = 36 / 8

So, k = 4.5.

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the binomial expansion of (x + y^2)^2 is

Answers

Express this as two expressions:
[tex](x+y^2)(x+y^2)[/tex]
Distribute,
[tex]x^2 + xy^2 + xy^2 + y^4[/tex]
And now simplify:
[tex]x^2 + 2xy^2 + y^4[/tex]

Answer:

[tex]x^{2}+y^{4}+2xy^{2}[/tex]

Step-by-step explanation:

The given expression is (x + y²)² and we have to simplify it to find the binomial expansion.

(x + y²)² is in the form of (a + b)².

When we expand (a + b)² we get the binomial expression

(a + b)² = a² + b² + 2ab

Now we put the value of a = x and b = y²

(x + y²)² = x² + (y²)² + 2(x)(y²)

= [tex]x^{2}+y^{4}+2xy^{2}[/tex]

Therefore answer is [tex]x^{2}+y^{4}+2xy^{2}[/tex]

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