yis inversely proportional to the square of x.

A table of values for x and y is shown.

a) Express y in terms of x.
b) Work out the positive value of x when y = 25

Answers

Answer 1

Answer:

(a) [tex]y = \frac{4}{x^2}[/tex]

(b) [tex]x = \frac{2}{5}[/tex]

Step-by-step explanation:

Given

Variation: Inverse proportional.

This is represented as:

[tex]y\ \alpha\ \frac{1}{x^2}[/tex]

See attachment for table

Solving (a):

First convert variation to equation

[tex]y = k\frac{1}{x^2}[/tex]

From the table:

[tex](x,y) = (1,4)[/tex]

So, we have:

[tex]4 = k * \frac{1}{1^2}[/tex]

[tex]4 = k * \frac{1}{1}[/tex]

[tex]4 = k * 1[/tex]

[tex]4 = k[/tex]

[tex]k = 4[/tex]

Substitute 4 for k in [tex]y = k\frac{1}{x^2}[/tex]

[tex]y = 4 * \frac{1}{x^2}[/tex]

[tex]y = \frac{4}{x^2}[/tex]

Solving (b): x when y = 25.

Substitute 25 for y in [tex]y = \frac{4}{x^2}[/tex]

[tex]25 = \frac{4}{x^2}[/tex]

Cross Multiply

[tex]25 * x^2 = 4[/tex]

Divide through by 25

[tex]x^2 = \frac{4}{25}[/tex]

Take positive square roots of both sides

[tex]x = \sqrt{\frac{4}{25}[/tex]

[tex]x = \frac{2}{5}[/tex]

Yis Inversely Proportional To The Square Of X.A Table Of Values For X And Y Is Shown.a) Express Y In

Related Questions

For what value of q is the equation -13(9 + 4) = 79 + 16 true?

Answers

Answer:

False, because the left side (-169), is not equal to the right side (95).

False






0w0 thank for tge points

Find values of x and y
someone help me plz!!!!

Answers

Answer:

Y=30

X=40

Step-by-step explanation:

for Y is because 46-16=30

for X is because 180÷3=60

80+60=140

180-140=40

27 is smaller than 5 times a number increased by 7​

Answers

Answer:

4

Step-by-step explanation:

this means that 5x+7=27

subtract 7 from both sides

5x=20

x=4

Can you please put thank you since you already got the answer please I need points

What is the term-to-term rule for this sequence?
64, 32, 16, 8,4​

Answers

Answer:

Divide previous term by 2

Step-by-step explanation:

Have a nice day :)

Answer:

every number is getting half one by one

Step-by-step explanation:

means getting divided by 2

have a cheerful day

PLEASE HELP!!!!!
A beach toy in the shape of a pyramid has a rectangular base with dimensions of 4 inches by 12 inches. The height of the rectangular pyramid is 10 inches. Sand fills half the volume of the beach toy. How many more cubic inches of sand is needed to finish filling the beach toy? Enter your answer in the box. ____in3

Answers

Answer:

80in3

Step-by-step explanation:

12 x 4 = 48

48 / 2 = 24

24 x 10 =240

240 / 3 = 80

           So your answer is 80in3

Answer: 80in

Step-by-step explanation:

PLEASE HELP ASAP, I ONLY HAVE AN HOUR!!!!!!!! HURRY!!!!!!!!!



If the sum of five consecutive odd integers is 405, what is the smallest of the five integers?

Answers

65 as smallest odd number possible.

14 less then 3 times a number is 31 written out and solved

Answers

Answer:

3x-14=31 ,= 15

Step-by-step explanation:

3x= 45

x= 45/3

x= 15

hope it helps

On average, Haley is able to read 4 5/6 Chapters in the her book each week . How many weeks will it take Haley to read 9 2/3 Chapters

Answers

Answer:

2 weeks

Step-by-step explanation:

y = mx + b

y = total number of chapters read = [tex]9\frac{2}{3}[/tex]

m = number of chapters read per week = [tex]4\frac{5}{6}[/tex]

x = number of weeks = what we're solving for

b is not needed to find this solution

[tex]9\frac{2}{3}[/tex] = [tex]4\frac{5}{6}[/tex] x                            divide [tex]4\frac{5}{6}[/tex] from both sides

x = 2 weeks

Which factor could be multiplied by the given function so that their product causes the graph of f(x) to decrease as x approaches negative infinity?

[tex]f(x)=(2x^2 + 5)(x - 7)[/tex]

Select all that apply.

• -3
• 0.2x
• 5x²
• [tex]-\frac{1}{2}(x + 8)[/tex]
• 4(2x - 7)

Answers

Answer:

5x²

-1/2( x+8)

Step-by-step explanation:

The dominant term is 2x^2 *x or 2x^3

We want to know what happens when x goes to negative ∞

2 ( -∞) ^3 → 2 * (-∞) → -∞

As long as we multiply by a positive number, we will still be approaching negative infinity ( or decreasing)

-3  is negative

.2x is negative when x approaches negative infinity

.5 x^2 = .5( -∞)^2 = 5 ( ∞) = ∞ which is positive

-1/2 x is the dominant term  = -1/2(- ∞) =   ∞ which is positive

4(2x) is the dominant term  = 8(- ∞) = - ∞ which is negative

Answer:

3rd and 4th Choices.

[tex]\displaystyle 5x^2\text{ and } -\frac{1}{2}(x+8)[/tex]

Step-by-step explanation:

We are given the function:

[tex]f(x)=(2x^2+5)(x-7)[/tex]

And we want to determine the factor(s) that we can multiply to the above function that will cause the graph of f to decrease as x approaches negative infinity.

We can see that the dominant term will be:

[tex]2x^2(x)=2x^3[/tex]

Thus:

[tex]2(-\infty)^3\Rightarrow -\infty[/tex]

It is already decreasing (shifting towards negative infinity) as x approaches negative infinity.

In order to preserve this, then, the factors must be positive as x approaches negative infinity.

The first factor is -3.

-3 is always negative, so it will make f increase.

The second factor is [tex]0.2x[/tex].

[tex]0.2(-\infty)\Rightarrow -\infty[/tex]

This will also make f increase.

The third factor is:

[tex]5(\infty)^2\Rightarrow \infty[/tex]

This is positive, so it will allow f to remain decreasing as x approaches negative infinity.

The fourth factor is:

[tex]\displaystyle -\frac{1}{2}(-\infty+8)\Rightarrow -\frac{1}{2}(-\infty)\Rightarrow \infty[/tex]

This is also positive, so it will also allow f to remain decreasing.

Lastly, the fifth factor is:

[tex]4(2(-\infty)-7)\Rightarrow 4(-\infty)\Rightarrow -\infty[/tex]

This is negative, so it will make f increasing.

Therefore, our answers are the third and fourth choices.  

What is tan K? help pleasee

Answers

8/15

Hope this helps!

Answer:

[tex]\frac{8}{15}[/tex]

Step-by-step explanation:

[tex]Tan(k)=\frac{24}{45} =\frac{8}{15}[/tex]

I really need help I will give brainliest

Answers

Answer:

64 degrees

Step-by-step explanation:

All angles in a triangle plus each other equals 180. First find the missing angle of the triangle with 2 given angles. The missing angle is 64 degrees because 68 plus 48 is 116 and 180 - 116 is 64. Vertical angles are always congruent and the missing angle is vertical to the missing angle on the first triangle.

f(x) = -2x + 2
g(x) = 3x^2– 3x
Find f (4) and g(-3)
helpp please i would appreciate it

Answers

Answer:

f(4) = -6, g(-3) = 36

Step-by-step explanation:

To find f(#) or g(#), plug the number into each x of the equation.

f(x) = -2x + 2

f(4) = -2(4) + 2

Simplify the parentheses by multiplying.

f(4) = -8 + 2

Add.

f(4) = -6

g(x) = 3x² - 3x

g(-3) = 3(-3)² - 3(-3)

Simplify the exponent first.

g(-3) = 3(9) - 3(-3)

Simplify the parentheses by multiplying.

g(-3) = 27 + 9

Add.

g(-3) = 36

2) f(x) = x2 - 6x +11
Degree:
Lead Coefficient:
End behavior:

Answers

Answer:

13 - 6 x

Step-by-step explanation:

How many times smaller will a number become if is it decreased by 20%?

Answers

Answer:

Step-by-step explanation:

I'm unsure why my answer was deleted, randomly deleted a thoroughly explained answer.

20% is 20/100, 1/5, or 0.2

The number will decrease by a factor of 5.

Answer:1.25

Step-by-step explanation: for example 100 decreased by 20 percent is 80 so 100 divided by 80 is 1.25

Odette solved this problem:

A piggy bank has nickles and dimes totaling $1.15. If the bank contains exactly 15
coins, how many of each coin are in the bank?

Complete the statement about Odette's solution.

Answers

Answer:

In Odette's solution, 7 is the number of

nickels and 8 is the number of dimes

(WILL GIVE BRAINLIEST PLS HELP) Marco is saving for tuition costs at a state university. He deposited $8500 in a 4-year certificate of deposit that earns 7.25% per year. What equation represents this scenario?
f(x)=4*7.25^x
f(x)=8500*4^x
f(x)=1.0725*8500^x
f(x)=8500*1.0725^x

Answers

Answer:

($8500)(0.0725)(4)

The expression f(x) = 8500*0.0725*x  represents the b best scenario. None of them are correct.

Equation that fit the scenario of He deposited $8500 in a 4-year certificate of deposit that earns 7.25% per year, to determine.

What is equation?

Equation are link of variables that contain equal sign.

Here,
He deposited $8500 in a 4-year certificate,
f(x) = 8500
Earns 7.25% per year,
f(x) = 8500*0.0725*4

Thus, the expression f(x) = 8500*0.0725*x  represents the b best scenario.

Learn more about equation here:
https://brainly.com/question/10413253

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3x - 2 y = 10 and 7 x + 2 y = 30

Answers

Answer:

Your answer is (4,1)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Hoped this helped!

brainly, please?

Will mark brainliest for correct answer, due soon!

Answers

circumference = pi*d

70cm*pi = 219.8cm

219.8cm × 240 rev = 52752 cm

52752cm/100 = 528m

PLZ HELP!!
What is the ratio of a:b, knowing that a-b/a+b=3/5

Answers

Answer:

1 : 4

Step-by-step explanation:

5(a - b) = 3(a + b) = 5a - 5b = 3a + 3b

2a - 5b = 3b

2a = 8b

2/8 is 1/4 simplified

please help !!!! The leg of a right triangle is 2 units and the hypotenuse is 5 units. What is the length, in units, of the other leg of the triangle?
3

Square root of 29

Square root of 21

7

Answers

Answer:

[tex]\sqrt{21}[/tex]

Step-by-step explanation:

Use the pythagorean theoreom, a^2+b^2=c^2.

We know the hypontenuse and one of the sdes

a^2+2^2=5^2

a^2+4=25

subract four from both sides to isolate variable

a^2=21

square root both sides and you have the answer of sq root 21!

Edit: the answer for your next question is the last one b/c it satisfies the Pythagorean Theorem

Which expression shows -5 3/5+9 1/5 as the sum of integer and fractional parts?

Answers

Answer:

-5 + 9 + (-3/5) + 1/5

Step-by-step explanation:

Find the measure of Angel 1 and 2.

Answers

You could use a ruler maybe or is it not that kind of question

BRAINLIEST AND ALSO 40 POINTS!!!!

Answers

Answer:

WOAH Sapnap!

Step-by-step explanation:

Conduct a Pareto analysis for the number of minutes that flights are late in the accompanying data. Interpret the results. LOADING... Click the icon to view the Atlanta Airline Data. Conduct a Pareto analysis for the number of minutes that flights are late. 15127137130.3074601124.053619303 192644911620.5010780515.163538874 192426514270.6153514455.158176944

Answers

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Please find the attached file for the solution:

20% of flights accounted for nearly 70 to 80% of delayed minutes.

A taxi driver had 31 fares to and from the airport last Monday. The price for a ride to the airport is $4.50, and the price for a ride from the airport is $11. The driver collected a total of $289 for the day.

Answers

Answer:

(8,23)

Step-by-step explanation:

x+y=31

4.5x + 11y = 289

x = 31 -y

4.5(31 - y) + 11y = 289

139.5 - 4.5y + 11y = 289

6.5y = 149.5

y = 23

x = 31 - 23 = 8

The ordered pair, (x, y) = (8, 23).

What is an ordered pair?

An ordered pair exists as a composition of the x coordinate (abscissa) and the y coordinate (ordinate), containing two values noted in a fixed order within parentheses.

Given: A taxi driver had 31 fares to and from the airport last Monday. The price for a ride to the airport exists $4.50, and the price for a ride from the airport exists $11. The driver collected a total of $289 for the day.

x + y = 31........(1)

4.5x + 11y = 289 ........(2)

From (1), we get

x + y = 31

x = 31 - y

Substitute the value of x in (2), and we get

4.5x + 11y = 289

4.5(31 - y) + 11y = 289

Simplifying the above equation, we get

139.5 - 4.5y + 11y = 289

6.5y = 149.5

y = 23

substitute the value of y, in (1) then we get

x = 31 - y

x = 31 - 23 = 8

The value of x = 8 and y = 23.

Therefore, the ordered pair, (x, y) = (8, 23).

Complete question

A taxi driver had 31 fares to and from the airport last Monday. The price for a ride to the airport is $4.50, and the price for a ride from the airport is $11. The driver collected a total of $289 for the day. Let 2 represent the number of trips to the airport and y represent the number of trips from the airport. Write the ordered pair, (x, y) that represents the situation.

What slope Line

pass through( 14, 4)( 21, 6 )

Answers

Answer:

2/7

Step-by-step explanation:

Slope of the line

[tex] = \frac{6 - 4}{21 - 14} \\ \\ = \frac{2}{7} [/tex]

14 n 477692 jansksnd sj asks s

A Solve the
1. The total number of books which were borrowed from a library from Monday to Sunday can be
modelled by the function F(x) = 200x + 542x² + 179x + 1605 and the number of visitors to the
library from Monday to Sunday can be modelled by G(x) = 100x + 321, where x is the number of
days since Monday Which of the following expressions correctly describes the average number of
books per visitor?​

Answers

Answer:

?

Step-by-step explanation:

13 as prime or composite

Answers

Answer:

prime

gggghfsssddfdfv ut b dc t

Answer:

the number 13 is a prime number

Maliki is building a ramp with a base of 4 feet and a vertical height of 2 feet. What is the length of the ramp?

Answers

Answer:

2√5

Step-by-step explanation:

By applying Pythagoras (hypotenuse)^2=(Base)^2 +(Height)^2

The length of the ramp is approximately 4.47 feet.

What is the Pythagorean theorem?

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

If the base of the ramp is 4 feet and the vertical height is 2 feet, we can use the Pythagorean theorem to find the length of the ramp:

ramp length² = base² + height²

ramp length² = 4² + 2²

ramp length² = 16 + 4

ramp length² = 20

Taking the square root of both sides, we get:

ramp length = √20

Simplifying the square root of 20, we get:

ramp length ≈ 4.47 feet

Therefore, the length of the ramp is approximately 4.47 feet.

Learn more about Pythagoras's theorem here:

brainly.com/question/343682

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The letters of "BEARS" should be evenly spaced across a 60-inch-wide banner, with no margins. Each letter is 8 inches wide. How many inches (x) should exist between each pair of letters? ​

Answers

Answer:

The answer is 10 inches, because first we multiply the letters and how wide they are then subtract that from 60 then divide that by our spaces (4)

Step-by-step explanation:

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