If x varies inversely as the square of y and if x=3 when y=-1, what is the value of x when y =3

Answers

Answer 1

Answer:

[tex]x[/tex] would be [tex](1/3)[/tex] when [tex]y = 3[/tex].

Step-by-step explanation:

The question states that [tex]x[/tex] varies "inversely" as [tex]y^2[/tex]. In other words, there is a non-zero number [tex]a[/tex] (a constant) such that:

[tex]\displaystyle x = \frac{a}{y^2}[/tex].

The challenging part is to find the value of [tex]a[/tex] in this equation.

Given that [tex]x = 3[/tex] when [tex]y = -1[/tex], replace the [tex]x[/tex] in this equation with [tex]3[/tex] and [tex]y[/tex] with [tex](-1)[/tex]. This equation should still be valid:

[tex]\displaystyle 3 = \frac{a}{(-1)^{2}}[/tex].

Solve for [tex]a[/tex]:

[tex]a = 3 \times (-1)^2 = 3[/tex].

Hence, the relation between [tex]x[/tex] and [tex]y[/tex] becomes:

[tex]\displaystyle x = \frac{3}{y^2}[/tex].

Find the value of [tex]x[/tex] when [tex]y = 3[/tex] by replacing the [tex]y[/tex] in this equation with [tex]3[/tex].

[tex]\displaystyle x = \frac{3}{3^2} = \frac{1}{3}[/tex].

In other words, the value of [tex]x[/tex] would be [tex]\displaystyle \frac{1}{3}[/tex] when [tex]y = 3[/tex].


Related Questions

can anyone help me please?

Answers

Answer:

yes i can help you with all the time

a 25% tip was payed on a 30$ meal what is the amount of the tip

Answers

Answer:

$7.50

Step-by-step explanation:

30 x 0.25= 7.50

the tip is 7.50 because 20% of 30 is 7.50

What effects do the values of a and b have on the graph of the linear relation y = ax + b?

Answers

a is the coefficient of x. It changes the slope of the line/the steepness. The b changes the point where the line crosses the y-axis. For instance if we had the equation y = x + 4 then the function would cross at the point (0,4)

A camera and a case cost 100 dollars. If the camera cost 90 more dollars than the case. How much does the case cost.

Answers

Answer:

Cost of case = $5

Step-by-step explanation:

x = cost of camera and y = cost of case

x = y + 90

x + y = 100

y + 90 + y = 100

2y = 10

y = 5

x = y + 90

x = 5 + 90

x = 95

Therefore, the cost of the camera is $95 and the cost of the case is $5.

The cost of case is 5 dollars.

What is the equation?

The equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Let,

Cost of camera = a and

Cost of case = b

Given that, camera and a case cost 100 dollars

a + b = 100

Since, the camera cost 90 more dollars than the case

So, a = b + 90

Substitute the value in the equation a + b = 100

b + 90 + b = 100

2b = 10

Divided by 2 both the sides

b = 5

Substitute the value of b in equation

a = b+ 90

a = 5 + 90

a = 95

So, the cost of the camera is $95 and the cost of the case is $5.

Hence, the cost of the case is 5 dollars.

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The expression 2 - x-1/x+2
is equivalent to

A. 1 - 3/x+2
B. 1 + 3/x+2
C. 1 - 1/x+2
D. 1 + 1/x+2

Answers

The answer is b I think

The expression [tex]2- \dfrac{x-1}{x+2}[/tex]  is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].

We have to find, which equation is equivalent to the given expression.

The given expression is,

[tex]= 2- \dfrac{x-1}{x+2}[/tex]

To determine the equivalent expression following all the steps given below.

Step1; Taking LCM in the equation,

                   [tex]\rm = 2-\dfrac{x-1}{x+2}\\\\= \dfrac{2(x+2) - (x-1)}{x+2}\\\\= \dfrac{2x+4-x+1}{x+2}\\\\[/tex]

Step2; Solving the equation,

                    [tex]= \dfrac{2x+4-x+1}{x+2}\\\\= \dfrac{x+5}{x+2}\\\\[/tex]

Step3; rewrite the equation in the small factors,

                    [tex]=\dfrac{x+5}{x+2}\\\\= \dfrac{x+ 2+3}{x+2}\\\\[/tex]

Step4; By using partial fraction rewrite the equation,

                    [tex]= \dfrac{x+2}{x+2} + \dfrac{3}{x+2}\\\\= 1 + \dfrac{3}{x+2}[/tex]

Hence, The expression [tex]2- \dfrac{x-1}{x+2}[/tex]  is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].

For more details refer to the link given below.

https://brainly.com/question/2264568

Help pls , will give brainliest!

Answers

Answer:  6

=======================================

Work Shown:

1 liter = 1000 mL

3 liters = 3000 mL

I multiplied both sides by 3.

Divide that result over 500 to get 3000/500 = 6

So she'll need to buy 6 cartons.

-------

You could also solve like this:

(1 carton)/(500 mL) = (x cartons)/(3000 mL)

1/500 = x/3000

1*3000 = 500*x ... cross multiply

3000 = 500x

500x = 3000

x = 3000/500 .... dividing both sides by 500

x = 6

What are the solutions of this quadratic equation? X2 − 10x = -34 A. X= -8, -2 B. X= 5 + 3i C. X= -5 + 3i D. X= -5 + square root of 59

Answers

Answer:

B. X= 5 + 3i

5 + 3i

Step-by-step explanation:

We are given the quadratic equation

x² - 10x = -34

x² - 10x + 34 = 0

Using Almighty formula

x = -b ± √b² - 4ac/2a

When given equation: ax² + bx + c

Where: a = 1, b = -10 , c = 34

x = -10 ± √-10² - 4 × 1 × 34/2 × 1

x = 10 ± √100 - 136/2

x = 10 ± √-36 /2

x = 10/2 ±. √-36/2

x = 5 ± 6i /2

x = 5 ± 3i

Hence: the roots of the equation are:

x = 5 - 3i , x = 5 + 3i

What is the value of y?
O A. 36°
O B. 72°
C. 54°
O D. 1080

Answers

sorry but can u show a picture of y?

Answer:

but where is que plz show your que

B E
400
(51)
А
C D
3t
Find the measure of ZF if mZD=88º.
A. 8°
B. 40°
C. 52°
D. 90°

Answers

the answer is c because you have to take the zf an time it by the zd

Answer:

C

Step-by-step explanation:

for the top of the triangle it has to be 40 and angle d has been declared as 88

so it is 40+88 = 128    now 180 -128 = 52 so the answer is C

Please help me. Study island is hard

Answers

Answer: 5/12

Step-by-step explanation:

13-7 = 5

16-4 = 12

A the answer is A have a nice day

What is the remainder when 19x^2+15x+12 is divided by x-2?

Answers

Answer:

118

Step-by-step explanation:


Can someone pleaseeee help and if you’re correct i’ll give brainliest

Answers

Answer:area of the circle=πr²

3.14 =3.14 ×r²

= 1

r. =1 millimeters

MARKING BRAINLIEST

PLS HELP

Answers

Answer:

25

Step-by-step explanation:

Moving it down does not change the length.

What is parallel to y=-5+4.2x

Answers

Any line that has the same slope as the given equation , 4.2

A jar contains quarters and nickels. There are 5 fewer quarters than nickels. The
total value of the coins is $4.45. Which system of equations can be used to
determine the number of quarters, q, and the number of nickels, n?

Answers

Given:

In a jar, there are 5 fewer quarters than nickels.

The total value of the coins is $4.45.

To find:

The system of equations can be used to determine the number of quarters, q, and the number of nickels, n.

Solution:

Let q be the number of quarters and n be the number of nickels.

It is given that there are 5 fewer quarters than nickels.

[tex]q=n-5[/tex]           ...(i)

We know that,

1 quarter = $0.25

1 nickel = $0.05

Using these conversions, we get

q quarters = $0.25q

n nickels = $0.05n

The total value of the coins is $4.45.

[tex]0.25q+0.05n=4.45[/tex]           ...(ii)

The equations (i) and (ii) are equations of required system of equations.

Therefore, the system of equations is:

[tex]q=n-5[/tex]  

[tex]0.25q+0.05n=4.45[/tex]

Write as a single power: (x^4)(x^10)/(x^3)^5​

Answers

X^22
Because, (x^4) (x^10) (x^3) (x^5)
= x^22 . I hope u have a great summer

The solution of the expression as a single power is X²⁹.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is (x⁴)(x¹⁰)/(x³)⁵. The equation will be solved by the property of exponents.

E = (x⁴)(x¹⁰)/(x³)⁵

Add all the powers of the same base x.

E =  (x⁴)(x¹⁰)/(x¹⁵)

E = x⁽⁴⁺¹⁰⁺¹⁵⁾

E = x²⁹

Therefore, the solution of the expression as a single power is X²⁹.

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which is a solution of the equation y=2x+8

Answers

To find the y-intercept, plug in 0 for x and you solve to get 8

y=−2x+8

y=−2(0)+8

y=0+8

y=0

To find the x-intercept, plug in 0 for y and you solve to get 4

y=−2x+8

0=−2x+8

2x=8

x=0

Step by step below in the pic

Please help. Thank you. (30 points included) (Shown work)

Answers

Answer:

True

Step-by-step explanation:

Supplementary angles are angles that add up to 180 degrees (straight line). *5 degrees + x create a straight line.

Aaron as 3 times as many sweets as Bola Aaron gives Bola 6 sweets and now he has twice as many as her new total How many sweets did they each begin with

Answers

Answer:

Aaron = 54

Bola = 18

Step-by-step explanation:

Let

[tex]A \to Aaron[/tex]

[tex]B \to Bola[/tex]

From the first statement, we have:

[tex]A = 3B[/tex]

After given Bola 6 sweets,

[tex]A - 6 = 2(B + 6)[/tex]

Required

The initial number of sweets each has

Substitute [tex]A = 3B[/tex] in [tex]A - 6 = 2(B + 6)[/tex]

[tex]3B - 6 = 2(B + 6)[/tex]

Open bracket

[tex]3B - 6 = 2B + 12[/tex]

Collect like terms

[tex]3B -2B = 12+6[/tex]

[tex]B = 18[/tex]

Substitute [tex]B = 18[/tex] in [tex]A = 3B[/tex]

[tex]A = 3 * 18[/tex]

[tex]A = 54[/tex]

What is the measure of arc XZ?​

Answers

ohh dear u still have school i have a holiday for two months

Please help me, please and thank you it would mean a lot.

Answers

Hey! 576 feet of lacquer will be needed to cover the floor. I know this because the formula to find this shape is base * night and 12 * 48 is 576.

For the next question the answer is that she needs 120 ft.

This confuses me a little because it keeps saying like “will the person have enough” but it does not say what the number is. I might be wrong for the second one and I am sorry if I am. Have a great summer!!!!

Which equation does not describe a linear function?
y = 7
y = 2x2 – 5
2y = 3x - 9
4x – 6y = 13

Answers

Answer:

The second option

Step-by-step explanation:

All the other choices can be graphed as straight lines, but only the second option is a parabola

Answer:

y = 2x² – 5

Step-by-step explanation:

y = 2x² – 5 is not lineal function since x is raises to an exponent.

4,570= 3thousands+___hundreds+ 7 tens

Answers

Answer: 4 thousands, 5 hundreds, 7 tens

Step-by-step explanation: 4,570 is pretty easy to break down. The first place value is 0 so nothing for that. As you have it there the tens place values has 7. Next is hundreds and there's a 5 there so 5 hundreds. If the number is 4,570 then it should be 4 thousands not three.

Solve the given portion 4/x=3/6 x=?

Answers

Answer:

8

Step-by-step explanation:

4/x=3/6

4=3/6x

4*6=3x

24/3=x

8=x

Please mark me as brainliest

It is a because it is half with the 3/6 so the what is double 4 so it is 8

Please answer properly.

Answers

Answer:

1) [tex]b=6[/tex]

2) [tex]m=4[/tex]

3) [tex]p=12[/tex]

4) [tex]x=-1\frac{2}{6}[/tex]

Step-by-step explanation:

[tex]b+6=12[/tex]

subtract 6 from both sides

[tex]b=6[/tex]

---------->>>>

[tex]9m=32+4[/tex]

combine like terms

[tex]9m=36[/tex]

divide both sides by 9

[tex]m=4[/tex]

---------->>>>

[tex]21=p+9[/tex]

Subtract 9 from both sides

[tex]12 = p[/tex]

---------->>>>

[tex](10+5)+3x=0[/tex]

Add within the parenthesis

[tex]5+3x=0[/tex]

subtract 5 from both sides

[tex]3x=-5[/tex]

divide both sides by 3

[tex]x=-1\frac{2}{6}[/tex]

Hope this is helpful to you.

For the function y = -2x + 4, the input is 3. What is the output?​

Answers

Answer:

The output is -2 when the input is 3.

Step-by-step explanation:

You're actually being asked to evaluate y = -2x + 4 at x = 3.  x is the 'input' and y is the 'output.'

At x = 3, y = -2(3) + 4 = -2

The output is -2 when the input is 3.

Question 1:

Solve this system of equations using any method.

4x – y = 5
3x + y = 16

a. (3, 5)

b. (4, 11)

c. (4, 4)

d. (3, 7)

Question 2:

Solve the following system of equations.

d + e = 6
d – e = 4

a. no solution

b. (5, 1)

c. (3, –1)

d. infinite number of solutions

Question 3:

Solve the following system of equations by linear combination:

4x + 3y = 12
y = x – 10

a. (3, –7)

b. (6, –4)

c. (–7, 3)

d. (–4, 6)

Answers

Answer:

Question 1: d. (3, 7)

Question 2: b. (5, 1)

Question 3: b. (6, –4)

Step-by-step explanation:

Question 1:

Solve this system of equations using any method.

4x – y = 5

3x + y = 16

Add the equations.

7x = 21

x = 3

4(3) - y = 5

-y = -7

y = 7

d. (3, 7)

Question 2:

Solve the following system of equations.

d + e = 6

d – e = 4

Add the equations.

2d = 10

d = 5

5 + e = 6

e = 1

b. (5, 1)

Question 3:

Solve the following system of equations by linear combination:

4x + 3y = 12

y = x – 10

4x + 3y = 12

-x + y = -10

Multiply the second equation by 4 and add to the first equation.

          4x + 3y = 12

(+)      -4x + 4y = -40

----------------------------

                  7y = -28

y = -4

-4 = x - 10

x = 6

b. (6, –4)

the top says for the first box : Part A Explain how Mrs. Soto could apply the
following theorem to the problem of restoring
the gate to its original rectangular shape.

Answers

Answer:

The given theorem proves that the door is not a rectangle right now since, the door came out of shape, it can be proved by the Pythagorean theorem. If the length is set to a certain shape, and the width is set to a certain shape, and drawn to diagonals. If solved by the Pythagorean Theorem, if the length of two diagonals are similar then and only then the door would be a rectangle.

Hope this helps!

Owen bought 4 pizzas for a class party. If each person ate 1/5 of a pizza, how many people could be served? Division and multiplecation please right the correct equation.

Answers

9514 1404 393

Answer:

  20 people

Step-by-step explanation:

Let n represent the number of people served. If each ate 1/5 of a pizza and there are 4 pizzas, we have ...

  (1/5)·n = 4

The solution can be found by multiplying both sides of the equation by 5.

  5(1/5)n = 5(4)

  n = 20

20 people could be served.

Given the points Q(-3, -4) and R(2, 0), find the coordinates of the point P on directed line segment QR that partitions segment QR such that the ratio of QP to PR is 2

Answers

Step-by-step explanation:

the answer in photo above

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