The variables x and y are inversely proportional, and y = 2 when x = 3. What is the value of y when x = 9?

Answers

Answer 1

Answer: $If\ x\ and\ y\ are\ inversely\ proportional\ then\ xy\ is\ constans.\n\n9y=2* 3\n\n9y=6\ \ \ \ \ \ /:9\n\ny=(6)/(9)\n\ny=(2)/(3)$

Answer 2

Answer: y=k/x
2=k/3
k=6
y=6/x
y=6/9=2/3

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How do you factor x squared plus 3x

Compute the sales tax on the following transactions. An article retails for $38.50. The city sales tax is 4%, and the federal excise tax is 7%. How much is the total tax? A. 1.54 B. 2.70
C. 4.24
D. 34.26

Answers

The answer is C) 4.24

4% + 7% = 11%

to get 11% of 38.50 you move the decimal two spaces to the left on the percent and multiply that number by the other number.

11% ---> .11

38.50 x .11= 4.24.

I hope this answer gave you a better understanding on how to work with percentages! :) Have a good day :)

What is the line symmetry for the graph of y= -3x^2+12x-11

Answers

Answer:

The line of symmetry is x=2

Step-by-step explanation:

Given: $y=-3x^2+12x-11$

We are given a quadratic equation and to find the line of symmetry.

As we know the line of symmetry of parabola passes through the x value of vertex.

If vertex of parabola is (h,k) then equation of line of symmetry x=h

So, first we find the vertex of parabola.

For equation: $y=ax^2+bx+c$

$x=-(b)/(2a)$

For given equation, a=-3 and b=12

Therefore, $x=-(12)/(2(-3))$

$x=2$

Hence, The line of symmetry of given parabola is x=2

The answer to your question is x=2. what you want to do is find both the x values for your quadratic equation and then add them and divide by 2.

If the hypotenuse of a right triangle is 2 cm and one leg is √ 3 cm, the exact length of the other leg is _______ cm. A. √ 3
B. 1
C. 3
D. 4

Answers

Answer:

The length of the other leg is 1 cm.

Step-by-step explanation:

By using the pythagorean theorem

Hypotenuse² = Perpendicular² + Base²

As given

If the hypotenuse of a right triangle is 2 cm and one leg is √ 3 cm.

Let us assume that the unknown length be x.

Thus

2² = Perpendicular² + Base²

$4^(2)= (√(3))^(2) + x^(2)$

$(√(3))^(2) = 3$

4 = 3 + x²

x² = 4 -3

$x = √(1)$

x = 1 cm

Therefore the length of the other leg is 1 cm.

The exact length of the other leg is B. 1 cm.

What are the values of a, b, and c in the quadratic equation –2x^2 + 4x – 3 = 0?a = 2, b = 4, c = 3

a = 2, b = 4, c = –3

a = –2, b = 4, c = 3

a = –2, b = 4, c = – 3

Answers

If you would like to find the values of a, b, and c in the quadratic equation, you can do this using the following steps:

ax^2 + bx + c = 0
-2x^2 + 4x - 3 = 0
a = -2
b = 4
c = -3

The correct result would be a = –2, b = 4, c = – 3.

Final answer:

The values of a, b, and c in the quadratic equation –2x^2 + 4x – 3 = 0 are: a = -2, b = 4, and c = -3.

Explanation:

The values of a, b, and c in the quadratic equation –2x^2 + 4x – 3 = 0 are:

a = -2

b = 4

c = -3

In a quadratic equation in the form ax^2 + bx + c = 0, the coefficients a, b, and c represent different values. In this equation, -2 is the coefficient of the x^2 term, 4 is the coefficient of the x term, and -3 is the constant term.

Learn more about Quadratic Equations here:

brainly.com/question/30098550

#SPJ12

Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Clare doesn't touch the money in her account, she can find the amount she'll have the next year by multiplying her current amount by 1.03. How much will she have in 30 years

Answers

Answer:

$388.36

Step-by-step explanation:

let us assume that the amount in her accounts compounds annually

Given data

principal p= $160

interest rate r= 3%= 0.03

time t= 30 years

At the end of 30 years the money she will will have can be expressed as

A= P(1+r)^t

A= 160(1+0.03)^30

A= 160(1.03)^30

A= 160*2.42726

A= $388.36

in 30 years she will have $388.36

Refer to the figure and find the volume V generated by rotating the given region about the specified line.R3 about AB

Answers

Answer:

Hence, volume is: $(34\pi)/(45)$ cubic units.

Step-by-step explanation:

We will first express our our equation of the curve and the line bounded by the region in terms of the variable y.

i.e. the curve is re $x=(1)/(16)y^4$

and the line is given as: $x=(1)/(2)y$

Since after rotating the given region $R_(3)$ about the line AB.

we see that for the following graph

the axis is located at x=1.

and the outer radius(R) is: $(1)/(16)y^4$

and the inner radius(r) is: $(1)/(2)y$

Now, the area of the graph= area of the disc.

Area of graph= $\pi(R^2-r^2)$

Now the volume is given as:

$Volume=\int\limits^2_0 {Area} \, dy$

On calculating we get:

Volume= $(34\pi)/(45)$ cubic units.

The volume V generated by rotating the given region about the specified line R3 about AB is $\boxed{\frac{{34\pi }}{{45}}{\text{ uni}}{{\text{t}}^3}}.$

Further explanation:

Given:

The coordinates of point A is $\left( {1,0} \right).$

The coordinates of point B is $\left( {1,2} \right).$

The coordinate of point C is $\left( {0,2} \right).$

The value of y is $y = 2\sqrt[4]{x}.$

Explanation:

The equation of the curve is $y = 2\sqrt[4]{x}.$

Solve the above equation to obtain the value of x in terms of y.

$\begin{aligned}{\left( y \right)^4}&={\left( {2\sqrt[4]{x}} \right)^4} \n{y^4}&=16x\n\frac{1}{{16}}{y^4}&= x\n\end{aligned}$

The equation of the line is $x = (1)/(2)y.$

After rotating the region ${R_3}$ is about the line AB.

From the graph the inner radius is ${{r_2} = (1)/(2)y$ and the outer radius is ${{r_1}=\frac{1}{{16}}{y^4}.$

${\text{Area of graph}}=\pi\left( {{r_1}^2 - {r_2}^2} \right)$

$Area = \pi\left( {{{\left({\frac{1}{{16}}{y^4}} \right)}^2} - {{\left({(1)/(2)y} \right)}^2}}\right)$

The volume can be obtained as follows,

$\begin{aligned}{\text{Volume}}&=\int\limits_0^2 {Area{\text{ }}dy}\n&=\int\limits_0^2{\pi \left( {{{\left({\frac{1}{{16}}{y^4}} \right)}^2} - {{\left( {(1)/(2)y} \right)}^2}} \right){\text{ }}dy}\n&= \pi \int\limits_0^2 {\left( {\frac{1}{{256}}{y^8} - (1)/(4){y^2}} \right){\text{ }}dy}\n\end{aligned}$

Further solve the above equation.

$\begin{aligned}{\text{Volume}}&=\pi \left[ {\int\limits_0^2 {\frac{1}{{256}}{y^8}dy - } \int\limits_0^2{(1)/(4){y^2}{\text{ }}dy} } \right]\n&= \frac{{34\pi }}{{45}}\n\end{aligned}$

The volume V generated by rotating the given region about the specified line R3 about AB is $\boxed{\frac{{34\pi }}{{45}}{\text{ uni}}{{\text{t}}^3}}.$

Learn more:

1. Learn more about inverse of the functionbrainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Volume of the curves

Keywords: area, volume of the region, rotating, generated, specified line, R3, AB, rotating region.

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