54 sq. Ft. Rectangle 9 ft. Lenght what is width

Suppose that x and y vary inversely and that y=1/6 when x=3. Write a function that models the inverse variation and find y when

juin [17]

Answer:

The Inverse variation states a relationship between the two variable in which the product is constant.

i.e $x \propto \frac{1}{y}$

then the equation is of the form: $xy = k$ where k is the constant of variation.

As per the given information: It is given that x and y vary inversely and that y = 1/6 when x = 3.

then, by definition of inverse variation;

xy = k ......[1]

Substitute the given values we have;

$3 \cdot \frac{1}{6} = k$

$\frac{1}{2} = k$

Now, find the value of y when x = 10.

Substitute the given values of x=10 and k = 1/2, in [1] we have;

$10y = \frac{1}{2}$

Divide both sides by 10 we get;

$y = \frac{1}{20}$

therefore, a function that models the inverse variation is; $xy = \frac{1}{2}$ and value of $y = \frac{1}{20}$ when x = 10.

4 0

4 years ago

Read 2 more answers

the sum of the digits of two digit number is 10. when 18 is added to the number is digit reversed find and number

Contact [7]

Answer:

The number is 46

Step-by-step explanation:

Equations

Suppose:

a = One digit of the number

b = Tens digit of the number

The sum of the digits is 10:

a + b = 10

The number expressed as two-digits quantity is ab, and its value is

10a+b

When we add 18 to that number, we have:

10a+b+18

And that is represented as the number reversed:

10a+b+18=10b+a

Simplifying:

9a+18=9b

Dividing by 9:

a + 2 = b

Substituting in the first equation:

a + a + 2 = 10

2a = 8

a = 4

b = a + 2 = 6

Thus the number is 46

4 0

3 years ago

What is the HCF of 3000 and 525 answer with process

yan [13]

Answer:

The HCF is 75

Step-by-step explanation:

Here, we want to get the highest common factors of the two numbers

To do this, we have to write the numbers as the product of their prime factors

We have;

3,000 = 2 * 2 * 2 * 3 * 5 * 5 * 5

525 = 3 * 5 * 5 * 7

now looking at this, we can see that in both numbers, we can have 3 * 5 * 5 taken out as it is common to both numbers

This represents the highest common factor of the two numbers

and that is 75

8 0

3 years ago

What’s the Area of the kite?

maria [59]

Answer:

54 m^2

Step-by-step explanation:

Area of a kite is the two diagonals multiplied and then divided by 2.

3+3=6

12+6=18

18(6)=108

108/2=54

Therefore, 54 m^2

I hope this helped and have a good rest of your day!

5 0

3 years ago

Plssssssssssssssssssss Answer this is Major?

julsineya [31]

Answer:

See below because there are 9 parts (A through I)

Explanation:

Part A: write an equation that models the area of the figure. Let y represent the area, and write your answer in the form y = ax2 + bx + c.

The figure shows a rectangular table with these dimensions:

Length: - x + 64
Witdth: x + 4

The area of a rectangle is width × length:

$(x + 4)\times (-x+64)$

Use distributive property:

$x\cdot (-x)+x\cdot(64)+4\cdot (-x)+4\cdot (64)=-x^2+64x-4x+256$

Simplify:

$-x^2+64x-4x+256=-x^2+60x+256$

Part B. Graph the equation you wrote in part A. Adjust the zoom of the graphing window so the vertex, x-intercepts, and y-intercept can be seen.

1. Factor the equation:

Common factor - 1:

$-x^2+60x+256=-(x^2-60x-256)$

Find two numbers that add - 60 and whose product is -256. Theyb are -64 and + 4

$-(x-64)(x+4)$

2. Find the roots:

Equal the expression to zero:

$-(x-64)(x+4)=0\\ \\ x-64=0\implies x=64\\ \\ x+4=0\implies x=-4$

Those are the x-intercepts: (-4,0) and (64,0)

3. Find the symmetry axis:

The simmetry axis is the line x = the middle value between the two roots:

$x=(64-4)/2=60/2=30$

4. Find the vertex

The vertex has x-coordinate equal to the x axis (30 in this case).

Substitute in the equation of find the y-coordinate:

$y=-(30-64)(30+4)=-(-34)(34)=1,156$

Hence, the vertex is (30, 1,156)

5. Find the y-intercept

Make x = 0

$y=-(x^2-60x-256)=-(0-256)=256$

Hence, the y-intercept is (0, 256)

With the x-incercepts, the y-intercept, the axis of symmetry, and the vertex, you can sketch the graph.

You can see now the graph in the attached figure

Part C. Extreme location of the graph

The graph shows that the parabola opens downward. That is due to the fact that the coefficient of the leading term (x²) is negative.

The parabola starts in the second quadrant. starts growing, crosses the x-axis at (-4,0), crosses the y-axis at (0,256), reaches the maximum value at (30, 1156), and then decreases toward the fouth quadrant, crossing the x-axis at (64,0).

Thus the vertex is a maximun, and the coordinates of the maximum are (30, 1156).

Part D. According to the graph, what is the maximum possible area of the game board? Give your answer to the nearest whole number. (Assume that the maximum area is not reduced by the open hole in the game board.)

The maximum possible area of the game is the maximum value of the function y = -x² + 60x + 256.

This value was calculated as y = 1156.

Part E. Use the original expressions for the length and width, and substitute the x-coordinate from the extreme location. What are the length and width of the game board at the extreme location?

The length is:

length = - x + 64 inches

x = 30

length = - 30 + 64 = 34 inches

The width is:

width = x + 4

x = 30

width = 30 + 4 = 34 inches

Part F. What type of quadrilateral will be formed when the game board covers the maximum possible area?

Since the length and the width are equal, the quadrilateral is a square.

Part G. Suppose the carnival director asks you to create a game board that is 1,120 square inches. Find the dimensions that would meet this request by setting the area equation equal to 1,120, solving for x, and substituting x into the expressions for the length and width.

$y=-x^2+60x+256\\ \\ 1,120=-x^2+60x+256\\ \\ x^2-60x-256+1120=0\\ \\ x^2-60x+864=0$

Factor:

Find two numbers whose sum is - 60 and the product os 864. They are -24 and - 34:

$x^2-60x+864=(x-24)(x-36)$

Use the zero product rule:

$(x-24)(x-36)=0\\ \\ x-24=0\implies x=24\\ \\ x-36=0\implies x=36$

Now substitute to find the dimensions:

x = 36

length = - x + 64

length = - 36 + 64 = 28

width = x + 4 = 36 + 4 = 40

Hence, legth = 28, width = 40

x = 24

length = - x + 64 = -24 + 64 = 40

width = x + 4 = 24 + 4 = 28

Part H. When you solved the area equation for x, did any extraneous solutions result? Describe how an extraneous solution would arise in this situation.

The two solutions are valid (non extraneous) because both leads to positive real dimensions for which the areas can be 1,120 in².

28×40 = 1,120

40×28 = 1,120

An extraneous solution could arise if you try to find areas for which x is greater than or equal to 64, because in that case - x + 64 would be zero or negative and dimensions must be positive.

For the same reason, also an extraneous solution would arise if you try to fix areas for which x is less than or equal to - 4.

So, the domain of your function has to be - 4 < x < 64.

Part I. What method of solving quadratics did you use to solve the equation set equal to 1,120? Why did you choose this method?

The method use was factoring.

Discuss the usefulness of other methods of solving quadratics as they pertain to this scenario.

The other importants methods are graphical and the quadratic equation.

For graphical method you graph your parabola and find the values of x that sitisfies the area searched (value of y).

The quadratic equation gives the y-values (areas) without factoring:

$\frac{-b+/-\sqrt{b^2-4(a)(c)} }{2(a)}$

8 0

3 years ago