Given that Please help

Order the following numbers from least to greatest : .83 , 7/8 , 0.32 , 1/2

miskamm [114]

0.32,1/2,7/8,.83 is your answer hope I helped

3 0

3 years ago

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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

1. Jenny has a brand new home, and would like to be very adventurous in her decorating. She would like to put a series of murals

VashaNatasha [74]

Rectangular implies the area to be length times height

let height=x

let width=2 more than the height or Length=2+x

Area=F(x)=(2+x)(x)=2x+x^2

f(x)=x^2+2x

****************To Answer your Additional question

You see the standard price is $100 for any mural, And also charges $40 per square foot.

So to show you the approach, Lets say that a mural of 1 square feet needs to be painted, then the charge will be $100 plus the $40 for every square feet, then it will be 100+40(1 square feet)=$140.

The problem asks for the charge of mural whose area is x, so lets do the same thing.

$100+40(x square feet)=100+40x and that is the function that gives the price of mural with an area of x.

so, g(x)=100+40x

7 0

3 years ago

Which expression represents rational numbers? Select all that apply

Masja [62]

Answer:

A, B, C and F

Step-by-step explanation:

We have according to the options:

A. $\sqrt{100} \times \sqrt{100}=10\times 10=20$

B. $13.5+\sqrt{81} =13.5+9=22.5$

C. $\sqrt{9}+\sqrt{729}=3+27=30$

D. $\sqrt{64}+\sqrt{353}=8+\sqrt{353}$ , which is not rational.

E. $\frac{1}{3}+\sqrt{216}=0.3+6\sqrt{6}$ , which is not rational.

F. $\frac{3}{5}+2.5=0.6+2.5=3.1$

Hence, the expressions representing rational numbers are A, B, C and F.

5 0

4 years ago

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A wooden cube of mahogany has a side length of 8 cm and a mass of 400 g. What is the density of the cube? Enter your answer in t

Y_Kistochka [10]

Density is a property of a material which describes the mass of a material per unit volume. It can be calculated by dividing the mass of the object with its volume. We calculate as follows:

Density = mass / volume = 400 / (8^3) = 0.78125 g/cm^3

3 0

3 years ago