Iliana was part of a group that was working on changing 0.4 repeated to a fraction. Each member of the group had a different answer. Which answer is correct?

  x^2 +(x-4)^2 =20^2

  x^2 +(x-4)^2 =400

x^2 +(x-4)^2 -400=0

factor:

2x^2-8x-384=0

Factor the 2 out of 2X^2

2(x-16) (x+12) =0

 Divide both sides by 2

(x-16) (x+12) =0

X=16 , x=-12

 Number cannot be negative so x=16

Answer:  D.) x = 16

Step-by-step explanation:

Given: The dimensions of the computer screen are modeled by the equation :

[tex]x^2+(x-4)^2=20^2[/tex]

To find the value of x , we need to solve the equation.

Now, the above equation can be written as :

[tex]x^2+x^2+16-8x=400\\\\\Rightarrow\ 2x^2-8x+16=400\\\\\Rightarrow2x^2-8x+384=0\\\\\Rightarrow\ 2(x^2-4x+192)=0\\\\\Rightarrow\ x^2-4x+192=0\\\\\Rightarrow(x-16)(x+12)=0\\\\\Rightarrow\ x=16\ or\ x=-12[/tex]

Since side cannot be negative therefore, x= 16

The two companies charge the same when transporting 20 tons of sugar, for $5015 for transporting that amount.

To determine what amount of sugar the two companies charge the same, we should set up an equation where both companies' cost functions are equal. For the first company, the cost function is C1 = 2510 + 125.25x, where x is the number of tons of sugar. For the second company, the cost function is C2 = 250.75x. To find the point at which C1 equals C2, we solve for x:

2510 + 125.25x = 250.75x

Subtract 125.25x from both sides:

2510 = (250.75 - 125.25)x

2510 = 125.5x

Divide both sides by 125.5:

x = 2510 / 125.5

x = 20 tons

Therefore, the two companies charge the same for transporting 20 tons of sugar. To find the cost when they charge the same, substitute x into one of the cost functions:

C1 = 2510 + 125.25(20) = 2510 + 2505 = $5015

Thus, the cost when the two companies charge the same is $5015 for 20 tons of sugar.

the approximate volume of the toy ice cream cone is around [tex]\( \frac{32}{3}π \)[/tex]cubic inches, considering the half-sphere as[tex]\( \frac{16}{3}π \)[/tex] and the cone as [tex]\( \frac{16}{3}π \).[/tex]

let's calculate the approximate volume of the toy ice cream cone step by step.

First, we need to determine the volume of the half-sphere, which is the ice cream part.

The formula for the volume of a sphere is:

[tex]\[ V_{\text{sphere}} = \frac{4}{3}πr^3 \][/tex]

But since we only have a half-sphere, we'll divide the result by 2.

Now, we need to find the radius ((r)) of the half-sphere. We can do this by measuring the radius of the ice cream cone's base.

Let's say the radius of the ice cream cone's base is (r = 2) inches.

Substituting the value of (r) into the formula:

[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{4}{3}π(2)^3 \][/tex]

[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{4}{3}π(8) \][/tex]

[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{32}{3}π \][/tex]

[tex]\[ V_{\text{half-sphere}} = \frac{16}{3}π \][/tex]

Now, let's find the volume of the cone part.

The formula for the volume of a cone is:

[tex]\[ V_{\text{cone}} = \frac{1}{3}πr^2h \][/tex]

Where (h) is the height of the cone.

Let's say the height of the cone is (h = 4) inches.

Substituting the values into the formula:

[tex]\[ V_{\text{cone}} = \frac{1}{3}π(2)^2(4) \][/tex]

[tex]\[ V_{\text{cone}} = \frac{1}{3}π(16) \][/tex]

[tex]\[ V_{\text{cone}} = \frac{16}{3}π \][/tex]

Now, to find the total volume of the ice cream cone, we'll add the volumes of the half-sphere and the cone together:

[tex]\[ V_{\text{total}} = V_{\text{half-sphere}} + V_{\text{cone}} \][/tex]

[tex]\[ V_{\text{total}} = \frac{16}{3}π + \frac{16}{3}π \][/tex]

[tex]\[ V_{\text{total}} = \frac{32}{3}π \][/tex]

So, the approximate volume of the toy ice cream cone is [tex]\( \frac{32}{3}π \)[/tex]cubic inches.

The arc length of a central angle of π/4 in a circle whose radius is 8 inches is 2π inches. Therefore, option B is the correct answer.

The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining the center to the end-points of the arc.

The formula to find the arc length of a circle is θ/360° ×2πr.

Given that, θ=π/4 =180/4 = 45° and radius = 8 inches.

Now, arc length = 45°/360° ×2×3.14×8

= 1/8×2×3.14×8

= 6.28 inches or 2π inches

Therefore, option B is the correct answer.

Learn more about the arc length of a circle here:

https://brainly.com/question/1577784.

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Answer:

A) 275.92sin(2Theta)=200

a p e x

Answer:

A rectangle that is not a square is the actual answer.

It is option A. A vertical compression means that the function is only a "fraction" of its original height, hence the fractional coefficient. 

REMEMBER, movement along the x-axis is always the OPPOSITE of what you think. So left = + and right = - 

So (x-6) actually means a shift 6 units to the right. (NOT left like you would naturally think) 

Answer:

D. 3

Step-by-step explanation:

Here h represents the horizontal shift. In the given graph, the graph shifted 3 units to the right from the origin.

Therefore, h = 3.

Answer: D. 3

Hope this will helpful.

Thank you.

Answer:

Option 1 - [tex]f(t)=-30 sin(\frac{\pi}{3}t)+20[/tex]

Step-by-step explanation:

Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.

To find : What is a cosine function that models this reaction?

Solution :

General form of cosine function is [tex]f(x)=A cos(Bx)+C[/tex]

Where A is the amplitude

[tex]B=\frac{2\pi}{\text{Period}}[/tex]

C is the midline    

Now, We have given

The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.

A is the average of temperature,

i.e, [tex]A=\frac{-10-50}{2}=-30[/tex]

Period of 1 cycle is 6 hour

So, [tex]B=\frac{2\pi}{6}=\frac{\pi}{3}[/tex]

The temperature is at its lowest point when t = 0 and we know lowest point is -10

So, [tex]f(t)=A\cos t+C[/tex]

[tex]-10=-30\cos 0+C[/tex]

[tex]C=20[/tex]

Substituting the values we get,

The cosine function is  [tex]f(t)=-30 sin(\frac{\pi}{3}t)+20[/tex]

Therefore, Option 1 is correct.

To find the probability of selecting an unshaded area within a circle where a square is inscribed, one must calculate the areas of the shaded and unshaded regions and use these areas to determine the ratio representing the probability.

The question seeks to determine the probability that a randomly selected point within a figure that includes both a circle and a square will be in the unshaded area. To solve this problem, we would typically need to calculate the area of the shaded and unshaded regions and then use these areas to determine the probability. When calculating probability in a geometric context, the ratio of the area of the desired region to the area of the entire space (in this case, the circle) gives the probability of randomly selecting a point in that region.

Similarly, if the question pertained to the probability of selecting a chord shorter than the side of an inscribed equilateral triangle, we would consider the probability distribution of chord lengths within the circle. This problem involves understanding that selecting a chord at random equates to selecting its midpoint at random. If the midpoint lies within a certain area, the chord will be shorter than the triangle's side.

When dealing with probability questions like the one about Times Square visitors, the random variable would typically represent the characteristic we're interested in, such as being a visitor versus a resident. In evaluating probabilities, graphical methods, such as shading areas on a graph, can be useful to visually represent and calculate the likelihood of a specific range of outcomes.

area for the hexagon = 1/2*p*a

p = perimeter = 18*6=108

a = apothem = 15.59

108*15.59 = 1683.72/2 = 841.86 sq units

Area of rectangle = 18 x 21 = 378

841.86-378 = 463.86 rounded to 464 square units

Answer: D IS THE ANSWER

Answer:

725, 1 per every 2 ft.

Step-by-step explanation:

It gives the actual height for the building, 1,450, and it says one block is two feet. Divide 1,450 by 2 and you'd get 725. And we already know dat one block is two feet so it's 1:2

(why did I start singing ``You Reposted in the Wrong Hero Academia?`` UwUz)