How do you do this problem?You have $22 and you use it four tickets and after you bought it, you have $6 left. How much did each ticket cost?

Answers

Answer 1

Answer: Answer: $4.

Explanation: Get $22 nd minus $6 you have left, and it equals $16 for the total of tickets. Then get $16 and divide it with the number of tickets, which is 4, so $4 for 1 ticket!

Hope this helps!

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A triangle is placed in a semicircle with a radius of 9 cmFind the area of the shaded region. Use the value 3.14 for π
, and do not round your answer. Be sure to include the correct unit in your answer.

Answers

Considering that the shaded area is the part of the semi circle outside the triangle:
Area of circle= Pi x radius2 (this means radius squared)
Area of triangle= 1/2 x base x height
1/2 (because it is a semi circle) x 3.14 (in replacement of pi as directed by question) x 9squared= 127.17

127.17 - (1/2 x 18 x 9) = 46.17cmsquared

Final answer:

The area of the shaded region can be found by subtracting the area of the triangle from the area of the semicircle.

Explanation:

To find the area of the shaded region, we need to calculate the area of the semicircle and subtract the area of the triangle from it. First, let's find the area of the semicircle. The formula to find the area of a semicircle is A = (π * $r^2$ ) / 2, where π is approximately 3.14 and r is the radius. Plugging in the values, we have A = (3.14 * $9^2$ ) / 2 = 127.26 square cm.

Next, let's find the area of the triangle. The formula to find the area of a triangle is A = (base * height) / 2. In this case, the base of the triangle is the diameter of the semicircle, which is 2 * 9 = 18 cm. The height of the triangle is the radius of the semicircle, which is 9 cm. Plugging in the values, we have A = (18 * 9) / 2 = 81 square cm.

Finally, to find the area of the shaded region, we subtract the area of the triangle from the area of the semicircle: 127.26 - 81 = 46.26 square cm. So, the area of the shaded region is 46.26 square cm.

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Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The three pens are to have the same area. Express the area function for the three pens in terms of x. Determine the domain and range for the area function

Answers

Answer:

The area function is

$A=(135)/(2)x-(9)/(2)x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-(3x)/(2)$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-(3x)/(2)\right)$

$\Rightarrow A=(135)/(2)x-(9)/(2)x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-(2y)/(3)$

$\Rightarrow x<15 m$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=(135)/(2)-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow (135)/(2)-9x=0$

$\Rightarrow x=(15)/(2)$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}<0$ , so, point $x=(15)/(2)$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=(135)/(2)* \frac {15}{2}-(9)/(2)* \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

Final answer:

The area of each pen can be expressed as A(x) = x * (90 - 2x) / 3. The domain of this function is 0 < x < 45, and the range is 0 < A(x) < 300

Explanation:

In this problem, since Pam has to divide the petting zoo into three parts, we can consider the width of each pet pen to be x and the total length of the three pens to be (90 - 2x)/3, given that the total fence is 90m and we have two fences that are x meters long separating the pens. So, the area, A of each pen can be expressed as a function of x: A(x) = x * (90 - 2x) / 3. The domain of this function, or the possible values of x, would be all the values that make the area positive, which are 0 < x < 45. For the range of the function, we analyze the quadratic function which will have a maximum value at x = 15, as the area will be largest when the space is divided evenly, so the maximum area is A(15)= 15 * (60) / 3 = 300. Therefore, the range of the function is 0 < A(x) < 300.

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3(x-2)>-3
solve each inequality

Answers

divide each side by the number that does not contain a variable
answer is x>1

Question 12 of 22What is sin 60°?
O A.
OB.
O C. 1
O D.
2
1
-
√2
OE 1/1/20
OF. √3