Divide8/9 and 8. Express your answer in simplest form

Answers

Answer 1

Answer:

Answer: The answer is 0.11 in decimal form.

Step-by-step explanation:

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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.

Learn more about Area and Functions here:

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Erica makes 4,840$ monthly. What is the maximum loan she can take out on a house?

Answers

The maximum loan she can take out on a house is $174,240

Siti had 135 buttons. 5/9 of the buttons were red and the rest were blue. She used 64 red buttons and bought some more blue buttons. She had 84 buttons left in the end. How many blue buttons did Siti buy?

Answers

Answer:

Siti bought 13 blue buttons

Step-by-step explanation:

for not to get confused, we are going to solve the problem step by step

Siti had 135 buttons

5/9 of the buttons were red and the rest were blue

let's calculate how many buttons were red out of 135

135 * 5/9 = 75

if 75 buttons were red and the rest were blue, we can calculate how many were blue

135 - 75 = 60

says she only use 64 red buttons

if we had 75 red buttons and she used 64

75 - 64 = 11

she tells us that she had 84 buttons left, from which we know she had 11 red buttons that had been left over and 60 blue ones that she did not use, so we can calculate how many blue buttons she bought since we have the total number of buttons that she has now

84 - 60 -11 = 13

Siti bought 13 blue buttons

Find the area of the blue sector. Use 3.14 for pi and round to the nearest hundredth.

Answers

Answer:

The area of blue sector is 25.64 in²

Step-by-step explanation:

In the given figure, we need to find the area of blue section whose central angle is 60°

Formula:

$\text{Area of sector}= (\theta)/(360^\circ)* \pi r^2$

Radius of circle (r)=7 in

$\theta = 60^\circ$

Substitute the value into formula and find area of sector.

$\text{Area of blue sector}= (60)/(360)*3.14* 7^2$

$\text{Area of blue sector}= 25.643\approx 25.64\text{ in}^2$

Hence, The area of blue sector is 25.64 in²

What's the next number?
7594, 3649, 9253, ......

Answers

7594 - 3649 = 3945
I subtracted 3945
9253 - 3649 = 5604
I subtracted 5604
Together I added 5604 from the second to the third number
So now the pattern is to subtract
3945
and then add
5604
7594⇒3649⇒9253⇒5308
I did that by doing: 9253-3945
Hope this helps

7594 - 3649 = 3945

So, from the first number to the second number we are subtracting 3945.

9253 - 3649 = 5604

So, from the second number to the third number we are adding 5604.

Now, from the third to the fourth number we should subtract 3945. And them from the fourth to the five number we should add 5604. And so on.

7594, 3649, 9253, 5308, 10912, 6967, 12571, ...

Someone help please ASAP.In∆ABC, m
a) How are the measures of m
b) Solve for x:

Answers

$3x+9+8x+11+5x-8=180\n16x=168\nx=10.5\n\nm\angle BAC=3\cdot10.5+9=40.5\nm\angle ABC=8\cdot10.5+11=95\nm\angle BCA=5\cdot10.5-8=44.5\n\n$

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