-3x+11=4x+2-(2x-4)

Please solve this problem with work.
Thanks!

Answers

Answer 1

Answer: $-3x+11=4x+2-(2x-4)\n\ -3x+11=4x+2-2x+4\n 5x=5\n x=1$

Answer 2

Answer: -3x+11=4x+2-2x+4
-3x-4x+2x=2+4-11
-5x=-5
x=1

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Pls, help Which of the following is true?|−6| < 5
|−6| < |5|
|−5| < |−6|
|−5| < −6

Answers

Answer:

Step-by-step explanation:

Its not A because The left side 6 is not less than the right side 5, which means that the given statement is false.

Its not B because The left side 6 is not less than the right side 5, which means that the given statement is false.

Its C because The left side 5 is less than the right side 6, which means that the given statement is always true.

Its not D because The left side is 5 is not less than the right side 6, which means that the given statement is false.

A 12-gallon tub has a faucet that lets water in at a rate of 3 gallons per minute, and a drain that lets water out at a rate of 1.5 gallons per minute. If you start with 3 gallons of water in the tub, how long will it take to ﬁll the tub completely?

Answers

Vol of water required to fill up the tub = 12-3 = 9
Rate of water per min =    3 -1.5 = 1.5/min
Using the formula           vol   =   rt
                                            t = v/r
                                            t =    9/1.5    =   6
time taken =    6 mins

Can anyone solve this word problem?

Answers

Answer:

Mrs. Davis package is 30 ounces

Step-by-step explanation:

x for ounces

mailbox plus=0.25x+5

united package=0.35x+2

since Mrs.Davis noticed that she is going to pay same price then:

0.25x+5=0.35x+2

5-2=0.35x-0.25x

3=0.10x

x=3/0.10

x=30 ounces

Mrs. Davis package is 30 ounces

check:

0.25x+5=0.25(30)+5= 12.5 dollars

o.35(30)+2=12.5 dollars

Why is 1/6 greater than 1/8 but less than 1/3

Answers

I would show it in decimals. Seeing it to show how close it is to one would make it a lot easier- 1/6= .16. 1/8=.125 and 1/3=.33 So looking at the decimals you can see how one would be bigger than the other

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:

brainly.com/question/29292490

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Please help me with this one
10x+5y=72
15x+4y=80

Answers

I hope this helps you

Problem: Solve 10x+5y=72;15x+4y=80 Steps: I will try to solve your system of equations. 10x+5y=72;15x+4y=80 Step: Solve10x+5y=72for x: 10x+5y+−5y=72+−5y(Add -5y to both sides) 10x=−5y+72 10x 10 = −5y+72 10 (Divide both sides by 10) x= −1/2 y+36 5 Step: Substitute −1 2 y+ 36 5 forxin15x+4y=80: 15x+4y=80 15( −1 2 y+ 36 5 )+4y=80 −7 2 y+108=80(Simplify both sides of the equation) −7 2 y+108+−108=80+−108(Add -108 to both sides) −7 2 y=−28 −7 2 y −7 2 = −28 −7 2 (Divide both sides by (-7)/2) y=8 Step: Substitute8foryinx= −1 2 y+ 36 5 : x= −1 2 y+ 36 5 x= −1 2 (8)+ 36 5 x= 16 5 (Simplify both sides of the equation) Answer: x=16/5 and y=8

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