A sheet of metal 12 inches by 10 inches is to be used to make a open box. Squares of equal sides x are cut out of each corner then the sides are folded to make the box. Find the value of x that makes the volume maximum.


*Round to 2 decimal places and write out "inches"

Answers

Answer 1

Answer:

1.81 inches

Step-by-step explanation:

We are told that the sheet of metal to be used measures 12 inches by 10 inches.

Squares of equal sides x are cut out of each corner. Thus, it means total of 2x is cut of the 12 inches side and 10 inches side.

Thus;

Length; L = 12 - 2x

Width; W = 10 - 2x

Height; H = x

Volume of the box is;

V = LWH

V = (12 - 2x)(10 - 2x)x

Factorizing out, we have;

V = 4x[(6 - x)(5 - x)]

Equating V to zero, we can find the domain of the function;

At V = 0,

4x = 0; 6 - x = 0 ; 5 - x = 0

x = 0, x = 6, x = 5

The dimensions have to be positive. Thus;

0 ≤ x ≤ 5

Expanding the volume equation;

V = 4x[30 - 5x - 6x + x²]

V = 4x[30 - 11x + x²]

V = 4x³ - 44x² + 120x

dV/dx = 12x² - 88x + 120

Equating to zero to find the value of x that makes volume maximum;

12x² - 88x + 120 = 0

Using quadratic formula gives;

x = 1.81 or 5.52

From our domain, we have 0 ≤ x ≤ 5.

1.81 falls within the domain and therefore we will pick it as the height that makes the volume maximum.

Answer 2

Answer:1.81

Step-by-step explanation:

x=1.81


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Answers

Answer:

x^2+5x-14=0

Step-by-step explanation:

(x+7)(x-2)=0

x (x-2)+7 (x-2)=0

x^2-2x+7x-14=0

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How do you say hi in chamoru?​

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Answer:

Step-by-step explanation:

To say Hi in Chamoru you say, "Håfa Adai" (Chamorro for "Hello").

Hope this helped!

PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
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If f(x) = -3x + 4, find f(-4)

Answers

Answer:

Step-by-step explanation:

-3x+4

-3(-4)+4

12+4

16

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answers

Answer:

x =2

x = -2

Step-by-step explanation:

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

(x - 2) = 0

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A tree is 72 feet (ft) tall. How many inches (in) is this? First fill in the blank on the left side of the equation using one of the ratios. Then write your answer on the right side of the equation.

Answers

1 foot = 12 inches:

1/72 = 12/x

Cross multiply:

1x = 72 * 12

x = 864 inches

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A) Definition of perpendicular

B) Vertical angles are equal

C) Reflexive

Answers

Answer:

Reflexive

Step-by-step explanation:

Because C and D are right angles. That’s def of perpendicular. I’m not sure about the vertical angles but it’s shown in the proof

Answer:

Reflexive

Step-by-step explanation:

2. Soive: (14x - 8) - 2(3x - 6)
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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

(I'LL BE GIVING BRAINLIEST AND EXTRA POINTS TO WHO EVER HELPS ME!! :D)



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B) one and seventeen twenty firsts pies

C) two and fifty eight eightieths pies

D) two and seventeen twenty firsts pies


(Here is an image if needed) :

Answers

Answer:

2 7/20

Step-by-step explanation:

The length of a rectangle is twice the width if the perimeter of the rectangle 60 units find the area of the rectangle

Answers

Answer:

200

Step-by-step explanation:

Length = 2w

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substitute l out with 2w

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Area = w • l

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        = 200

The diagram compares the ratio of girls in the chorus to boys in the chorus. What is the ratio of girls to boys? If there are 30 students in the chorus, how many are girls and how many are boys.

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Answers

Answer:

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Step-by-step explanation:

i just messed around with a calculator and found it.

PLEASE HELP!!

Use the expression 9i+2(7+3i) to answer this question!
Which property or properties should you use to simplify this expression?

Apply those properties to each term

Answers

Answer:

Please check the explanation.

Step-by-step explanation:

Considering the expression

[tex]9i+2\left(7+3i\right)[/tex]

Applying the distributive law

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Group like terms

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Add similar elements: 9i+6i=15i

[tex]=15i+14[/tex]

Question 5 of 8
Put these substances in order of density with the most dense first and the
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1 iron
Trubber
cotton ball
Ti helium

Answers

Answer:

cf

cf

centru. toc htc. toc cf. activ. cfc fgfvxv. chvv

(Giving brainliets to who ever helps me!!


Solve eight and three fifths minus two and four ninths.

A) six and seven forty fifths
B) six and seven fourteenths
C) seven and seven forty fifths
D) seven and seven fourteenths

Answers

Answer:

6.1555

Step-by-step explanation:

the 5 is infinite in 6.15 such as 6.155555555 it does not stop

Answer:

6 [tex]\frac{7}{45}[/tex]

Step-by-step explanation:

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Answers

Answer:

15/19

Step-by-step explanation:

60/4 = 15

76/4 = 19

15/19

Answer:

76/60 i think

Step-by-step explanation:

Find the equation of the linear function represented by the table below in slope-intercept form.

Answers

First find slope: (y2-y1)/(x2-x1)
pick 2 points: (-3,9), (1,-7)
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y = -4x + b, plug in a point
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the is factoring quadratics with a leading coefficient: 5x to the 2 power - 14x + 8

Answers

Answer:

The factorization of [tex]5x^2-14x+8[/tex] is (5x-4)(x-2)

Step-by-step explanation:

Given quadratic polynomial is:

[tex]5x^2-14x+8[/tex]

To factor a quadratic polynomial with leading co-efficient has to be factorized, the leading co-efficient and the constant are multiplied and pairs(a,b) of the product are made so that their sum or subtraction is equal to the co-efficient of x

We get 40 by multiplying 8 and 5

And the pair we get are: 10 and 4

[tex]=5x^2-10x-4x+8\\=5x(x-2)-4(x-2)\\=(5x-4)(x-2)[/tex]

Hence,

The factorization of [tex]5x^2-14x+8[/tex] is (5x-4)(x-2)

Mia has 12 boxes of cookies. Each box contains 36 cookies. she has another 258 cookies in the pantry. How many cookies does she have in all?

Answers

690

12×36 + 258 = 690 For extending to 20 characters

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B(-1, -13)
C(14,7)
D(7,31)
Is rhombus ABCD a square, and why?

Answers

Answer: No because BC is not perpendicular to AB.

Step-by-step explanation:

Yes, rhombus ABCD is a square as all four angles of the rhombus are right angles.

A square is a special type of rhombus where all four sides have the same length and all four angles are right angles.

In this case, we can see that all four sides of the rhombus have the same length by calculating the distance between each pair of vertices. For example, the distance between A and B is:

distance = [tex]\sqrt{[/tex] [tex]((-8 - (-1))^2[/tex] + [tex](11 - (-13))^2[/tex])

distance = [tex]\sqrt{[/tex] ([tex]7^2[/tex] + [tex]24^2[/tex])

distance = [tex]\sqrt{[/tex] (625) = 25

The distance between each other pair of vertices is also 25, so all four sides of the rhombus have the same length.

We can also see that all four angles of the rhombus are right angles by calculating the angles between each pair of adjacent sides. For example, the angle between sides AB and BC is:

angle = arctan((13 - (-13))/(-8 - (-1)))

angle = arctan(26/7)

angle = 78.6°

The angle between each other pair of adjacent sides is also 78.6°, so all four angles of the rhombus are right angles.

Therefore, rhombus ABCD is a square.

To learn more about rhombus here:

https://brainly.com/question/12665650

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Find the values of a and b such that x² - 2x + 2 = ( x - a )² + b

Answers

Answer:

a = b = 1

Step-by-step explanation:

x² - 2x + 2 = ( x - a )² + b

x² - 2x + 2 = ( x² - 2x + 1) - 1 + 2 = (x - 1)² + 1

a = b = 1  

Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, 5 want a ice cream party, 7 want a movie, 10 want a costume party, and the rest want are undecided. If 20% want a ice cream party, how many students are in class?

Answers

Answer:

25

Step-by-step explanation:

3/2 x + 5 = 5 -2 (x+7)

Answers

Answer is: x = -4
If you need step by step lmk
The steps are too long.

add on sc alawad2003

Answers

Answer:

Mkay?

Step-by-step explanation:

Write equations (both, Point Slope & Slope Intercept Forms) of the line with
slope of -2 and point (9,2).

Answers

Answer:

Equation of line in Point Slope Form is [tex]\mathbf{y-2=-2(x-9)}[/tex]

Equation of line in Slope Intercept Form is: [tex]\mathbf{y=-2x+20}[/tex]

Step-by-step explanation:

We need to write equation of line having slope -2 and point (9,2)

a) Equation in Point Slope Form

The general equation of point slope form is: [tex]y-y_1=m(x-x_1)[/tex]

Where x₁ and y₁ are the points of line and m is slope.

x₁=9 and y₁=2 and m=-2

Putting values in formula and finding equation:

[tex]y-y_1=m(x-x_1)\\y-2=-2(x-9)[/tex]

So, Equation of line in Point Slope Form is [tex]\mathbf{y-2=-2(x-9)}[/tex]

b) Equation in Slope Intercept Form

The general equation of Slope Intercept Form is: [tex]y=mx+b[/tex]

where m is slope and b is y-intercept

Finding y-intercept using slope m=-2 and point(9,2)

[tex]y=mx+b\\2=-2(9)+b\\2=-18+b\\b=2+18\\b=20[/tex]

The equation in slope m=-2 and b=20 is:

[tex]y=mx+b\\y=-2x+20[/tex]

So, equation of line in Slope Intercept Form is: [tex]\mathbf{y=-2x+20}[/tex]

Penelope buys bracelets in bulk at a cost of $8 each to sell at her store. She uses a markup rate of 125%, which is added to the bracelet cost. What is the retail price of a bracelet?

Answers

Answer:

$18.00

Step-by-step explanation:

8 x 1.25 = 10

8 + 10 = 18

Help. Thank you in advance.

Answers

Answer:

option 2. mean is larger than median.

Step-by-step explanation:

mean of the set = ( 88+81+93+85+98)/5

= 445/5

= 89

median of the set = 88

the mean of the set is greater than the median.

Marco paid $42.40 for 6.4 Gallons of gas. What is the price of 1 gallon of gas? Group of answer choices

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Answer:

6.63

Step-by-step explanation:

Please help it would help alot

Answers

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Michael’s father bought him a 16-foot board to cut into shelves for his bedroom. michael plans to cut the board into 11 equal size lengths for his shelves.the saw blade that michael will use to cut the board will change the length of the board by -0.125 inches for each cut. how will this affect the total length of the board?

Answers

Step-by-step explanation:

you have to know how many inches make a foot or vice versa the you do simple proportion by equating the inches to the foot to get the answer. simple as abc

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Answers

the answers is c 78 degrees
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