An open box is to be made out of a 6-inch by 18-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. find the dimensions of the resulting box that has the largest volume.
dimensions of the bottom of the box:
height of the box:

The approximated value of π using the integer digits 1 2 3 4 5 6 7 8 is is 3.142857

The integers are given as:

1 2 3 4 5 6 7 8

The value of π is:

π = 22/7

Evaluate the quotient

π = 3.14285714286

From the question, the digits 1 to 8 have to appear just once.

So, we approximate the number up to the point where any of the given digits has more than one occurrence.

So, we have:

π = 3.142857

Hence, the approximated value of π is 3.142857

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the standard equation of the circle having the given center and radius is [tex](x-9)^2+(y-2)^2=\frac{9}{25}[/tex].

Answer & step-by-step explanation:

Corresponding Angles:   m∠1 = m∠5;  m∠2 = m∠6;

                                          m∠3 = m∠7;  m∠4 = m∠8

Alternate Interior Angles: m∠3 = m∠6;  m∠4 = m∠5

Alternate Exterior Angles: m∠1 = m∠8;  m∠2 = m∠7

As you can see on the picture below:

Answer:

Angle 1 = 63.3

Angle 2 = 37.3

Angle 3 = 63.3

Angle 4 = 142.7

Step-by-step explanation:

When a line intersects two parallel lines the interior angles are equal. So angle 2 = 37.3

Angle 3 = 180 - (79.4 + 37.3) = 63.3 since the sum of the angles on a straight line must be 180

Ange 1 = Angle 3 = 63.3

Angle 4 = 180-37.3 = 142.7

Answer:

80

Step-by-step explanation:

5b^2

=5(4^2)

=5(16)

=80

Answer:

[tex]\sf \tan(C)=\dfrac{3}{4}[/tex]

Step-by-step explanation:

First, find the missing side length (DE) by using Pythagoras' Theorem:

a² + b² = c²  

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ 36² + DE² = 45²  

⇒ DE² = 45² - 36²

⇒ DE² = 729

⇒ DE = √729

⇒ DE = 27

Tan trig ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

Substituting the given values into the formula:

[tex]\implies \sf \tan(C)=\dfrac{27}{36}=\dfrac{3}{4}[/tex]

Answer:

3/4

Step-by-step explanation:

Finding the missing side by applying the Pythagorean Theorem :

Finding tan C :

Answer:

∠ ABC = 67°

Step-by-step explanation:

the angle between a tangent and a chord is equal to the angle in the opposite segment, that is

∠ ABC = ∠EAC = 67°

The system of equations can be used to determine how much of product x and product y the store owner bought is x + y = 4,000

0.10x + 0.04y = 352

The equation:

x + y = 4,000

0.10x + 0.04y = 352

Therefore, the system of equations can be used to determine how much of product x and product y the store owner bought is x + y = 4,000

0.10x + 0.04y = 352

Learn more about simultaneous equation:

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Answer:

C

Step-by-step explanation:

       [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

       Find the slope of the line that goes through (2, 8) and (4, 6)

     [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

The slope formula will help us find the slope, Here it is:-

[tex]\Large\text{$\displaystyle\frac{y_2-y_1}{x_2-x_1}$}[/tex]

Now, replace y2 with 6, y1 with 8, x2 with 4, and x1 with 2:-

[tex]\Large\text{$\displaystyle\frac{6-8}{4-2}$}[/tex]

Simplifying,

[tex]\Large\text{$\displaystyle\frac{-2}{2}$}[/tex]

Simplifying further,

[tex]\hookrightarrow\underline{\boxed{\sf{Slope=-1}}}[/tex]

#TogetherWeGoFar

[tex]\rule{300}{1}[/tex]

Answer:

[tex]\sf \boxed{-1} \ \ is \ the \ slope[/tex]

Explanation:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here given points: A(2,8) and B(4,6)

Find slope (m):

[tex]\sf \rightarrow \dfrac{6-8}{4-2}[/tex]

simplify

[tex]\sf \rightarrow -1[/tex]

To find equation:

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

[tex]\rightarrow y-8 = -1(x-2)[/tex]

[tex]\rightarrow y = -x+2+8[/tex]

[tex]\rightarrow y = -x+10[/tex]

Answer:

Step-by-step explanation:

Since the x-axis is the line of symmetry, the missing vertex is the reflection of the given vertex over the line of symmetry.

Connect these points with the vertex on the x-axis to complete the triangle.

See the attachment

Answer:

the answer for all of this question should be

C=( -10, -2)

D=(0, -2)

E=(0,8)

F=(-10,8)

so remember the quadruants and remember if the x is negative or positive and if the y is either negative or positive so hopefully those are the correct one and if not tell me whats wrong so i can edit it to make it better.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The logical step is to factorize the left side of the equation, which becomes:

Then, you can take the square root on both sides.

Not asked, but good to understand the procedure regardless.

Answer:

21.27 cubic meters

22.30 cubic meters

Step-by-step explanation:

We find volume by multiplying height, width, and length.

21.

3x3x3=27 cubic meters

22.

5x2x3=30 cubic meters

Answer:

    21. 27 cubic meters

   22. 30 cubic meters

Step-by-step explanation:

Question 21

Question 22

Step-by-step explanation:

6 ( 3x - 5 ) - 7x = 25..

18x - 30 - 7x = 25

18x - 7x = 25 + 30

11x = 55

x = 55 / 11

x = 5

[tex]...[/tex]

x=5

Step-by-step explanation:

6(3x-5)-7x=25

18x-30-7x=25

11x-30=25

x=5

Answer:

$82.50

Step-by-step explanation:

25% of $110.00 is $27.5, which means 110.0 - 27.5 is equal to = 82.50.

Answer:82.50

Step-by-step explanation:

Answer:

Step-by-step explanation:

A hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero.

Answer:

[tex] \frac{5}{36} [/tex]

Step-by-step explanation:

[tex] \frac{15}{18} \div 6 \\ = \frac{15}{18} \times \frac{1}{6} = \frac{5}{18\times 2} = \frac{5}{36} [/tex]

Answer:

0.625

Step-by-step explanation:

5/8 because there are 5 blue marbles and there are 3 yellow marbles. If you add them it equals 8.

The probability is 5/8.

If you do 5 divided by 8 it gives you 0.625.

Honestly i don't know what you mean by "rounded to three decimal places."

Sorry if it's not really healpful.

Answer:

$ 471.78

Step-by-step explanation:

This describes an 'ordinary annuity' ====>   FORMULA:

PV= C [  1-(1+i)^-n / i ]    Looking for C    i = .05/12   n =60   PV = 25000

 plug in the numbers and calculate   C = 471.78

The equation that can be determined by the coordinates for point B will be 25 = (x - 6)² + (y - 5)².

The study of geometry using points in space is known as coordinate geometry. This may be used to discover the length between the endpoints, the dividing line's m:n ratio, the line's mid-point, and so on.

Segment AB has point A located at (6, 5). If the distance from A to B is 5 units.

Then the equation that can be determined by the coordinates for point B will be

[tex]\rm 5 = \sqrt{(x-6)^2 +(y-5)^2}[/tex]

This can be written as

25 = (x - 6)² + (y - 5)²

More about the coordinate geometry link is given below.

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9%

I need 20 letters so I'm just typing this but it is 9%

Answer:

the answer is B or at Least I think

Answer: Choice A

f(x) is exponential

g(x) is quadratic

========================================================

Explanation:

Exponential functions are when the variarble is in the exponent only.

Quadratic functions are polynomials with the largest exponent being 2.

Answer:

f(x) is exponential; g(x) is Quadratic

Answer:5/18

Step-by-step explanation:

1. Find how many minutes (90 minutes in all but you were there for 25)

2. Put 25 over 90 to find the probability in the time that you were not there.

3. Simplify the fraction to 5/18.

Answer:

No figure?

We need a figure to solve for this, please post the figure and I am ready to help!

Answer:

Step-by-step explanation:

= -40 + 56i -30i +42i

= 68i - 40

Answer:

x= -2 y= 36 (-2. 36)

x = -1 y = 6 (-1, 6)

x = 1 y = [tex]\frac{1}{6}[/tex] (1, [tex]\frac{1}{6}[/tex])

Step-by-step explanation:

Our function is [tex]y = (\frac{1}{6})^x[/tex]

all we need to do is fill in our x (given in the table) to solve for y

[tex]y = (\frac{1}{6})^{-2}[/tex]

[tex]y = 36[/tex]

[tex]y = (\frac{1}{6})^{-1}[/tex]

[tex]y = 6[/tex]

[tex]y = (\frac{1}{6})^1 = \frac{1}{6}[/tex]

Answer:  [tex]1.0535 \times 10^{24} \text{ molecules of manganese}[/tex]

The result is approximate.

=========================================================

Work Shown:

[tex]1.75 \text{ moles} \times \frac{6.02 \times 10^{23} \text{ molecules}}{1 \text{ mole}}\\\\(1.75 \times 6.02) \times 10^{23} \text{ molecules}\\\\(10.535) \times 10^{23} \text{ molecules}\\\\(1.0535 \times 10^1) \times 10^{23} \text{ molecules}\\\\1.0535 \times (10^1 \times 10^{23}) \text{ molecules}\\\\1.0535 \times 10^{1+23} \text{ molecules}\\\\1.0535 \times 10^{24} \text{ molecules}\\\\[/tex]

Note: In the second step, the "mole" units cancel when dividing.

Answer: 9

Step-by-step explanation:

78 subtract 51 is 27. One third of 27 is 9.