for the diagram below, which equation is the correct use of the distance formula?

Answer:

Box Dimensions:

L  = 15.15 ul

W = 7.15 ul

h = x = 2.43 ul

V(max) =    263.22 cu

Step-by-step explanation:

We call x the length of the square to be cut in the corners then:

Are of the base of the box is:

(20 - 2*x)  is the future length of the box and

(12 - 2*x) will be the width

The heigh is x  then the volume of the box is:

V = ( 20 - 2*x )* ( 12 - 2*x ) * h

And the volume as a function of x is:

V(x) = ( 20 - 2*x) * ( 12 - 2*x ) * x     or   V(x) = (240 -40*x -24*x + 4*x²) * x

V(x) =  240*x - 64*x² + 4*x³

Taking derivatives on both sides of the equation we get:

V´(x) = 240 - 128*x + 12*x²

V´(x)  =  0              240 - 128*x + 12*x²  = 0    or     60 - 32*x + 3*x²

3*x²  -  32*x  +  60  = 0

Solving:

x₁,₂  =  32  ± √ (32)² - 4*3*60 ]/ 2*3

x₁,₂  =  32  ± √ 1024 - 720 )/6

x₁,₂  = ( 32  ± √ 304 )/6

x₁,₂  = ( 32  ± 17.44 )/6

x₁  =  8.23      ( we dismiss this solution because is not feasible 2*x > 12

x₂ = 2.43  u.l ( units of length)

Then

L  =  20 - 2*x      L  = 20  - 4.85     L  = 15.15 ul

W =  12 - 2*x      W = 12 - 4.85      W = 7.15 ul

h  =  2.43 ul

V = 2.43*7.15*15.15  cubic units

V =  263.22 cu

To see if when x = 2.43   function V has a maximum we go to the second derivative

V´´(x)  = - 128  + (24)*2.43

V´´(x) = - 69.68      as        V´´(x)  < 0   then we have a maximum for V(x) in the point x = 2.43

Answer:

-4 square inches

Step-by-step explanation:

its because the 5 pictures together make 21

Answer: A. perpendicular

Step-by-step explanation: First, you have to determine the slope of both lines and you can do so using the slope formula: (y2 - y1)/(x2 - x1). You should get the slope -2/5 for the first line and 5/2 for the second. Because one line has a slope that is the negative reciprocal of the other, these lines are perpendicular.

Answer:

1/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

probability that he pulls out a red marble = number of red marbles / total number of marbles

= 4/20 = 1/5

Answer: X would be 84 degrees.

Step-by-step explanation: APB is a straight angle, which adds up to 180 degrees. TPQ is  90 degrees, and QPB is 32 degrees, so 180-90-32=58. APT is 58 degrees. APT and PTR are alternate interior angles, therefore they have the same angle measure. So PTR is also 58 degrees. A quadrilateral adds up to 360 degrees, so add up the three known angles in the quadrilateral, 58+90+128, which gives you 276 degrees. 360-276=84 degrees, therefore X would be 84 degrees.

Answer: 7 red marbles.

Step-by-step explanation:

Since we are given the information that there are only red marbles and blue marbles in the bag and that the probability of randomly choosing a red marble is 1 /9 while there are 63 marbles in total.

Then the number of red marbles will be:

= 1/9 × 63

= 7

There are 7 red marbles

The number if blue marbles will be:

= 63 - 7

= 56 blue marbles

Answer:

im not sure but pls gimme brainlyist bc im a dum dum

Step-by-step explanation:

Answer:

may be the answer is 1000.not sure.

Answer:

answer is c 1600

hope it helps

Answer:

55 degrees

Step-by-step explanation:

First, we can use Thales' Theorem to determine that because AC is along the circle's diameter, angle B (the angle opposite to that side) is a right angle.

Next, we know that an inscribed angle with its vertex on the circle, formed by two intersecting chords (A in this case) is equal to 1/2 of its intercepted arc, so angle A = 70/2=35

We can then use the fact that a triangle adds up to 180 degrees here to get

35+90+C=180

C=55 degrees

Step-by-step explanation:

2x+1

x = 5

2(5)+1

=10+1=11

Answer:

2(5)+1

10+1

11

Hope This Helps!!!

Answer:

12 sides.

Step-by-step explanation:

the sum of every pair of interior and exterior angle is always 180 degrees.

x = exterior angle.

the interior angle is then x+120.

so then exterior and interior angle together must be 180.

x + x + 120 = 180

2x + 120 = 180

2x = 60

x = 30 degrees

how many sides ?

the sum of all exterior angles must be 360 degrees.

all exterior angles are the same (because all the interior angles must be the same due to "regular polygon").

so, how many times does 30 fit into 360 ?

360/30 = 36/3 = 12

it has 12 corners and also sides.

Answer:

A

Step-by-step explanation:

Write the nunber in scientific notation which we need to add -1 to 10 power to made it 3.07.

Answer:

z = 1539.44230769

Step-by-step explanation:

360000 + 102 = 360102

360102 - 200000 = 160102

160102/104z = 1539.44230769

z = 1539.44230769

Answer:

8 and 9

Step-by-step explanation:

Let the two consecutive integers be x - 1 and x

Smaller = x-1

Largere = x

If the square of the smaller integer is nineteen more than five times the larger integer, then;

(x-1)² = 19 + 5x

Expand

x²-2x+1= 19+5x

x²-2x-5x+1-19 -0

x²-7x-18 =0

Factorize

x²-9x+2x-18 =0

x(x-9)+2(x-9) = 0

(x+2) = 0 and x - 9 = 0

x = -2 and 9

SInce x cannot be negative;

x = 9

Smaller number = 9-1

Smaller number = 8

Hence the two consecutive integers are 8 and 9

Answer:

Bicycles = 315

Scooters = 630, basic mathematics. The most effective method for these questions is substitution. But I might have intermingled them so double check

Answer:

The surface charge density is [tex]7.8\times10^{-8} C/m^2[/tex].

Step-by-step explanation:

separation, d = 85 mm

Work, W = 6 x 10^-3 J

charge , Q = 8µC

The potential difference is given by

W = q V

[tex]V=\frac{6\times 10^{-3}}{8\times 10^{-6}}=750 V[/tex]

Let the charge on he capacitor is q.

[tex]q = CV\\\\q = \frac{\varepsilon oA}{d}\times V\\\\\frac{q}{A} = \frac{8.85\times 10^{-12}\times750}{0.085} =7.8\times10^{-8} C/m^2[/tex]

Step-by-step explanation:

✓44×11

=✓2²×11²

=22

!!!!????!!!!!!

Answer:

22

Step-by-step explanation:

First, multiply 11 and 44

11 × 44 = 484

[tex]\sqrt{484}[/tex] = 22

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Have a great summer :)

Answer:

105 cm

Step-by-step explanation:

3/7 = 45/x

cross-multiply:

3x = 315

x = 105

Answer:

Step-by-step explanation:

AP 1 : 12, 15 , 18 , 21, 24, 27, 30 , 33 , 36, 39,.....

AP 2 : 17 , 21 , 25 , 29, 33, 37 , 41, 45,.....

AP formed with the common terms:  21, 33, 45 , ......

a = 21 , d = 33-21 = 12 ; n = 100

Sum = [tex]\frac{n}{2}(2a +(n-1)d)[/tex]

       [tex]=\frac{100}{2}[2*21+99*12]\\\\=50 * [42+1188]\\\\=50*1230\\\\= 61500[/tex]

Answer:

[tex]\frac{10969}{260}[/tex]

Step-by-step explanation:

Answer:  To find the average rate of change, evaluate the function at the given points.

Evaluate the difference of the function at the given points.

Divide the difference of the function at the given points with the difference of the given points.

Step-by-step explanation:

The Average of rate is -1.

Everytime it goes up by one the y goes down by 1 so it would be -1.

The average rate of change of the function in the table given is: -1.

Average rate of change of a function = change in y / change in x = rise/run.

Given the table representing a function, and using two set of ordered pairs, (-2, 7) and (0, 5):

Average rate of change of the function = (7 - 5)/(-2 - 0)

Average rate of change of the function = 2/-2

Average rate of change of the function = -1.

Learn more about average rate of change on:

https://brainly.com/question/11627203

wait do you want it step by step or just the answer?

the answer is 400

Answer:

h = 7.5 cm

Step-by-step explanation:

Firstly, we find the area of the triangular base

Mathematically, we have the area of a triangle as;

A = 1/2 * b * h

A = 1/2 * 5 * 8 = 20 cm^2

Mathematically, we have the formula as;

V= 1/3 * A * h

A is base area and h is height

50 = 1/3 * 20 * h

20h = 3 * 50

20h = 150

h = 150/20

h = 7.5 cm

Answer: y=2/4x+6

I think it´s right sorry if it is´nt

Answer:

ss

Step-by-step explanation:

s

Answer:

C

Step-by-step explanation:

average, average, average

if there is one dot to the right that is far away and 3 dots to the left that are close to the like, estimated distance of the right dot would be 3 and the total distance sum of each dot to the left is 3, so the line would be between the 1 right dot and 3 left dots

Answer:

D

Step-by-step explanation:

D has three dots near to the line

Answer:

x = 8/3, 2/3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

(x + 1)² - 25/9 = 0

Step 2: Solve for x

Step-by-step explanation:

Hey there!

Given equation is:

(x+1)² - 25/9 = 0

Then;

(x+1)² - (5/3)² = 0 ( since 5² = 25 and 3² = 9)

or, {(x+1)+5/3} { (x+1)-5/3} = 0. { use a² - b² = (a+b)(a-b) formula}

[tex]( \frac{3x + 3 + 5}{3} )( \frac{3x + 3 - 5}{3} ) = 0[/tex]

[tex]( \frac{3x + 8}{3} )( \frac{3x - 2}{3}) = 0[/tex]

Now;

Either;

( \frac{3x + 8}{3}= 0

or, X = 8/3

Or,

( \frac{3x -2}{3} = 0

x = 2/3

Therefore, X = 8/3 or 2/3.

Hope it helps!

Answer:

-6.13406 and 61.13406

Step-by-step explanation:

x + y = 55

x × y = -375

y = 55 - x

x × (55 - x) = -375

55x -x² = -375

x² - 55x - 375 = 0

solution of a quadratic equation :

x = (-b ± sqrt(b² - 4ac))/(2a)

a=1

b=-55

c=-375

x = (55 ± sqrt(55² + 4×375))/2 = (55 ± sqrt(4525))/2 =

= (55 ± sqrt(25 × 181))/2 = (5×11 ± 5×sqrt(181))/2 =

= 5/2 × (11 ± sqrt(181)) =

= 61.13406... or -6.13406...

y = 55 - 5/2×(11 ± sqrt(181)) = 55/2 ± 5/2×sqrt(181) =

= -6.13406... or 61.13406...