I'm having trouble solving this:
Corry collects cube containers. She fills them with water and pours them into a rectangular prism. She was playing with them and discovered something interesting. She had three cube containers. One cube was 1 inch by 1 inch by 1 inch. A second cube was 2 inches by 2 inches by 2 inches and a third cube was 3 inches by 3inches by 3 inches.
She filled all three with water. Then Corry poured all three cubes into a rectangular prism filling it exactly! The rectangular prism has a square base with a side length (1+2+3 = 6) inches and the height is 1 inch.
Corry wonders whether she has found a pattern. Investigate using more cube containers to fill square base prisms with heights of 1 in. Describe any conjectures you discover.

Answers

Answer 1

Corry's conjecture is right, and the volume follows a pattern

The volume of a cube of side length l is:

[tex]V = l^3[/tex]

For the first cube of length 1 in, the volume is:

[tex]V = 1^3[/tex]

[tex]V = 1[/tex]

For the second cube of length 2 in, the volume is:

[tex]V = 2^3[/tex]

[tex]V = 8[/tex]

For the third cube of length 1 in, the volume is:

[tex]V = 3^3[/tex]

[tex]V = 27[/tex]

So, the total volume is:

[tex]Total =1 + 8 + 27[/tex]

[tex]Total =36[/tex]

The volume of a rectangular prism of base lengths 6 in and height 1 in is:

[tex]Volume = 6^2 \times 1[/tex]

[tex]Volume = 36[/tex]

Assume, he adds a cube of side length 4 in, the volume is:

[tex]V = 4^3[/tex]

[tex]V = 64[/tex]

The total volume would be:

[tex]V =36 + 64[/tex]

[tex]V =100[/tex]

The base length of the rectangular prism would be:

[tex]Length =1+2+3+4[/tex]

[tex]Length =10[/tex]

The volume of the rectangular prism would be:

[tex]Volume = 10^2 \times 1[/tex]

[tex]Volume = 100[/tex]

So, the pattern is:

Cubes                Volumes

1, 2, 3                    36

1, 2, 3,4                  100

Corry's conjecture is right, and the volume follows a pattern

Read more about conjectures at:

https://brainly.com/question/4125198


Related Questions

please no links!!!!!!!!!!!

Suppose a trip is 355.1 miles long and you want to spend 2 days driving. How many miles
should you drive each day?

Answers

Answer: 177.55 miles

Step-by-step explanation: 355.1/2

                                            = 177.55 miles each day

Answer:

177.55mi/day

Step-by-step explanation:

If you travel for x number of days and want to split your trip evenly across those days, simply divide the distance you need to travel by the number of days.

through:(-3,-1), slope=4/3

Answers

Answer:

I need more info

Step-by-step explanation:

5 2/12 x 10/11
Simplify the answer completely and change to a mixed number

Answers

Answer:

[tex]4\frac{23}{33}[/tex]

Step-by-step explanation:

[tex]5 \frac{2}{12}[/tex]    ×    [tex]\frac{10}{11}[/tex]

[tex]\frac{62}{12}[/tex]    ×   [tex]\frac{10}{11}[/tex]

[tex]\frac{62*10}{12*11}[/tex]

[tex]\frac{620}{132}[/tex]

Divide both sides by 4

[tex]\frac{155}{33}[/tex]

Now let us write it as a mixed number

[tex]4\frac{23}{33}[/tex]

Hope this helps you :-)

Answer:

Question :

[tex] \dashrightarrow{5 \dfrac{2}{12} \times \dfrac{10}{11}}[/tex]

Solution :

[tex] \dashrightarrow{5 \dfrac{2}{12} \times \dfrac{10}{11}}[/tex]

Coverting 5-1/2 into improper fraction :

[tex] \dashrightarrow{\dfrac{(5 \times 12) + (2)}{12} \times \dfrac{10}{11}}[/tex]

[tex] \dashrightarrow{\dfrac{(60) + (2)}{12} \times \dfrac{10}{11}}[/tex]

[tex] \dashrightarrow{\dfrac{60 + 2}{12} \times \dfrac{10}{11}}[/tex]

[tex] \dashrightarrow{\dfrac{62}{12} \times \dfrac{10}{11}}[/tex]

Performing multiplication :

[tex] \dashrightarrow{\dfrac{62 \times 10}{12 \times 11}}[/tex]

[tex] \dashrightarrow{\dfrac{620}{132}}[/tex]

Cutting the fraction into simplest form :

[tex] \dashrightarrow{ \cancel{\dfrac{620}{132}}}[/tex]

[tex] \dashrightarrow{ \dfrac{155}{33}}[/tex]

Coverting the improper fraction into mixed fraction :

[tex]{\dashrightarrow{\sf{\underline{\underline{\red{4 \dfrac{22}{33}}}}}}}[/tex]

Hence, the answer is [tex]\bf{4 \dfrac{22}{33}}[/tex].

Rachael is placing a protective cover on a glass case. The case is a cube, and the perimeter of one cube face is 56 inches.

How many square inches of the protective covering does she need for the case?

Answers

Answer:

336

Step-by-step explanation:

We know that a cube has 6 faces which means we can use this equation:

56 x 6 = 336

336 square inches is the answer.

Perimeter=56in

Side=56)4=14in

So area of one side=

(side)^2=(14)^2=196in^2

Cube has 6sides

So total protection:-

6(196)1176in^2

Can someone please help me with this one? Thank you I appreciate it!

Answers

Answer:

25.92 sorry if i get this wrong!

Step-by-step explanation:

So to do the math properly you have to convert the 7.20 into a fraction as well so the 7$ will be a while number and the .20 would be over 100 being 20/100 since there’s 100cents in 1$, so that would be 7 20/100 and since the pounds is 3 3/5 the denominators have to be the same so you’ll have to divide the 20/100 until you have a same denominator so if you dive the numerator and denominator by 5 you get 4/20 (20/5=4, 100/5=20) then again you divide them both by 4 being 1/5 so that would be 7 1/5 x 3 1/5 so for each of them you multiply the bottom and add the top so 7x5 = 35+1= 36 so that’s your new numerator but the denominator remains the same so 36/5 and you do the same with 3 3/5 you multiply 3x5=15+ the 3 = 18/5 so then that would be 36/5 x 18/5 now you multiply both the numerators and denominators equaling 648/25 then that equals to 25.92$

The price of an item at the store can be defined by the variable w.

Based on this information, which of the options below represents a markup in price for that item? Select all that apply.


A)0.85w
B)0.92w
C)1.1w
D)1.15w
E)1.25w

Answers

Answer:

  C)  1.1w

  D)  1.15w

  E)  1.25w

Step-by-step explanation:

A markup is an added value. The effective multiplier of price will be greater than 1 when the markup is added. Such a multiplier is indicated in choices C, D, and E.

___

Choices A and B represent a markdown, or discount.

help!!!!

Find the slope of the line below. Enter your answer as a fraction or decimal.
Use a slash mark (/) as the fraction bar if necessary.
10
10
(7.-2)
10
6
09
(-3,-8)
10
-10

Answers

Answer:  3/5

This is equivalent to 0.6 in decimal form

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

Explanation:

To find the slope, divide the rise over run

rise = change in y = how far to move up or downrun = change in x = how far to move to the right

In this case, we have:

rise = 6run = 10

Therefore,

slope = rise/run = 6/10 = 3/5 = 0.6

The slope of the line that passes through (-3, -8) and (7, -2) will be 3/5.

What is the slope?

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

From the graph, the points are (-3, -8) and (7, -2). Then the slope of the line is calculated as,

m = (- 8 + 2) / (- 3 - 7)

m = 6 / 10

m = 3/5

The slope of the line that passes through (-3, -8) and (7, -2) will be 3/5.

More about the slope link is given below.

https://brainly.com/question/3605446

#SPJ7

Kevin drank
2
3
liter of water Monday before going jogging. He drank
5
7
liter of water after his jog. How much water did Kevin drink altogether? Write your answer as a mixed number.

Answers

Answer:

80 Liters

Step-by-step explanation:

23 + 57 = 80

80 = 57 + 23


I’m so confused help please

Answers

Answer:

  B.  0

Step-by-step explanation:

If you subtract the right side expression and simplify, you get ...

  4/5(20x +5) -(16x -2) = 0

  16x +4 -16x +2 = 0

  6 = 0 . . . . . . . . . . . . false

There is no value of x that will make this true. There are no solutions.

QUESTION
[tex] {45}^{4} + {72}^{3} [/tex]
note: bye, i'm go back to Indonesian server. my rank in Indonesian server is ace. si hebat=ace​

Answers

Step by step explanation:

4100625+373248

so the answer is;

4473873

answer in Alternative Form

4.473873x10

trust my answer and liked and make it brainliest please

find the indefinite integrals ​

Answers

Answer:

Below in bold

Step-by-step explanation:

dx / (x^2√(9-x^2))

Substitute x = 3sinu and dx = 3cosu du

then the √(9-x^2) = √( 9 - 9sin^2u) = 3 cos u  and u = arcsin(x/3)

= 3 ∫(csc^2 u du )/ 27

= 1/9 ∫(csc^2 u du

= -1/9 cot u

= -√9-x^2) / 9x.

Isa is building a picture frame. The perimeter of the frame is 114 cm. If the frame is 30 cm tall, how wide is it? And how much cloth Isa will need to cover the frame?

Answers

Answer:

810 cm squared

Step-by-step explanation:

30 = height

multiply 30 by 2 = 60

subtract 60 from 114 = 54

divide 54 by 2 = 27 = width

multiply 27 x 30 to get 810 cm squared

How do you write an equation of a line given y-intercept -8 and slope 3/4

Answers

Answer:

[tex]y = \frac{3}{4} x-8[/tex]

Step-by-step explanation:

You can us the equation y = m x + c to answer this question.

In ,

y = m x + c

m = slope

c = y - intercept

So, they have already given in the question that,

m = 3/4

c = (-8)

Therefore, you can simply put 3/4 and (-8) instead of m and c respectively like this.

y = m x + c

y = 3/4x - 8

Hope this helps you.

Let me know if you have any other questions :-)

Can you help me with this please.

Answers

Answer:

c, i believe!!

Step-by-step explanation:

have a good day! <33

Answer:

t = 6n

Step-by-step explanation:

6 divided by 1 = 6

Based on the Rational Zero Test, which of the following is
NOT a possible zero of f(x) given below after the reciprocal
of LCD is factored out?

f(x)=x^3 -5x + (2/5)

(A) 1/2
(B) 1/5
(C) 1
(D) -1

Answers

The rational zero test is also known as the rational root test, and it is used to determine the potential root of a function.

(a) 1/2 is not a possible zero of the function

The function is given as:

[tex]f(x) =x^3 - 5x + \frac 25[/tex]

For a function,

[tex]f(x) = px^n +......q[/tex]

The list of possible roots is:

[tex]Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}[/tex]

Multiply both sides of [tex]f(x) =x^3 - 5x + \frac 25[/tex] by 5

[tex]5f(x) = 5x^3 - 25x + 2[/tex]

So, we have:

[tex]p= 5[/tex]

[tex]q = 2[/tex]

The factors are:

[tex]p =\pm 1, \pm 5[/tex]

[tex]q =\pm 1, \pm 2[/tex]

So, the possible roots are:

[tex]Roots = \pm\frac{1,2}{1,5}[/tex]

Split

[tex]Roots = \pm1, \pm \frac 15, \pm 2, \pm \frac 25}[/tex]

Hence, 1/2 is not a possible zero of the function

Read more about rational zero test at:

https://brainly.com/question/12860313

What is the slope of the line through (6,9)(6,9)left parenthesis, 6, comma, 9, right parenthesis and (7,1)(7,1)

Answers

Answer:

-8

Step-by-step explanation:

I don't really have an explenation

Answer:

y = -8x + 57

Step-by-step explanation:

hope this helps! :)

geometry PLEASE HELP and explain how???

Answers

Answer:

x means times

Step-by-step explanation:

help I have foreign parents.....they will literally disown me if I fail - ♥️​

Answers

Answer:m∠1 = 51°Step-by-step explanation:

We know that:

Total degrees of triangle: 180°

Using this clue, we can find m∠1.

=> 67 + 62 + m∠1 = 180=> 129 + m∠1 = 180=> m∠1 = 180 - 129=> m∠1 = 51°Conclusion:

We have finally found the answer to the missing angle. The answer is 51°.

Hoped this helped.

[tex]BrainiacUser1357[/tex]


The steps for solving 7x + 3 = 52 are shown. Explain how each step helps solve the
equation. Include the phrases, "Isolate the variable by -" "Simplify," and "Isolate
the variable term by -" in your answers.
Original equation
7x +3 - 52
7x +3-3-52-3
7x = 49
7x49
TT
x = 7

Answers

Answer:

The steps for solving 7x + 3 = 52 are shown. Explain how each step helps solve the

Step-by-step explanation:

Simplifying

7x + 3 = 52

Reorder the terms:

3 + 7x = 52

Solving

3 + 7x = 52

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + -3 + 7x = 52 + -3

Combine like terms: 3 + -3 = 0

0 + 7x = 52 + -3

7x = 52 + -3

Combine like terms: 52 + -3 = 49

7x = 49

Divide each side by '7'.

x = 7

Simplifying

x = 7

Write an expression to model each situation.


Sandra picked 10 blue flowers and 16 red flowers. Then she divided the flowers equally into 2 bouquets. _______________



A recipe called for 2/3 cup flour. Kyle doubled the recipe. Then he added 1/4 cup more flour to make the dough less sticky. ________________

Answers

The first one should be:
(10 + 16) ÷ 2
because if you didnt have any parentheses, it would have a different answer.

the second one should be:
2/3 x 2 + 1/4

For the given conditions expressions 1 and 2 are obtained as (10 + 16) ÷ 2 and 2/3 x 2 + 1/4 respectively.

What is a mathematical expression?

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression

It is given that the expression is,

Sandra selected 16 red flowers as well as 10 blue blooms. She then equally split the flowers into 2 bouquets.

The expression for the given condition is,

=(10 + 16) ÷ 2

If a recipe required 2/3 cup of flour. The recipe was quadrupled by Kyle. He then increased the flour by 1/4 cup to make the dough less sticky. The expression for the given condition is,

=2/3 x 2 + 1/4

Thus, the obtained expressions are (10 + 16) ÷ 2 and 2/3 x 2 + 1/4.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ2

find the derivative of x³/tanx​

Answers

Answer:

Below.

Step-by-step explanation:

We apply the quotient rule:

dy/dx = ( tanx * 3x^2 - x^3 * sec^2x)  /  (tan^2 x)

= x^2( 3tanx - xsec^2x) / tan^2x

From her eye, which stands 1.74 meters above the ground, Sophia measures the angle of elevation to the top of a prominent skyscraper to be 44∘If she is standing at a horizontal distance of 369 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.

Answers

The height of the skyscraper for the considered case is evaluated being of 358 meters approx.

What is angle of elevation?

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

How to use right triangles to find the height of the specified sky scrapper?

Remember that we assume that building is vertical to the ground. This means, there is 90° formation.

For this case, referring to the figure attached below, we get:

The height of the skyscraper = h = length of ED (which is h - 1.74 meters) + 1.74 meters

Using the tangent ratio for triangle CDE, from the perspective of angle of elevation, we get:

[tex]\tan(44^\circ) = \dfrac{|ED|}{|CD|} = \dfrac{h-1.74}{|AB|} \\0.9656 \approx \dfrac{h-1.74}{369}\\\\h \approx 0.9656 \times 369 + 1.74 \approx 358 \: \rm m[/tex]

(from calculator, we obtained [tex]tan(44^\circ) \approx 0.9656[/tex] )

Thus, the height of the skyscraper for the considered case is evaluated being of 358 meters approx.

Learn more about tangent ratio here:

https://brainly.com/question/19594654

If the length of the rectangle measures (2x -4) cm and the width measures (3x) cm, what is the area of the rectangle in terms of x?




pls ANSWER THIS CORRECTLY WITH A COMPLETE SOLUTION

Answers

[tex]\large\huge\green{\sf{Given:-}}[/tex]

length of the rectangle= (2x-4)cmbreadth of the rectangle =3x cm

[tex]\large\huge\green{\sf{ToFind:-}}[/tex]

Area of triangle=??

[tex]\large\huge\green{\sf{FormulaRequired:-}}[/tex]

Area of rectangle= lxb

[tex]\large\huge\green{\sf{Solution:-}}[/tex]

➡Area of rectangle= lxb

➡Area of rectangle= (2x - 4) x (3x) cm²

➡Area of rectangle= 6x²-12x

At a local college there are five women enrolled for every two men. (A) If there are 5,000 men enrolled how many women are enrolled? (B) What is the constant of proportionally in this situation?

Answers

Answer:

A: 25,000 Woman Enrolled. B: For Every 5 woman Enrolled 2 men are Enrolled also so the constant rate is 5 x 2

Step-by-step explanation:

35 is more than the product of 5 and the difference of a number and 1.

Answers

35+5-1 is the answer

Given the function f(x) = √x. If the function is shifted right 2 units, then shifted down 1.5 units and reflected about the x-axis, what is the equation of the new function?

Answers

Answer:

f(x) = -√(x-2) + 1.5.

Step-by-step explanation:

y = √x

2 units to right:

y = √(x-2)

1.5 down:

y = √(x-2) - 1.5

Reflect about x-axis

y = -(√(x-2) - 1.5)

y = -√(x-2) + 1.5.

What is the value of the expression?

(514−212)+(623−312)

Enter your answer as a mixed number in simplest form by filling in the boxes.

Answers

Answer:

[tex] = { \rm{(514 - 212) + (623 - 312)}} \\ \\ = { \rm{(302) + (311)}} \\ \\ ={ \underline{ \: \: {}^{ - } 9 \: \: }}[/tex]

I didn't pay attention to day​

Answers

Answer:

%2.9

Step-by-step explanation:

Step-by-step explanation:

please complete your question

f(x) = (x - 1) (4x + 3) (3x - 8) has zeros at x = 3/4, x= 1, and x = 8/3.
What is the sign of f on the interval - 3/4

Answers

Using the given roots, it is found that on the interval [tex]-\frac{3}{4} < x < 1[/tex], the function is positive.

The function is:

[tex]f(x) = (x - 1)(4x + 3)(3x - 8)[/tex]

The zeroes are:

[tex]x = -\frac{3}{4}, x = 1, x = \frac{8}{3}[/tex]

Between two zeroes, the function has the same sign, hence, to find the sign on the interval [tex]-\frac{3}{4} < x < 1[/tex], we find the numeric value of the function of a value of x on the interval, for example f(0), for x = 0.

Then:

[tex]f(0) = (0 - 1)[4(0) + 3][3(0) - 8] = (-1)(3)(-8) = 24[/tex]

Since f(0) is positive, the function is positive on the interval [tex]-\frac{3}{4} < x < 1[/tex].

A similar problem, in which it is desired to find the sign of the function, is given at https://brainly.com/question/4787253

The ground temperature at an airport is 14 °C. The temperature decreases by 62 °C for every increase of 1 kilometer above the ground. What is the temperature outside a plane flying at an altitude of 5 kilometers?​

Answers

Answer:

52°C

Step-by-step explanation:

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