Cubes are to be stacked in perfectly square layers that can be 5x5 (25 cubes), 4x4 (16 cubes), 3x3 (9 cubes), 2x2 (4 cubes), and 1x1 (1 cube). Each layer above the bottom one must have fewer cubes in it than the layer below it. If you have 54 cubes, and all of them must be stacked, what is the smallest bottom layer you can possibly have?​

Answers

Answer 1

Answer:

25 cubes

Step-by-step explanation:

Conditions are:

Each layer must be a perfect squareThe layers must be smaller starting from the bottom layerThere are 54 cubes and all of them must be stacked

Then the the option is:

5*5 + 4*4 + 3*3 + 2*2 = 25 + 16 + 9 + 4 =54

So the smallest bottom layer is 5*5 = 25 cubes and the layers from the bottom are:

25, 16, 9, 4 cubes

Related Questions

Calculate the total surface area of a rectangular box 10cm long, 8cm wide and 6cm tall.

Answers

Answer:

The answer is

376 cm²

Step-by-step explanation:

Since the rectangular box is a cuboid,

Total surface area of a cuboid is given by

2( lw + wh + lh)

Where

l is the length

w is the width

h is the height

From the question

l = 10 cm

w = 8cm

h = 6cm

Substitute the values into the above formula

That's

Total surface area of the rectangular box is

2 [ (10)(8) + (8)(6) + (10)(6) ]

2 [ 80 + 48 + 60 ]

2( 188)

We have the final answer as

Total surface area = 376 cm²

Hope this helps you

What is the value of 4 in the number 45?

Answers

Answer:

40

Step-by-step explanation:

The 4 in 45 is 40 because it is in the tens place, 4 times 10= 40.  The 5 is 5 becasue it's in the ones place.  :)

It's just place value:

Answer:

The first digit i.e. 4 is called the tens' place. Here, there are 4 tens. The last or right digit i.e. 5 is called the ones' place. Therefore, in the number 45 = 4 tens plus 5 ones = 40 + 5 = 45

Numbers 2-4 Will choose brainliest

Answers

Answer:

2. 9, 8+9

3. 17-8=9, 17, 8, 9

4. 13-7=6

Step-by-step explanation:

logx+log(3x-5)=log2​

Answers

Answer:

x=2

Step-by-step explanation:

Two cities, Ashville and Boulder, are 2.5 inches
apart on a map. A third city, Wellspring, is
located exactly halfway between Ashville
and Boulder. If the map uses a scale of 0.5
inch = 15 miles, find the actual distance from
Wellspring to Boulder.

Answers

Answer:

The distance between W and B is 18.75 mi.

Step-by-step explanation:

2.5 inches converts to

 2.5 in        15 mi

------------ * ---------- = 37.5 mi

     1             1 in

Half of this distances places us at the midpoint between W and B:

 37.5 mi

--------------- = 18.75 mi

       2

Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)

Answers

Answer:

2x^3-11x^2+9x+18

Step-by-step explanation:

By multiplying both the binomial and the trinomial given, we obtain a polynomial which contains both as factors. We notice as well that the given trinomial doesn't have 3 as a root (so there is no multiple root x = 3 in the product we obtain:

[tex](-x+3)\,(-2x^2+5x+6)=2\,x^3-5x^2-6x-6x^2+15x+18=2x^3-11x^2+9x+18[/tex]

Then, this new polynomial

[tex]2x^3-11x^2+9x+18[/tex]

has both given polynomials as factors.

please fine me the solution​

Answers

Answer:

16/3a^22b^2

I used a calculator to solve this

                                                                           

Evaluate the expression when x= -3 X^2+8x-7

Answers

(-3)^2+8(-3)-7
9-24-7
= -22

Your answer is -22.

rounds the capacity of a 1.85 liter jug ​​to the tenth

Answers

Answer:

1.9 liters.

Step-by-step explanation:

The hundredths digit is 5 so we add 1 to the tenths digit.

Answer: 1.9 liter

Step-by-step explanation: the tenth is the first digit after the decimal point. Anything greater than it equal to 5 will be rounded up. So 1.85 is rounded up to 1.9

arrange the following fraction in ascending order 2/3 1/6 3/5

Answers

Answer:

2/3 3/5 1/6

Step-by-step explanation:

look at the denominators and arrange from least to greater

You need a total of 60 pounds of two commodities costing $1.35 and $2.85 per pound.
A) Verify that the total cost is y = 1.35x + 2.85(60 - x), where x is the number of pounds of the less expensive commodity.
Let x be the number of pounds of the commodity costing $1.35 per pound. Because there are_____pounds total, the amount of the second commodity is______. The total cost, in dollars, is y = 1.35x + 2.85(60 - x).
B) Find the inverse function of the cost function.
What does each variable represent in the inverse function?
1) X represents the commodity costing $1.35 per pound and Y represents the commodity costing $2.85 per pound.
2) X represents pounds and Y represents cost.
3) X represents the commodity costing $2.85 per pound and Y represents the commodity costing $1.35 per pound.
4) X represents cost and Y represents pounds.
5) X represents the commodity costing $1.35 per pound and Y represents cost.
C) What is the domain of the inverse function?
Validate or explain your answer using the context of the problem.
1. The domain of the inverse function is equal to the range of the original function.
2. The domain of the inverse function is equal to the domain of the original function.
3. The domain of an inverse function is always R.
D) Determine the number of pounds of the less expensive commodity purchased when the total cost is $78.

Answers

Answer: provided in the explanation section

Step-by-step explanation:

We will take this problem step by step to ensure we have easy understanding of the problem at hand.

(a). taking x as the number of pounds of the commodity costing $1.35  per pound.

Also since we have 60 pounds as total

The amount of second commodity is 60 - x

then the total cost (in dollars) is

y = 1.35x + 2.85(60 - x)

(b). since we have that;

y = 1.35x + 2.85(60 - x)

solving for y gives

y = 1.35x + 171 - 2.85x

y = 171 - 1.5x

doing exchange of variables y and x we have;

x = 171 - 1.5y

where;

1.5y = 171 - x

y = 171 - x / 1.5

f(x) = y and y = f⁻¹(x)

f⁻¹(x) = 2/3 [171 - x]    ------------- (1)

Here x represents the cost and y represents the pounds

(c). Given that less commodity is purchased, the Cost will be at  its lowest and will be 60 (1.35) = $81.

Also, if only the more expensive commodity is purchased, the Cost will be at its maximum and will be 60(2.85) = $171

Therefore the domain of inverse becomes [81,171]

That is to say that the domain of inverse function is equal to the range of original  function.

(d). plug in x = $78 in the inverse function

where y = 2/3 [171-78]

y = 2/3[93] = 2[31]

y = 62

The number of pounds of the less expensive commodity purchased when the total cost is $78 is given as

y = 62

cheeers i hope this solution was helpful

if you bought a stock last year for $59 and it risen 13% how much is the stock worth now

Answers

Answer:

$ [tex] \underline{ \underline { \sf{ \bold{66.67}}}}[/tex]

Step-by-step explanation:

Price of stock bought = $ 59

% rise = 13%

Price of stock rise :

⇒[tex] \sf{13\% \: of \: 59}[/tex]

⇒[tex] \sf{ \frac{13}{100} \times 59}[/tex]

⇒$ [tex] \sf{7.67}[/tex]

New price is 13% more than $ 59

Hence, New price = $ 57 + $ 7.67

= $ 66.67

Hope I helped!

Best regards!!

What is the vertex for y=|x-3|-2

Answers

Answer:

The vertex is [3,0]

Step-by-step explanation:

y=a(x−h)2+k , where ( h,k ) is the vertex of the parabola. By comparing the two equations, we see that h=3 and k=0 . The vertex is at ( 3,0 ).

Answer:

The vertex is [3,0]

Step-by-step explanation:

y=a(x−h)2+k , where ( h,k ) is the vertex of the parabola. By comparing the two equations, we see that h=3 and k=0 . The vertex is at ( 3,0 ).

when the polynomial f(x)=2x^3+ax^2+b is divisible by (x+1) and that there is a remainder of 16 when it is divided by (x-3) find the values of a and b

Answers

Answer:

hjgyjgyjyjhhh

Step-by-step explanation:

ygjyjygyjjg

What are the explicit equation and domain for a geometric sequence with a first term of 5 and a second term of −10? an = 5(−2)n − 1; all integers where n ≥ 1 an = 5(−2)n − 1; all integers where n ≥ 0 an = 5(−15)n − 1; all integers where n ≥ 1 an = 5(−15)n − 1; all integers where n ≥ 0

Answers

Answer:

A

Step-by-step explanation:

The standard form of an explicit formula for a geometric sequence is given by:

[tex]x_n=a(r)^{n-1}[/tex]

Where n is the nth term, a is the initial term, and r is the common ratio.

We are given that the first term is 5. Hence, a = 5.

Also, we are given that the second term is -10. Therefore, the common ratio r is -2, because we multiply the first term by -2 to acquire -10.

Substituting yields:

[tex]x_n=5(-2)^{n-1}, n\geq 1, n\in\mathbb{Z}[/tex]

(Note: Z means the set of all integers. This is required because the term number can only be positive starting from one. For instance, we can't have the 0th term or the 1.5th term.)

In conclusion, the answer is A.

What the answer S4• s8 •s3

Answers

Answer:

s^15

Step-by-step explanation:

When multiplying exponents with the same base, add the exponents

Tan45degree - 10cos60degree

Answers

Answer:

- 4

Step-by-step explanation:

Tan(45°) - 10 * cos (60°) =     - 4

19. If the polynomial P(x) = 27x^3 + 9x^2 – 3x – 10 is divided by 3x – 2, the remainder will be
options:
A) 1
B) 2
C) 3
D) 0

Answers

Answer:

D) 0

Step-by-step explanation:

Remainder is zero as 10 is fully divisible by 2.

Proof:

27x^3 + 9x^2 – 3x – 10 = (3x -2) (9x^ 2 +9x+5)

Correct choice is D) 0

Solve the following:
2x – 7 > 9
a
3> 8
b
x > 1
C
3 < 8
d
x>-1

Answers

Answer: x > 8

2x - 7 > 9

2x > 9+7

2x > 16

2x / 2 > 16 / 2

x > 8

A. 3/4=a/36
B.4/9=b/36

Answers

Answer:

A. = 27 B. = 16

Step-by-step explanation:

A. 36/4 = 9 3X9 = 27

B. 36/9 = 4 4X4 =16

A bottle of hot sauce is 3/4 full. Leigh uses 2/9 of the contents of the hot sauce bottle for lunch. How much of a full bottle of hot sauce did Leigh use for lunch?

Answers

Leigh uses  [tex]\frac{1}{6}[/tex] of full bottle of hot sauce

What is Unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

A bottle of hot sauce is 3/4 full.

Leigh uses 2/9 of the contents of the hot sauce bottle for lunch.

Therefore

How much of a full bottle of hot sauce did Leigh use for lunch = [tex](\frac{3}{4}).(\frac{2}{9})[/tex]

= [tex]\frac{1}{6}[/tex]

Hence, Leigh uses  [tex]\frac{1}{6}[/tex] of full bottle of hot sauce

Learn more about Unitary method here

https://brainly.com/question/22056199

#SPJ2

Draw a square with side-length x. Write an expression that represents the perimeter.

Answers

Answer:

4x

Step-by-step explanation:

Length of square = x cm

Perimeter; p = 4 × length of square

p = 4x

How many times larger than the number (1 − 8 /15 ) is the number (1.2 + 2/ 3 )?

Answers

Answer:

1- 8/15= 7/15 = 0.4(6)

1.2 + 2/3 = 28/15 = 1.8 (6)

If y varies inversely with x and y=11 when x=3, find the equation that relates x and y.

Answers

Answer:

y = [tex]\frac{33}{x}[/tex]

Step-by-step explanation:

Use the inverse relationship equation, y = [tex]\frac{k}{x}[/tex]

Plug in what we know to solve for k:

11 = [tex]\frac{k}{3}[/tex]

33 = k

Plug 33 in as k to find the equation:

The equation will be y = [tex]\frac{33}{x}[/tex]

Which expression is the simplest form of...

Answers

Answer:

The answer is option A

Step-by-step explanation:

[tex]( {x}^{ - \frac{4}{7} } )^{7} [/tex]

Using the rules of indices

That's

[tex]( { {a}^{x} })^{y} = {a}^{x \times y} [/tex]

Simplify the expression

We have

[tex]( { {x}^{ - \frac{4}{7} } })^{7} = {x}^{ - \frac{4}{7} \times 7 } \\ = {x}^{ - 4} [/tex]

Again using the rules of indices

That's

[tex] {x}^{ - y} = \frac{1}{ {x}^{y} } [/tex]

The final answer is

[tex] \frac{1}{ {x}^{4} } [/tex]

Hope this helps you

The answer is the first one

the ratio of Encik Arif's mass to his sons mass is 3:2 . If his son's mass is 42 kg, find Encik Arif's mass.​

Answers

Answer:

Encik Arif's mass is 63kg

Step-by-step explanation:

Let Encik Arif's mass be x

the ratio of Encik Arif's mass to his son's mass is 3:2

That's

[tex] \frac{3}{2} [/tex]

The son's mass is 42, so the ratio of Encik Arif's mass to his son's is

x : 42

That's

[tex] \frac{x}{42} [/tex]

Now equate the two fractions

That's

[tex] \frac{3}{2} = \frac{x}{42} [/tex]

Cross multiply

3(42) = 2x

126 = 2x

Divide both sides by 2

We have the final answer as

x = 63

Hope this helps you

I need help with #66 and #68

Answers

Step-by-step explanation:

66. Δy = -3.4 Δx

Δy/Δx = -3.4

The slope of the line is -3.4. Slope-intercept equation of the line is:

y = -3.4x + b

Plug in the given point to find b:

2 = -3.4(4) + b

b = 15.6

Therefore, the equation is y = -3.4x + 15.6.

Use the equation to find the y coordinates.

[tex]\left[\begin{array}{cc}x&y\\-4&29.2\\4&2\\6&-4.8\\18&-45.6\end{array}\right][/tex]

68. Repeat the same steps as 66.

Δy = -1.7 Δx

Δy/Δx = -1.7

The slope of the line is -1.7. Slope-intercept equation of the line is:

y = -1.7x + b

Plug in the given point to find b:

3 = -1.7(-7) + b

b = -8.9

Therefore, the equation is y = -1.7x − 8.9.

Use the equation to find the x or y coordinates.

[tex]\left[\begin{array}{cc}x&y\\-19&23.4\\-7&3\\-2.412&-4.8\\3.2&-14.34\\9.1&-24.37\end{array}\right][/tex]

Solve -4r + 18= 6 I need this equation

Answers

the answer I got is R=3

Answer:

r = 3

Step-by-step explanation:

[tex]-4r + 18= 6\\\\\mathrm{Subtract\:}18\mathrm{\:from\:both\:sides}\\\\-4r+18-18=6-18\\\\\mathrm{Simplify}\\\\-4r=-12\\\\\mathrm{Divide\:both\:sides\:by\:}-4\\\\\frac{-4r}{-4}=\frac{-12}{-4}\\\\\mathrm{Simplify}\\\\r=3[/tex]

Let f(x) = 1/x+2 and g (x) = 1/x-3. Find (f/g) (x). Assume all appropriate restrictions to the domain. help!!!!

Answers

Answer:(f/g)(x)=(1+2x)/(1-3x) where x<>0

Step-by-step explanation:

f(x)= 1/x+2= (1+2x)/x  ,   x<>0

g(x)=1/x-3=(1-3x)/x    , x<>0

=>f(x)/g(x)= (1+2x)/(1-3x)    ,  x<>0

(3+4i)+(8+2i) complex number in standard form

Answers

Answer:

(3 + 4i) + (8 + 2i) = 3 + 4i + 8 + 2i

(3 + 4i) + (8 + 2i) = (3 + 8) + (4i + 2i)

(3 + 4i) + (8 + 2i) = 11 + 6i

hope it helps if yes mark me BRAINLIEST!

Tysm!

:)

Answer:

11 + 6i

Step-by-step explanation:

Well, by the looks of it, you're combining like terms.  Just add numbers that have the same variable or jut add coefficients:

(3 + 4i) + (8 + 2i)

=  3 + 4i + 8 + 2i

= (3 + 8) + (4i + 2i)

= 11 + 6i

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