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3 years ago

A rectangular prism is made of 81 unit cubes. The prism is 9 unit cubes long.

Mathematics

1 answer:

dimaraw [331]3 years ago

4 0

Answer:

A width: 3 unit cubes

height 3 unit cubes

Step-by-step explanation:

Volume of rectangular prism = 81 unit cubes

$l$ = Length of rectangular prism = 9 unit cubes

$w$ = Width of rectangular prism

$h$ = Height of rectangular prism

Volume of a rectangular prism is given by

$V=lwh\\\Rightarrow 81=9wh\\\Rightarrow wh=\dfrac{81}{9}\\\Rightarrow wh=9$

The product of width and height must be 9 so from the options this is only possible when width and height both are 3 units.

So, the width is 3 unit cubes and the height is 3 unit cubes.

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Answer:

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Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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3 years ago

A solid box of 90cm, width 30cm and length 80cm needs to be painted. The paint costs £0.03 per cm². How much will it cost to pai

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Step-by-step explanation:

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3 years ago

Which function transforms the graph of y=x^2 so that it is first shifted down 4 units and is then reflected across the y-axis?

Xelga [282]

$\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
% templates
f(x)= A( Bx+ C)+ D
\\\\
~~~~y= A( Bx+ C)+ D
\\\\
f(x)= A\sqrt{ Bx+ C}+ D
\\\\
f(x)= A(\mathbb{R})^{ Bx+ C}+ D
\\\\
f(x)= A sin\left( B x+ C \right)+ D
\\\\
--------------------$

$\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\
\bullet \textit{ flips it upside-down if } A\textit{ is negative}\\
~~~~~~\textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if } B\textit{ is negative}\\
~~~~~~\textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\
~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\
~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by } D\\
~~~~~~if\ D\textit{ is negative, downwards}\\\\
~~~~~~if\ D\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{ B}$

with that template in mind, let's check,

down 4 units, D = -4

flipped over the y-axis, B = -1

$\bf y=x^2\implies y=\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{+0})^2\stackrel{D}{+0}\qquad \qquad \stackrel{shifted}{y=\stackrel{A}{1}(\stackrel{B}{-1}x\stackrel{C}{+0})^2\stackrel{D}{-4}}
\\\\\\
y=-x^2-4$

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3 years ago

Explain in your own words how to rewrite an equation (function) in slope-intercept form if the equation is presented to you in s

Elena L [17]

Standard form : Ax + By = C
slope intercept form : y = mx + b

example :
2x + 3y = 10....we want the 3y term by itself...so subtract 2x from both sides
3y = -2x + 10 .....now we have to divide both sides by 3 to get y alone
y = (-2/3)x + 10/3 <== slope intercept form...u dont need the parenthesis in there, I was just showing u that I divided by 3

another one..
-4x + 5y = 9.....got to get 5y by itself....this time we add 4x
5y = 4x + 9...now divide both sides by 5 to get y alone
y = 4/5x + 9/5

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4 years ago

Read 2 more answers