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pentagon [3]
3 years ago
13

There are three separate, equal-size boxes, and inside each box there are four separate small boxes, and inside each of the smal

l boxes there are three even smaller boxes. how many boxes are there all together?

Mathematics
1 answer:
VMariaS [17]3 years ago
7 0

3 big + 3 x 4 small  x 3 x 4 x 3 smaller

= 3 big + 12 small + 36 smaller

= 51 total

see attachment for visualization

Answer: 51

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Use complete sentences to describe why √-1 ≠ -√1
tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

<u>D</u><u>e</u><u>f</u><u>i</u><u>n</u><u>i</u><u>t</u><u>i</u><u>o</u><u>n</u>

\displaystyle \large{ {y}^{2}  = x} \\  \displaystyle \large{ y =  \pm  \sqrt{x} }

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

<u>D</u><u>e</u><u>f</u><u>i</u><u>n</u><u>i</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>I</u><u>I</u>

\displaystyle \large{  {a}^{2}  = a \times a =  |b| }

Where b is the result from a×a. Let's see an example.

<u>E</u><u>x</u><u>a</u><u>m</u><u>p</u><u>l</u><u>e</u><u>s</u>

\displaystyle \large{  {2}^{2}  = 2 \times 2 = 4} \\  \displaystyle \large{  {( - 2)}^{2}  = ( - 2) \times ( - 2) =  | - 4|  = 4}

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

\displaystyle \large{   {y}^{2}  =  - 1}

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

\displaystyle \large{   \sqrt{ {y}^{2} } =   \sqrt{ - 1}  }

Then where does plus-minus come from? It comes from one of Absolute Value propety.

<u>A</u><u>b</u><u>s</u><u>o</u><u>l</u><u>u</u><u>t</u><u>e</u><u> </u><u>V</u><u>a</u><u>l</u><u>u</u><u>e</u><u> </u><u>P</u><u>r</u><u>o</u><u>p</u><u>e</u><u>r</u><u>t</u><u>y</u><u> </u><u>I</u>

\displaystyle \large{  \sqrt{ {x}^{2}  } =  |x|  }

Solving absolute value always gives the plus-minus. Therefore...

\displaystyle \large{  y =   \pm \sqrt{ - 1}  }

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

\displaystyle \large{   {y}^{2}  = 1} \\  \displaystyle \large{    \sqrt{ {y}^{2} }  =  \sqrt{1} } \\  \displaystyle \large{  y  =  \pm  \sqrt{1} }

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

<u>C</u><u>o</u><u>n</u><u>c</u><u>l</u><u>u</u><u>s</u><u>i</u><u>o</u><u>n</u>

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

5 0
2 years ago
Read 2 more answers
Nicole sold 1 cherry pie and 9 pumpkin pies for $60. Lisa sold 11 cheery pies and 4 pumpkin pies for $90. what's the cost each o
zubka84 [21]
X= cost per cherry pie
y= cost per pumpkin pie

NICOLE
1x + 9y= $60

LISA
11x + 4y= $90


STEP 1
multiply Nicole's equation by -11

-11(1x + 9y)= -11($60)
multiply -11 by all terms

(-11 * x) + (-11 * 9y)= (-11 * 60)

-11x - 99y= -660


STEP 2
add Nicole's new equation from step 1 to Lisa's equation to solve for y (using the elimination method)

-11x - 99y= -660
11x + 4y= 90
the x terms "cancel out"

-95y= -570
divide both sides by -95

y= $6 per pumpkin pie


STEP 3
substitute y value into either original equation to solve for x

x + 9y= $60

x + 9(6)= 60

x + 54= 60
subtract 54 from both sides

x= $6 per cherry pie


CHECK
11x + 4y= $90
11(6) + 4(6)= 90
66 + 24= 90
90= 90


ANSWER: Each cherry pie costs $6 and each pumpkin pie costs $6.

Hope this helps! :)
3 0
3 years ago
❗❗❗PLS I NEED HELP ON THIS I DON'T UNDERSTAND PLS HELP❗❗❗❗❗❗
andrezito [222]
Where yo mamas attttt , 5-(4)= 23

8 0
3 years ago
Item 2<br> Write the word sentence as an equation.<br><br> A number m<br> increased by 5 is 7.
Alex

Answer:

m+5=7

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
(2x³+4x²-x+8) / (x² + 3x + 2)
a_sh-v [17]

\dfrac{2x^3+4x^2 -x+8}{x^2 +3x+2}\\\\\\=\dfrac{2x^3+6x^2+4x-2x^2-6x-4+x+12}{}\\\\=\dfrac{2x(x^2 +3x+2)-2(x^2 +3x+2)+x+12}{x^2 +3x+2}\\\\\\=\dfrac{2x(x^2+3x+2)}{x^2 +3x +2 }- \dfrac{2(x^2 +3x +2)}{x^2 +3x +2 } + \dfrac{x+12}{x^2 +3x+2}\\\\\\=2x-2 + \dfrac{x+2}{x^2 +3x +2}\\\\\\=2x-2 + \dfrac{x+12}{x^2 +2x +x +2}\\\\\\=2x-2 + \dfrac{x+12}{x(x+2) + x+2}\\\\\\=2x-2 + \dfrac{x+12}{(x+1)(x+2)}\\

3 0
2 years ago
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