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3 years ago

Can someone please help me with 2 and explain the steps to 3 thanks!

Mathematics

1 answer:

Gelneren [198K]3 years ago

7 0

Answer:

#2 is a ratio so you gotta add.

#3 it’s just adding it for example 2p + 5a = 7pa

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What is the 12th term of the sequence 3,6,12,24....

Sati [7]

$a_{0}$ =3

r=common ratio: 12/6=2; 6/3=2

r=2, $a_{n}$ = $2^{n-1}$ *3

plug in 12 for n:

$a_{12}$ = $2^{12-1}$ *3

$a_{12}$ = $2^{11}$ *3

$a_{12}$ =2048*3

$a_{12}$ =6144

The twelfth term in the sequence is 6144

7 0

4 years ago

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Which expression is a sum of cubes?

erik [133]

we know that

A polynomial in the form $a^{3} +b^{3}$ is called a sum of cubes

Let's verify each case to determine the solution

<u>case A)</u> $-64x^{6} y^{12} +125x^{16} y^{3}$

we know that

$-64=-4^{3}$

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{16}=x^{15} *x=x*(x^{5})^{3}$ -------> is not a perfect cube

$y^{3}= (y)^{3}$

therefore

the case A) is not a sum of cubes

<u>case B)</u> $-32x^{6} y^{12} +125x^{16} y^{3}$

we know that

$-32=-2^{5}$ -------> is not a perfect cube

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{16}=x^{15} *x=x*(x^{5})^{3}$ -------> is not a perfect cube

$y^{3}= (y)^{3}$

therefore

the case B) is not a sum of cubes

<u>case C)</u> $32x^{6} y^{12} +125x^{9} y^{3}$

we know that

$32=2^{5}$ -------> is not a perfect cube

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{9}=(x^{3})^{3}$

$y^{3}= (y)^{3}$

therefore

the case C) is not a sum of cubes

<u>case A)</u> $64x^{6} y^{12} +125x^{9} y^{3}$

we know that

$64=4^{3}$

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{9}=(x^{3})^{3}$

$y^{3}= (y)^{3}$

Substitute

$4^{3}(x^{2})^{3}(y^{4})^{3} +5^{3}(x^{3})^{3}(y)^{3}$

$(4x^{2}y^{4})^{3} +(5x^{3}y)^{3}$

therefore

<u>the answer is</u>

$64x^{6} y^{12} +125x^{9} y^{3}$ is a sum of cubes

6 0

3 years ago

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Juan has 6 times as many baseball cards as Nick. If Juan has 192 cards, how many does Nick have?

inessss [21]

<h3>Answer:</h3>

<h3>Step-by-step explanation:</h3>

Divide 192 by 6, to find the amount of baseball cards Nick has.

192 ÷ 6 = <u>32</u>

<h3><u>Check:</u></h3>

32 · 6 = 192

192 ÷ 6 = 32

Nick has 32 baseball cards, which is 6 times less than Juan's amount.

7 0

3 years ago

Georgia has some 4-inch cubes like the one shown below. Georgia will put the cubes in the box shown below.

marishachu [46]

The question is incomplete. The complete question is :

Georgia has some 4-inch cubes like the one shown below. Georgia will put the cubes in the box shown below. What is the total number of cubes that Georgia needs to exactly cover the bottom of the box with a layer one cube deep?

Solution :

It is given that :

There are small cubes that has a dimension of 4 in x 4 in x 4 in.

There is also a box which has a dimension of 24 in x 20 in x 12 in.

We need to find out how many small cubes will Georgia need to cover the bottom of the box.

So, we need to find out the surface area of the one cube and the box.

Therefore, the surface area of one cube = side x side

= 4 inch x 4 inch

= 16 square inches

Similarly the area of the box can be find by = length x breath

= 24 in x 20 in

= 480 square inches

Therefore, dividing the area of the box by the area of the cube, we get

$=\frac{480}{16}$

= 30

So Georgia will require exactly 30 cubes to cover the bottom of the box with a layer of one cube deep.

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3 years ago

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dexar [7]

The absolute value of a number gives its distance from zero

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