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lara [203]
3 years ago
14

Expand completely using the Binomial Theorem (3y - x)^4

Mathematics
1 answer:
AleksAgata [21]3 years ago
4 0

Answer:

In standard form it is x^4 - 12x^3y + 54x^2y^2 - 108x y^3 + 81y^4.

Step-by-step explanation:

(3y)^4 + 4C1(3y)^3(-x) + 4C2(3y)^2(-x)^2 + 4C3(3y)(-x)^3  + (-x)^4

= 81y^4 - 108y^3x + 54y^2x^2 - 12yx^3 + x^4

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Find the distance between these points. <br> A(5,8), B(-3,4)
konstantin123 [22]

Answer:

<u>Distance</u><u> </u><u>between</u><u> </u><u>the</u><u> </u><u>points</u><u> </u><u>is</u><u> </u><u>8</u><u>.</u><u>9</u><u>4</u><u> </u><u>units</u>

Step-by-step explanation:

General formula:

{ \boxed{ \bf{distance =  \sqrt{ {(x_{1} - x _{2} )}^{2} +  {(y _{1} - y _{2} ) }^{2}  } }}}

substitute:

{ \sf{ =  \sqrt{ {(5 - ( - 3))}^{2}  +  {(8 - 4)}^{2} } }} \\  = {  \sf{ \sqrt{64 + 16} }} \\  = { \sf{ \sqrt{80} }} \\  = 8.94 \: units

{ \underline{ \sf{ \blue{christ \: † \: alone}}}}

6 0
3 years ago
Read 2 more answers
Which of the following comparisons is correct?<br>-2 2<br>4&lt;−4<br>−6&lt; −5
zlopas [31]
<h3>Answer: Choice D)   -6 < -5</h3>

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

Explanation:

Let's go through the answer choices

  • A) This is false because -2 is actually larger than -5. Make a number line and you'll see that -2 is to the right of -5. Numbers on the right are larger than numbers on the left.
  • B) This is also false. The value 0 is smaller than 2. A number line might help show this.
  • C) Also false. It should be 4 > -4. Any positive number is always larger than any negative number.
  • D) This is true. On a number line, -6 is to the left of -5, so -6 is smaller than -5. This makes -6 < -5 a true statement.

4 0
3 years ago
FIND THE GCF. Mathematics
Rom4ik [11]

The G.C.F of the given algebraic expression is; ⁴⁹/₆a xy

<h3>What is the G.C.F (Greatest Common Factor)?</h3>

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.

We are given the algebraic expression;

(3 x y * 4x²y * ¹/₁ * 5x³y ^ z * 4)7a * 1/1 * 7*6

Expanding this further gives;

⁴⁹/₆a((3xy * 4x²y * 20x³y ^ z )

Now, the GCF of the terms inside the bracket would be x y. Thus, expanding the GCF  we have;

⁴⁹/₆a xy((3 * 4x * 20x²y^(z - 1))

Read more about G.C.F at; brainly.com/question/219464

#SPJ1

5 0
2 years ago
Donovan reaches into a jar containing 6 red marbles, 3 blue marbles, 4 yellow marbles, and 5 green marbles,
vredina [299]
12 out of 18. This is because there is 6 red marbles and 18 of them all together. The question states the probability of the red marble NOT being chosen therefore you need to take away 6 from 18 leaving you with 12. I hope this made sense :)
5 0
3 years ago
What is the area of the shaded region <br> 1cm is in the middle
Archy [21]

Answer:

Area of the shaded region= 128.86\,cm^2

Step-by-step explanation:

Area of the shaded region=Area of the rectangle-Area of the circle

Area of rectangle= Length\times Width

Length=11\,cm\\Width=12\,cm

Area is:

           =11\times 12\\\\=132\,cm^2

Area of the circle = \pi \times r^2

r=1\,cm

As,        \pi =\dfrac{22}{7} =3.14

Area of the Circle is :

           =3.14\times 1 \times 1\\\\=3.14\times 1\\\\=3.14\,cm^2

Area of the Shaded region:

Area of the shaded region=132-3.14\\\\=128.86\,cm^2

5 0
3 years ago
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