Use Pascal's triangle or the Binomial theorem to expand the binomials. 1. (3c-2d)^4
2. (2n+3)^5
3. (x^2+4)^3

Answers

Answer 1

Answer: $(3c-2d)^4=(3c)^4-4(3c)^3\cdot2d+6\cdot(3c)^2\cdot(2d)^2-4\cdot3c\cdot(2d)^3-(2d)^4\n\n=81c^4-216c^3d+216c^2d^2-96cd^3-16d^4\n-------------------------------\n(2n+3)^2\n=(2n)^5+5(2n)^4\cdot3+10(2n)^3\cdot3^2+10(2n)^2\cdot3^3+5\cdot2n\cdot3^4+3^5\n\n=32n^5+240n^4+720n^3+1080n^2+810n+243\n-------------------------------\n(x^2+4)^3=(x^2)^3+3(x^2)^2\cdot4+3x^2\cdot4^2+4^3\n\n=x^6+12x^4+48x^2+64$

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1, 5, 9, 13...Generalize the pattern by finding the nth term.

A) n2
B) n + 4
C) 4n - 3
D) 3n + 1

Answers

C. ................jhAn

16 raised to the second power + X raised to the second power = 30 raised to the second power. QUESTION: What does X equal?

Answers

$16^2+x^2=30^2\n x^2=900-256\n x^2=644\n x=√(644) \vee x=-√(644)\n x=2√(161) \vee x=-2√(161)$

Round 342 to the nearest ten

Answers

342 rounded to the nearest ten is,340.

Which image (A'B'C'D') of ABCD cannot be produced using only reflection?

Answers

The image (A'B'C'D') of ABCD , in Option C cannot be produced using only reflection.

What is an Image of a Figure ?

Image is the copy of a figure made along the axis.

The figure attached as two figures , object and image ,the image has some transformation done to it

Figure 1 , option 1 :

In the figure

Object Coordinates :

ABCD : ( -6 ,4) , (-6,6) , (-2,6) , (-4,4)

A'B'C'D' : ( 6,-4) , (6,-6) , (2,-6) , (4,-4)

Figure 2 :

Object Coordinates :

ABCD : ( -6 ,4) , (-6,6) , (-2,6) , (-4,4)

A'B'C'D' : ( 4 , -6) , (6,-6) , (6,-2 ) , (4,-4)

Figure 3

Object Coordinates :

ABCD : ( -6 ,4) , (-6,6) , (-2,6) , (-4,4)

A'B'C'D' : ( 6 , -6) , (6,-4) , (2,-4 ) , (4,-6)

Figure 4

Object Coordinates :

ABCD : ( -6 ,4) , (-6,6) , (-2,6) , (-4,4)

A'B'C'D' : (4 , 6) , (6,6) , (2,6 ) , (4,4)

As all the image formed is just by reflection except of Option C , Figure 3.

Therefore Option C is the answer.

To know more about Image

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If you multiply an inequality by a positive number _____.switch the inequality sign
keep the inequality sign the same

Answers

Answer: If you multiply an inequality by a positive number keep the inequality sign the same

Explanation: There are certain rules that should be kept in mind while solving the inequality:

1. When a number is added or subtracted from each side of an inequality the direction of the inequality does not change

2. When each side of an inequality is multiplied or divided by a positive number the direction of the inequality does not change

3. When each side of an inequality is multiplied or divided by a negative number the direction of the inequality does change

Keep the inequality sign the same

The formula P = ns gives the formula for the perimeter of a regular polygon with n sides and side length s.What is the length of each side of a regular octagon with a perimeter of 54.4 cm? A regular octagon has 8 equal sides.