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4 years ago

15

Is the following sequence arithmetic? If so, identify the common difference.

1 answer:

melisa1 [442]4 years ago

4 0

Answer:

D(Yes;-5) is correct.

Step-by-step explanation:

Let's check 2 consecutive numbers

A(1) = 18

A(2) =13

=> common difference=A(2)-A(1) = 13-18 =-5

(Also, we see A(4)-A(3) = A(3)-A(2) =-5)

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In the expansion (ax+by)^7, the coefficients of the first two terms are 128 and -224, respectively. Find the values of a and b

madam [21]

Answer:

a = 2, b = 3.5

Step-by-step explanation:

Expanding $(ax+by)^7$ using Binomial expansion, we have that:

$(ax+by)^7$ =

$(ax)^7(by)^0 + (ax)^6(by)^1 + (ax)^5(by)^2 + (ax)^4(by)^3 + (ax)^3(by)^4 + (ax)^2(by)^5 + (ax)^1(by)^6 + (ax)^0(by)^7$

$= (a)^7(x)^7+ (a)^6(x)^6(b)(y) + (a)^5(x)^5(b)^2(y)^2 + (a)^4(x)^4(b)^3(y)^3 + (a)^3(x)^3(b)^4(y)^4 + (a)^2(x)^2(b)^5(y)^5 + (a)(x)(b)^6(y)^6 + (b)^7(y)^7\\\\\\= (a)^7(x)^7+ (a)^6(b)(x)^6(y) + (a)^5(b)^2(x)^5(y)^2 + (a)^4(b)^3(x)^4(y)^3 + (a)^3(b)^4(x)^3(y)^4 + (a)^2(b)^5(x)^2(y)^5 + (a)(b)^6(x)(y)^6 + (b)^7(y)^7$

We have that the coefficients of the first two terms are 128 and -224.

For the first term:

=> $a^7 = 128$

=> $a = \sqrt[7]{128}\\ \\\\a = 2$

For the second term:

$a^6b = -224$

$b = \frac{-224}{a^6}$

$b = \frac{-224}{2^6} \\\\\\b = \frac{-224}{64} \\\\\\b = 3.5$

Therefore, a = 2, b = 3.5

5 0

3 years ago

Write a verbal expression for 2n+7

dimaraw [331]

7 more than twice a number, c

7 0

3 years ago

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Part A: The area of a square is (9x2 + 24x + 16) square units. Determine the length of each side of the square by factoring the

ella [17]

Answer:

Step-by-step explanation:

Part A

9x^2 + 24x + 16

= (3x + 4)(3x + 4)

length of each side = 3x + 4 units.

Par B

16x^2 - 25y^2

= (4x + 5y )( 4x - 5y)

length = 4x + 5y and width = 4x - 5y

4 0

3 years ago

The seniors on the student council bought a total of 36 plants to use in landscaping the front of the school. They bought some a

Artyom0805 [142]

Answer: B

Step-by-step explanation:

y = azaleas

x = lilies

6y + 5x =196 total cost

y + x = 36 total number of items

y = 36 – x

6(36 -x ) +5x =196

216 – 6x + 5x = 196

-x = 196 – 216

-x = -20

Divide by -1

X = 20 lilies

Plug into y equation

Y = 36 – 20

Y= 16 azaleas

To check

6(16) + 5(20) = 196

96 + 100 = 196

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3 years ago

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Molly is studying two number pattems. Patter A starts at 0 and has the rule "add 3." Pattern B starts at 0 and has the rule "add

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Answer: See explanation..

Step-by-step explanation: Click here for your answer brainly.com/question/27458283

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2 years ago