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3 years ago

Find the common ratio of the geometric sequence -14, -84, -504,

Mathematics

1 answer:

Phantasy [73]3 years ago

8 0

Answer:

0.166667 - Common Ratio

step by step

Formula Used: Common Ratio=First term/Consecutive Term

Calculation: 0.166667=(-14)/(-84)

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There were 63 equal piles of plantain fruit put together and 7 single fruits. They were divided evenly among 23 travelers. What

antiseptic1488 [7]

Answer:

There are 28 fruits in each pile.

Step-by-step explanation:

We are given the following in the question:

Let x denote the number of fruits in each pile and y denote the number of fruits that every traveler receive.

Consider the diophantine equation:

$63x + 7 = 23y\\63x-23y = -7$

We obtain the greatest common divisor of (63,-23).

The greatest common divisor f 63 and -23 is 1.

Therefore, there exist $\alpha,\beta$ such that

$-23\alpha+63\beta=1$

By applying extended Euclidean Algorithm, we have,

$1 = (1\times 6)+(-1\times 5)\\1 = (1\times 17)+(3\times 6)\\1 = (3\times 23)+(-4\times 17)\\1 = (-4\times 40)+(7\times 23)\\1 = (7\times 63)+(-11\times 40)\\1 = (-11\times -23)+(-4\times 63)$

$1 = (-11\times -23) + (-4\times 63)$

Multiplying -7 on both sides, we get,

$-7 = (77\times -23) + 28\times 63)$

Thus, we get,

$x = 28\\y=77$

Thus, there are 28 fruits in each pile.

7 0

3 years ago

Mr Nelson paid $3.84 tax he pay the sales tax rate of 8% how much was item he was buying before sales tax was added

UkoKoshka [18]

Answer:

Mr. Nelson paid $48 befor tax.

Step-by-step explanation:

Let x be the price of the item before tax.

108 % * x - x = 3.84 (the tax itself)

27/25x - x = 3.84

2/25 x = 3.84

x = 48

3 0

2 years ago

Jacob is a teacher. He made 75 cookies to give to his students on the first day of school. He gave 2 cookies to each student who

Lisa [10]

Answer:

See explanation

Step-by-step explanation:

Jacob has 75 cookies.

He gave 2 cookies to each student.

Complete the table:

$\begin{array}{cc}\text{Number of student arrived}&\text{Number of cookies left}\\1&75-2=73\\2&73-2=71\\3&71-2=69\\...&...\end{array}$

Let n be the number of students. After nth student arrived Jacob had left

$g(n)=75-2n$

cookies.

This is an arithmetic sequence with

$g_1=g(1)=73\\ \\d=-2$

Thus,

$g_{n}=g_{n-1}-2\\ \\g(n)=g(n-1)-2$

3 0

3 years ago

Read 2 more answers

Solve the system of equations displayed in the picture.

bagirrra123 [75]

The answer is D) (-1,-12)

Reason:

1) substitute 2x-10 for y in y=4x-8

2) 2x-10=4x-8

3) -2x-10=-8

4) -2x=2

5) x=-1

6) substitute -1 for x in y=2x-10

7) y=(2)(-1)-10

8) y=-12

Answer

x=-1 and y=-12

7 0

3 years ago

How do you calculate the LCM for 128 and 256

Neporo4naja [7]

Answer:

I think its 256

Step-by-step explanation:

The LCM of 128 and 256 is 256. Steps to find LCM. Find the prime factorization of 128 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2; Find the prime factorization of 256.

6 0

2 years ago

Read 2 more answers