Don saves $1 the first week, 2$ the second week, $3 the third week, and $4 the fourth week. If he continues in this way, how many weeks will it take before Don has saved at least $50?Please show me the simplest and quickest way to solve this problem. EXPLAIN YOUR STEPS THOROUGHLY!!

Answers

Answer 1

Answer: This forms an arithmetic sequence, where the first term = 1, common difference = 1, and number of terms = n.

The formula for the sum of an arithmetic sequence is

$S_(n) = (1)/(2)n(2a + (n - 1)d)$

Where a = the first term and d = the common difference.

We want the sum to be at least $50, so
$50 \leq (1)/(2)n(2a + (n - 1)d)$

Substituting in a and d
$50 \leq (1)/(2)n(2(1) + (n - 1)(1))$

Rearranging
$50 \leq (1)/(2)n(2 + (n - 1))$
$50 \leq (1)/(2)n(1 + n)$
$100 \leq n(1 + n)$
$100 \leq n^2 + n$
$0 \leq n^2 + n - 100$

$\text{Let } n^2 + n -100 = 0$
$n = (-1 \pm √(1-4(1)(-100)))/(2)$
$n = (-1 \pm √(401))/(2)$
$n \geq 0 \implies n = (-1 + √(401))/(2)$
$n \approx 9.51$

So it will take 9.51 weeks, or 10 weeks to the nearest week.

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Write a number that is greater than 8.604 but less than 8.643

Find the domain:

y= (6+9x)/(6−|x−1|)

Answers

Answer:

The domain = {x : x ≠ -5 , 7}

Step-by-step explanation:

- The domain of the function is the values of x which makes the function

defined

- If the function has a denominator then the domain is all the values of x

except the zeroes of the denominator

- Zeroes of the denominator means the values of x when the

denominator = 0

- The function is $y=(6+9x)/((6-Ix-1I))$

- To find the domain of the function find the zeroes of the denominator

∵ The denominator is ⇒ 6 - Ix - 1I

∴ 6 - Ix - 1I = 0

- Subtract 6 from both sides

∴ - Ix - 1I = -6

- Multiply both sides by -1

∴ Ix - 1I = 6

- The absolute value of x - 1 = 6 that means x - 1 = 6 OR x - 1 = -6

∵ x - 1 = 6

- Add 1 to both sides

∴ x = 7

∵ x - 1 = -6

- Add 1 to both sides

∴ x = -5

∴ The zeroes of the denominator are -5 and 7

∵ x = -5 and x = 7 make the denominator = 0

- Any value divided by 0 is undefined

∴ x can be any value except -5 and 7

∴ The domain of the function is all real values of x except -5 and 7

* The domain = {x : x ≠ -5 , 7}

A line passes through (6,3),(8,4),and (n,-2). Find the value of n.
please help :)

Answers

You would do 8-6=2 4-3=1

1/2 is your slope

1/2(6)=3
3-3=0

Your equation would be y=1/2x

So your n value is -4

Micah has 294 songs stored in his phone which is 70% of the songs that Jorge has stored on his phone. How many songs are stored on Jorge's phone?

Answers

Since we know that 70% of then number of Jorge's songs is 294, we can represent this with the ratio 70/100 (70%) = 294/x, with x being the total number of songs Jorge has.
To solve this, cross multiply.
70 * x = 100 * 294 ----------> 70x=29400
Divide both sides by 70
x=420

Answer:

jorge has 420 song

Step-by-step explanation:

If y=14 when x=8, find y when x=12

Answers

x=12 because 4x=7y so if there were 21y then it would be 4 * 3 which is 12

List all of the prime numbers less than 20 in numerical order

Answers

a prime number is a number only divisible by itself and 1 (this excludes decimals and fractions)

surprise, 1 is not prime because it must be divisible by itself and 1 and the factors of 1 are 1 and 1 so 1 is not prime

2 is prime because it is the first even counting number and since all even numbers after 2 are divisble by 2 you can cross out all odd numbers after 2
3 is prime because it is the first odd counting number that satisfies the condition
4 is not because it is even
5 is prime
6 is not because it is even
7 is prime
8 is not because it is even
9 is not
10 is not because it is even
11 is prime
12 is not because it is even
13 is prime
14 is not because it is even
15 is not
16 is not because it is even
17 is prime
18 is not because it is even
19 is prime
20 is not because it is even

so the numbers are 2,3,5,7,11,13,17,19

19, 17, 13, 11, 7, 5, 3, 2

Sarah is solving the equation -7/8x=24

Answers

the answer would be -21 because you would have to multiply the 24 by -7 because it is dividing on the other side. and then you would have to divide the number you get by 8

so basically, it will look like this step by step:

-7/8x=24

8x=24*-7

8x=-168

x=-168/8

x= -21

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