Solve the equation for y.<br>28 = 24x

Calculate the sum of the first 36 terms of the arithmetic sequence defined in which a36=14 and the common difference is d=1/8

user100 [1]

Answer:

425.25

Step-by-step explanation:

Since we are given 36th term as 14 and we know common difference is $\frac{1}{8}$ , it means that from the first term, we add $\frac{1}{8}$ to each and get 14 on the 36th term. To figure out the first term, thus, we have to subtract $\frac{1}{8}$ 35 times from 14. Let's do it to get first term:

$14-35(\frac{1}{8})=\frac{77}{8}=9.625$

The sum of arithmetic sequence formula is:

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

Where,

$S_{n}$ is the sum of nth term (we want to figure this out for first 36 terms)
$a$ is the first term (we figured this out to be 9.625)
$n$ is the term number (36 for our case)
$d$ is the common difference (given as $\frac{1}{8}$ )

Substituting all the values, we get:

$S_{36}=\frac{36}{2}[2(9.625)+(36-1)(\frac{1}{8})]\\S_{36}=18[19.25+4.375]\\S_{36}=18[23.625]\\S_{36}=425.25$

First answer choice is right.

7 0

3 years ago

Read 2 more answers

1. A supermarket display consists of boxes of soda. The bottom row has 38 boxes. Each row has four fewer boxes than the row belo

Andreas93 [3]

Answer:

10 boxes in the top row.

192 boxes in entire display.

Step-by-step explanation:

Let n be the number of rows.

Given:

Total number of rows = 8

Boxes in bottom row = 38

And each row has four fewer boxes than the row below it.

Solution:

Part A:

We know that the bottom row has 38 boxes and each row has four fewer boxes than the row below it.

Using below function for determining the number of boxes in each rows.

$f(n)=38-(8-n)4$

Where:

n = Number of row.

We need to find the boxes in the first row.

So, substitute n = 1 in above function.

$f(1)=38-(8-1)4$

$f(1)=38-7\times 4$

$f(1)=38-28$

$f(1)=10$

Therefore, 10 boxes in the top row.

Part B:

Total boxes in the entire display.

Using formula as given below to determine the sum of the boxes in entire display.

$S_{n} = \frac{n}{2}(f(1)+f(n))$

Substitute n = 8, f(1) = 10 and f(8) = 38 in the above equation.

$S_{8} = \frac{8}{2}(10+38)$

$S_{8} = 4(48)$

$S_{8} = 4\times 48$

$S_{8} = 192\ boxes$

Therefore, 192 boxes in the entire display.

5 0

3 years ago

The function C(x) = 25x + 50 represents the labor cost (in dollars) for Certified Remodeling to build a deck, where x is

Whitepunk [10]

Answer:

Master Remodeling

Step-by-step explanation:

<em>Original question is attached</em>

<h3>Option 1</h3>

C(x) = 25x + 50
C(8) = 25*8 + 50 = $250

<h3>Option 2</h3>

As per table, the rate of change is $30 per 2 hours.
So 8 hours will cost
$190 + $30 = $220

As we see the second option is cheaper so we should hire the Master Remodeling

5 0

3 years ago

Let f(x) = -3x + 2 and g(x) = 2x – 5;<br> compute g(f(x))

ki77a [65]

Answer:

g(f(x)) = -6x+6.

Step-by-step explanation:

It is given that,

f(x) = -3x + 2 and g(x) = 2x – 5

We need to find g(f(x)).

Put it into g(x).

g(f(x)) = 2(-3x + 2)+2

= -6x+4+2

=-6x+6

Hence, the value of g(f(x)) is -6x+6.

8 0

2 years ago

Evaluate: 30 - 12÷3×2 =

lara [203]

Answer:

22

Step-by-step explanation:

We can use the order of operations (PEMDAS), to solve this equation.

We must first multiply and divide, and order. This means we divide 12 by 3 and get 4, then multiply that by 2 and get 8. (30-12÷3×2,30-4×2,30-8). Now we just subtract 8 from 30 and get 22 as our answer.

7 0

3 years ago

Solve the equation for y.28 = 24x – 7y​

Solve the equation for y.28 = 24x – 7y