MATHEMATICS HIGH SCHOOL

Firewood is stacked in a pile. The bottom row has 20 logs, and the top row was 14 logs. Each row has one more log than the row above it. How many logs are in the pile?

Answers

Answer 1

Answer:

Since, each row has one more log than the row above it

so, this is arithematic sequence

We are given that

First row is

$=14$

so,

$a_1=14$

Last row is

$=20$

so,

$a_n=14$

Each row has one more log than the row above it

so,

$d=1$

now, we can find number of rows

$a_n=a_1+(n-1)d$

we can plug values

$20=14+(n-1)1$

we can solve for n

$6=(n-1)1$

$n=7$

now, we can find total number of logs

$S=(n(a_1+a_n))/(2)$

now, we can plug values

$S=(7(14+20))/(2)$

$S=119$

So,

Number of logs in the pile are 119........Answer

Answer 2

Answer:

The log in the pile is an illustration of arithmetic progression.

The number of logs in the pile is 119.

The first term of the progression is:

$\mathbf{a =14}$

The last term is:

$\mathbf{L =20}$

The common difference is:

$\mathbf{d =1}$

First, we calculate the number of terms using:

$\mathbf{L = a +(n - 1)d}$

So, we have:

$\mathbf{20= 14 +(n - 1) * 1}$

$\mathbf{20 = 14 +(n - 1) }$

Subtract 14 from both sides

$\mathbf{n - 1 = 6}$

Add 1 to both sides

$\mathbf{n = 7}$

The number of logs in the pile is calculated using the sum of n terms of an AP formula:

$\mathbf{S_n = (n)/(2)(a + L)}$

So, we have:

$\mathbf{S_n = (7)/(2)(14 + 20)}$

$\mathbf{S_n = 3.5(34)}$

$\mathbf{S_n = 119}$

Hence, the number of logs in the pile is 119.

Read more about arithmetic progressions at:

brainly.com/question/13989292

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The following function represents the value of a house, in dollars, after x years:f(x) = 242,000(1.04)x

What does 242,000 represent?

The present value of the house
The value of the house after x years
The increase in the value of the house each year
The increase in the value of the house after x years

Answers

Answer: The present value of the house

Step-by-step explanation:

Given: The following function represents the value of a house, in dollars, after x years:

$f(x) = 242,000(1.04)^x$

When we substitute x=0 in the above equation, we get

$f(0)=242,000(1.04)^0=242,000(1)=242,000$

Since at x=0, the function represent the initial value of a function.

Therefore, 242,000 represents the value of house in 0 years i.e. it represents the present value of the house.

A. The present value of the house

What is the fraction ten twelthes in its simplest form

Answers

ten twelfths in simplest form is five sixths.

10/12 in simplest form =5/6

PLEASE HELPWhat is the perimeter of DEFG, shown?

A. 26.12
B. 18.06
C. 36.12
D. 13.06

Answers

The answer is the option A: A. 26.12

The explanation is shown below:

1. As you need the perimeter, you can divide the figure into three triangles (as you can see in the figure attached) to calculate the length of the diagonal lines, which would be the hypotenuses of the triangles.

2. You must apply the Pythagorean Theorem to calculate the hypotenuse of each triangle:

- Red triangle (The legs are 3 and 4):

$h=\sqrt{3^(2)+4^(2)} =5$

- Blue triangle (The legs are 1 and 2):

$h=\sqrt{1^(2)+2^(2)} =2.23$

-Green triangle (The legs are 3 and 5):

$h=\sqrt{3^(2)+5^(2)} =5.83$

3. The figure has is symmetric with respect to the y-axis. So, you can multiply the sum of the hypotenuses obtained by two to calculate the perimeter:

$Perimeter=2(5+2.23+5.83)=26.12$

Need help ASAP! What similarity property, if any, can be used to show that the following two triangles are similar?A.) SAS
B.) Not enough information given
C.) SSS