Expand and Simplify<br> 3(p+5)-3(p+2)

The fourth term of an Arithmetic Sequence is equal to 3 times the first term, and the seventh term exceeds twice the third term

11Alexandr11 [23.1K]

Answer:

The first term is 3. The common difference is 2.

Step-by-step explanation:

The first term is x.

The common difference is d.

The second term is x + d.

3rd term: x + 2d

4th term: x + 3d

7th term: x + 6d

"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"

x + 3d = 3 * x Eq. 1

"the seventh term exceeds twice the third term by 1"

x + 6d = 2(x + 2d) + 1 Eq. 2

Simplify Eq. 1:

2x = 3d

Simplify Eq. 2:

x + 6d = 2x + 4d + 1

x = 2d - 1

Multiply both sides of the last equation by 2.

2x = 4d - 2

2x = 3d (simplified Eq. 1)

Since 2x = 2x, then the right sides are equal.

3d = 4d - 2

d = 2

2x = 3d

2x = 3(2)

2x = 6

x = 3

Answer: The first term is 3. The common difference is 2.

8 0

3 years ago

What is 2.99 as a fraction

Serga [27]

2.99

2 is a whole number

0.99 = 99/100

your fraction is:

mixed number = 2 99/100
improper fraction = 299/100 (multiply whole number to denominator & then add numerator)

hope this helps

8 0

3 years ago

Read 2 more answers

Which is the solution to (8.5 x 103)(2 x 105) expressed in scientific notation?

kenny6666 [7]

We have been given an expression $(8.5\times 10^3)(2\times 10^5)$ . We are asked to find the solution to our given expression expressed as scientific notation.

Let us simplify our given expression.

Using exponent property $a^m\cdot a^n=a^{m+n}$ , we will get:

$8.5\times 2\times 10^3\times 10^5$

$17\times 10^{3+5}$

$17\times 10^{8}$

Now to write our answer in scientific notation, we need our 1st multiple between 1 and 10. So we will rewrite our expression as:

$1.7\times 10\times 10^{8}$

$1.7\times 10^{1+8}$

$1.7\times 10^{9}$

Therefore, our required solution would be $1.7\times 10^{9}$ .

8 0

3 years ago

HELP MEEEEE PLEASEEEEEE

Sindrei [870]

Answer:

$x=16\dfrac{28}{37}\\ \\y=5\dfrac{1}{3}\\ \\z=7.5$

Step-by-step explanation:

The diagram shows three paralel lines which divide the large triangle into three similar triangles.

By Thales theorem,

$\dfrac{5}{z}=\dfrac{y}{8}=\dfrac{2}{3}$

Then

$\dfrac{5}{z}=\dfrac{2}{3}\Rightarrow 2z=15,\ z=7.5\\ \\\dfrac{y}{8}=\dfrac{2}{3}\Rightarrow 3y=16,\ y=\dfrac{16}{3}=5\dfrac{1}{3}$

From the similarity of triangles,

$\dfrac{x}{20}=\dfrac{z+8}{z+8+3}\\ \\\dfrac{x}{20}=\dfrac{7.5+8}{7.5+8+3}\\ \\\dfrac{x}{20}=\dfrac{15.5}{18.5}\\ \\x=20\cdot \dfrac{155}{185}=20\cdot \dfrac{31}{37}=\dfrac{620}{37}=16\dfrac{28}{37}$

6 0

3 years ago

Find X and Y please explain

Alex777 [14]

In this diagram we see that 80 and 3x+4y are both vertical angles and vertical angles are congruent or always equal so we can set those two equations equal to each other then we can see that a line splits two angles making them supplementary (they equal 180 degrees) So we can have another equation, the two equations are:

3x+4y=80 and 3x+4y+7x-8y=180 (add like terms to simplify and get 10x-4y=180

Then use elimination to get rid of the y variables

10x-4y=180 (plus)

+3x+4y=80 (the negative 4 and positive 4 cancels each other out so you are left with:)

13x=160 (divide by x)

x=12.30769 which can be rounded to x=12.31

Then we have to plug in x into the first equation:

3(12.31) + 4y = 80

36.93 + 4y = 80 (subtract 36.93 from 80)

4y = 43.07 (divide)

y=10.7675 or rounded to 10.77

so x=12.31 and y=10.77

5 0

3 years ago

Expand and Simplify 3(p+5)-3(p+2)