The measures of the angles of a triangle are shown in the figure below. Solve for X.
75°
(7X+14)
49°

Geometric sequence is characterized by a common ratio

(1) Sum of first 5 terms

The first term of the sequence is:

[tex]\mathbf{a = 3}[/tex]

The common ratio (r) is:

[tex]\mathbf{r = 6 \div 3 = 2}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]

So, we have:

[tex]\mathbf{S_5 = \frac{3 \times (2^5 - 1)}{2 - 1}}[/tex]

[tex]\mathbf{S_5 = \frac{93}{1}}[/tex]

[tex]\mathbf{S_5 = 93}[/tex]

Hence, the sum of the first five terms is 93

(2) Sum of first 5 terms

The first term of the sequence is:

[tex]\mathbf{a = 14}[/tex]

The common ratio (r) is:

[tex]\mathbf{r = 3}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]

So, we have:

[tex]\mathbf{S_5 = \frac{14 \times (3^5 - 1)}{3 - 1}}[/tex]

[tex]\mathbf{S_5 = \frac{3388}{2}}[/tex]

[tex]\mathbf{S_5 = 1694}[/tex]

Hence, the sum of the first five terms is 1694

(3) Sum of first n terms

The first term of the sequence is:

[tex]\mathbf{a = 318}[/tex]

The common ratio (r) is:

[tex]\mathbf{r = \frac12}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(1 - r^n)}{1 - r}}[/tex]

So, we have:

[tex]\mathbf{S_n = \frac{318 \times (1 - \frac 12^n)}{1 - \frac 12}}[/tex]

[tex]\mathbf{S_n = \frac{318 \times (1 - \frac 12^n)}{\frac 12}}[/tex]

[tex]\mathbf{S_n = 636 (1 - \frac 12^n)}[/tex]

Hence, the sum of the first n terms is [tex]\mathbf{ 636 (1 - \frac 12^n)}[/tex]

(4) The first term

The sum of the first 7th term of the sequence is:

[tex]\mathbf{S_7 = 547}[/tex]

The common ratio (r) is:

[tex]\mathbf{r = -3}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(1 - r^n)}{1 - r}}[/tex]

So, we have:

[tex]\mathbf{547 = \frac{a(1 - (-3)^7)}{1 - -3}}[/tex]

[tex]\mathbf{547 = \frac{a(2188)}{4}}[/tex]

Multiply both sides by 4

[tex]\mathbf{2188= a(2188)}[/tex]

Divide both sides by 2188

[tex]\mathbf{1= a}[/tex]

Rewrite as:

[tex]\mathbf{a = 1}[/tex]

Hence, the first term is 1

(5) Find the 7th term

The first term of the sequence is:

[tex]\mathbf{a=2}[/tex]

The common ratio (r) is:

[tex]\mathbf{r=3}[/tex]

The nth term of a geometric sequence is:

[tex]\mathbf{T_n = ar^{n -1}}[/tex]

So, we have:

[tex]\mathbf{T_7 = 2 \times 3^{7 -1}}[/tex]

[tex]\mathbf{T_7 = 1458}[/tex]

Hence, the seventh term is 1458

(6) Sum of geometric sequence

The first term of the sequence is:

[tex]\mathbf{a=2}[/tex]

The common ratio of the sequence is:

[tex]\mathbf{r = 6 \div 2 = 3}[/tex]

The number of terms is:

[tex]\mathbf{n = 5}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]

So, we have:

[tex]\mathbf{S_5 = \frac{2 \times (3^5 - 1)}{3 - 1}}[/tex]

[tex]\mathbf{S_5 = \frac{484}{2}}[/tex]

[tex]\mathbf{S_5 = 242}[/tex]

Hence, the sum of the first five terms is 242

(7) The first term

The sum of the first five terms is given as:

[tex]\mathbf{S_5 = 341}[/tex]

The common ratio is:

[tex]\mathbf{r = 4}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]

So, we have:

[tex]\mathbf{341 = \frac{a \times (4^5 - 1)}{4 - 1}}[/tex]

[tex]\mathbf{341 = \frac{a \times 1023}{3}}[/tex]

Solve for a

[tex]\mathbf{a = \frac{3 \times 341}{1023}}[/tex]

[tex]\mathbf{a = 1}[/tex]

Hence, the first terms is 1

(8) Sum to infinite

The first term of the sequence is:

[tex]\mathbf{a = 192}[/tex]

The common ratio (r) is:

[tex]\mathbf{r = \frac 14}[/tex]

The sum to infinite is:

[tex]\mathbf{S_{\infty} = \frac{a}{1 - r}}[/tex]

So, we have:

[tex]\mathbf{S_{\infty} = \frac{192}{1 - 1/4}}[/tex]

[tex]\mathbf{S_{\infty} = \frac{192}{3/4}}[/tex]

[tex]\mathbf{S_{\infty} = 256}[/tex]

Hence, the sum to infinite is 256

Read more about geometric sequence at:

https://brainly.com/question/18109692

Answer: An equation: d = 40r. 3. A tabulation of values. 4. A graph showing the relationship between time and distance. We have already used word sentences and equations to describe such relationships; in this chapter, we will deal with tabular and graphical representations.

Step-by-step explanation:

Hope this helps!

Answer:

the equation is - [tex]y=x[/tex]

Explanation:

Given -

[tex]y=x+4[/tex]

We have to find a line passing through the point [tex](2,2)[/tex] nd parallel to the given line.

Find the slope of the given line.

It is the coefficeint of [tex]x[/tex]

m₁ = 1

The two lines are parallel. Hence

m₂=m₁=1 Where m₂is the slope of the second line.

You have slope and the points [tex](2,2)[/tex]

Find the Y intercept

[tex]y=mx+c\\2=(1)(2)+C\\2=2+C\\C=2-2=0[/tex]

Y-Intercept [tex]C=0[/tex] and slope m₂=1

Fix the equation

[tex]y=x[/tex]

Answer:

Use the coordinate plane below to answer the following questions. a. Use a straightedge to construct a line that goes.

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

720 degrees in a 6 sided shape. already have 2 right angles so its 720- 180 = 540

540÷4 is 135

Answer:

6

Step-by-step explanation:

not sure but it hope that helps

Answer:

4/3 lemons

Step-by-step explanation:

For 16 lemons per 12 cups, simplify the ratio to 4 lemons per 3 cups.

The required rate of lemon per cup of lemonade is 1.34 lemons per cup.

Given that,
For Allison's lemonade recipe, 16 lemons are required to make 12 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade to be determined.

The rate of change is defined as the change in value with the rest of the time is called the rate of change.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Since
Let the rate of lemon per cup of lemonade is x,
Total lemon = 16
To a cup of lemonade = 12
Rate of lemon per cup of lemonade
x = 16/12
x = 1.34

Thus, the required rate of lemon per cup of lemonade is 1.34 lemons per cup.

Learn more about the rate of change here: https://brainly.com/question/13103052

#SPJ5

Answer:

D

Step-by-step explanation:

because the angles are across from each other, they are equivalent

you would set up the equation like this

8x - 8 = 7x + 8

then you could add 8 to each side

8x = 7x + 16

then subtract 7x from each side

x = 16

The 1/4x is the slope and +2 is (2,0).

Step-by-step explanation:

write this equation on a pice of paper then go to the camera button select which one you want and then take a pic of it. i am in a math class a year above me and this is what we are learning these types of problems confuse me I wish I could help

Answer:

16 students

Step-by-step explanation:

Answer:

20 students

Step-by-step explanation:

7+(-3x)

7+(-36)

-29

I hope this helps!

Answer: Every answer choice is to be selected

Explanation:

The following angles are adjacent to angle 8

Adjacent angles share a common line segment, line, or ray. Think of it like a shared wall. The other remaining angles are non-adjacent even though something like angle 6 shares a common vertex with angle 8, they don't share a common wall. In a sense, the person living in apartment 6 isn't a direct next door neighbor to the person in apartment 8.

So that's why we select angles 2, 4, 5, 1 and 3 as our answers. In short, we click each box to select all answer options.

Answer:

221

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

...............................

Answer:

40 ounces

Step-by-step explanation:

Answer:

[tex] r = \frac{tw}{(t - 1)} [/tex]

Step-by-step explanation:

[tex]t = \frac{r}{(r - w)} \\ t(r - w) = r \\ tr - tw = r \\ tr - r = tw \\ r(t - 1) = tw \\ \frac{r(t - 1)}{(t - 1)} = \frac{tw}{(t - 1)} \\ r = \frac{tw}{(t - 1)} [/tex]

Hope this helps you.

Let me know if you have any other questions :-):-)

Answer:

3

Step-by-step explanation:

3 is the only number here with factors of itself (3) and 1

Answer:

3

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Answer:

You are correct! It is the answer you have selected in the picture!

Step-by-step explanation:

Hope this helps :)

4x4=16

-4x-4=16 too

Answer:

a

Step-by-step explanation:

square root both sides and youll get x=4

can i get a brainliest

Answer:

252, 259 and 266

Step-by-step explanation:

Multiples of a number are those numbers that are divisible by that. Like if x and y are any two numbers then if y is a multiple of x then the remainder should be equal to zero when x is divided from y.

Answer:

Three consecutive multiples of 7 whose sum is equal to 777 are 252, 259 and 266.

Please click above answer.

Please do 3 brainliests because I need.

Answer:

c = -1/4

e = 1 2/5

Step-by-step explanation:

4c - 5 = -6

add 5 to both sides

4c = -1

divide each side by 4

c = -1/4

5e + 2 = 9

subtract 2 from both sides

5e = 7

divide both sides by 5

e = 1 2/5

-Chetan K

Answer:

c = -1/4

e = 7/5

Step-by-step explanation:

1. 4c - 5 = -6, 4c = -1, c = -1/4

2. 5e + 2 = 9, 5e = 7, e = 7/5

Answer:

It takes Katie 66 2/3 seconds to run 400m. Min conversion: 1 min and 6 2/3 secs

Step-by-step explanation:

Answer:

You returned 5 shirt.

Step-by-step explanation:

$30.60 ÷ $6.12 = 5

Answer:

5 shirts

Equation:

-$30.60 / -$6.12 = 5

So 5 would be your answer! :)

Answer:

z=56

Step-by-step explanation:

trust me

z=56  pay attention in school‍