Multiply 3hrs 40mins by 7
​

The terms a1, a2 and a3 do not have a common difference, and the value of a1 in the geometric sequence is 10/9

The arithmetic sequence is given as:

a₁, a₂ and a₃

The geometric sequence is given as:

a₄, a₇ and a₁₂

The common ratio of a geometric sequence is:

[tex]r = \frac{T_2}{T_1}[/tex]

So,we have:

[tex]\frac{a_7}{a_4} = \frac{a_{12}}{a_7}[/tex]

Cross multiply

[tex]a_{12} * a_4 = a_7 * a_7[/tex]

Given that a7 = 30, the equation becomes

[tex]a_{12} * a_4 = 30 * 30[/tex]

Evaluate the product

[tex]a_{12} * a_4 = 900[/tex]

Rewrite as:

[tex]a_{4} * a_{12} = 900[/tex]

Express 900 as 10 * 90

[tex]a_{4} * a_{12} = 10 * 90[/tex]

By comparison, we have:

a₄ = 10 and a₁₂ = 90

This means that the geometric sequence is:

10, 30, 90 ---- it has a common ratio of 3

The nth term of a geometric sequence is:

[tex]a_n = ar^{n-1}[/tex]

So, we have:

[tex]a_7 = ar^6[/tex]

[tex]a_4 = ar^3[/tex]

Substitute values for a7 and 14

[tex]ar^6 = 30[/tex]

[tex]ar^4 = 10[/tex]

Divide both equations

[tex]r^2 = 3[/tex]

Take the cube of both sides

[tex]r^6 = 27[/tex]

Substitute [tex]r^6 = 27[/tex] in [tex]ar^6 = 30[/tex]

[tex]a * 27 = 30[/tex]

Divide both sides by 27

[tex]a = \frac{10}{9}[/tex]

Hence, the value of a1 in the geometric sequence is 10/9

Read more about sequence at:

https://brainly.com/question/7882626

#SPJ1

Answer:

Ib = $16 per lb

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

21 = 3 x 7

35 = 7 x 5

70 = 2 x 5 x 7

The greatest common factor of 21, 35 and 70 is 7.

Note : -

The greatest common factor ( GCF ) of a set of numbers is the largest factor that all the numbers share.

Answer:

30 grames.

Step-by-step explanation:

5 x 6 = 30.

Your answer is B.

Vertical goes straight up and down.

Horizontal lines go side to side

A diagonal line is slanted.

Answer:

2513 miles

Explanation:

[tex]\sf Length \ of \ arc = \dfrac{\theta}{360} * 2\pi r[/tex]

Here given:

∅ = 36°

radius = 4000 miles

Insert following:

[tex]\sf \rightarrow \dfrac{36}{360} * 2\pi (4000)[/tex]

[tex]\sf \rightarrow 800\pi \ \ \ (in \ terms \ of \ \pi )[/tex]

[tex]\sf \rightarrow 2513.3 \ \ (rounded \ to \ nearest \ tenth)[/tex]

[tex]\sf \rightarrow 2513 \ \ (rounded \ to \ nearest \ mile)[/tex]

Answer:

a = 6

Step-by-step explanation:

Given information:

Slope = 6

Coordinates: (-9, 0) and (-8, a)

Slope formula = y2 - y1 / x2 - x1

Substitute the given values into the formula.

6 = a - 0 / -8 - (-9)

6 = a - 0 / 1

6 = a - 0

a = 6

hope this helps!! p.s. i really need brainliest :)

Answer:

Daniel =Were you thinking of perpendicular lines?

Oris= It seems like you've got the basic idea, but your definition could be more precise.

Kaoris= Yes well done...

Using proportions, it is found that the dimensions of the reception area of of 12 feet by 20 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the scale factor is of 1 inch = 4 feet, meaning that each inch on the drawing represents a dimension of 4 feet.

The drawing is of 3 inches by 5 inches, hence the real dimensions are given by;

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Because this is a right triangle, we can use a trigonometric function to solve for the missing side.

Remember: SOH-CAH-TOA

We are given an angle, as well as the adjacent side and hypotenuse. Therefore, we should use the cosine function to solve for x.

cos(67) = x / 15

x = cos(67) * 15

x = 5.9

Answer: 5.9

Hope this helps!

B. chair no costume also whips

Answer:

Picture Below :)

Step-by-step explanation:

*ta da*

- Have a great day -

Original: y = 3^x

---To find the inverse, switch the x and y, then solve for y.

Inverse: x = 3^y

---Take the log base 3 of both sides to get y by itself

Answer: [tex]log_{3}(x) = y[/tex]

[tex]y = log_{3}(x)[/tex]

Hope this helps!

Answer: Reflection followed by a translation

Step-by-step explanation:

     First, RST is reflected along the x-axis.

     Then, RST is translated one unit down into R'S'T' giving us what we're looking for.

Answer:

[tex]\sf \dfrac{1}{4}[/tex]

Step-by-step explanation:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

From inspection of the diagram:

[tex]\implies \textsf{P(landing on a pawn)} \sf = \dfrac{\textsf{Total number of pawns}}{\textsf{Total number of squares}}[/tex]

[tex]\implies \textsf{P(landing on a pawn)} \sf = \dfrac{16}{64}=\dfrac{1}{4}[/tex]

[tex]\sf probability : \bf 0.25[/tex]

[tex]\sf Probability = \dfrac{favorable \ outcomes}{total \ outcomes}[/tex]

[tex]\dashrightarrow \ \sf probability : \ \bf \dfrac{16}{64}[/tex]

[tex]\dashrightarrow \ \sf probability : \ \bf \dfrac{1}{4} \ \ \approx \ \ 0.25 \ \ (as \ a \ decimal)[/tex]

Answer:

4 bulbs

Step-by-step explanation:

The population (number of bacteria in the colony), 950 hours from that time, will be 260 bacteria

From the question, we are to determine what the population will be after 950 hours

From the given information,

The number of bacteria in a colony doubles every 475 hours

The current population is 65 bacteria

∴ After 475 hours, the new population will be 2 × 65 bacteria

New population after 475 hours = 130 bacteria

After another 475 hours (that is, 950 hours from the initial time),

The population will be 2 × 130 bacteria = 260 bacteria

Hence, the population, 950 hours from that time, will be 260 bacteria

Learn more on Calculating population here: https://brainly.com/question/9422367

#SPJ1

Answer:

The answer to ur question is C

Answer:

35 square feet

Step-by-step explanation:

Area of the rug :

The product and the sum of the functions will be 3x² - 6x - 24 and 4x + 2. The value of the function (f - g) at x = 4 is negative 18.

In mathematics, functions are everywhere and are necessary for constructing physical connections. A function is a statement, rule, or law that establishes the connection between two variables.

The functions are given below.

f(x) = x - 4

g(x) = 3x + 6

Then the product of the functions will be

(f × g)(x) = (x - 4)(3x + 6)

(f × g)(x) = 3x² -12x + 6x - 24

(f × g)(x) = 3x² - 6x - 24

Then the sum of the functions will be

(f + g)(x) = x - 4 + 3x + 6

(f + g)(x) = 4x + 2

Then the difference in the functions at x = 4 will be

(f - g)(4) = (x - 4) - (3x + 6)

(f - g)(4) = x - 4 - 3x - 6

(f - g)(4) = -2x - 10

(f - g)(4) = -2 (4) - 10

(f - g)(4) = -8 -10

(f - g)(4) = -18

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

Answer:

31 degrees

Step-by-step explanation:

90-59

=31

~rere

Answer:

<b = 31 °

Step-by-step explanation:

When the sum of two angles is equal to 90 degrees, they are called complementary angles

So . .

Because the sum is 90 subtract!

<b = 31 °

Answer:

Yes

Step-by-step explanation:

Because when you draw it u get a right angle

The expression for the perimeter of the pool is 8x + 20 and the cost of fencing the pool is 27.76x + 69.4

There are two missing sides in the figure, and they can be calculated using the subtraction operation.

The equations to calculate the missing sides are:

Missing side 1 = 5x - 2 - (-6 + 4x)

Missing side 2 = 12 - x - (3x - 3)

Evaluate the equations

Side 1 = x + 4

Side 2 = 15 - 4x

Hence, the missing sides are x + 4 and 15 - 4x

This is the sum of the side lengths of the pool.

So, we have:

Perimeter = 5x - 2 + 12 - x - 6 + 4x + 3x - 3 + x + 4 + 15 - 4x

Collect like terms

Perimeter = 5x - x + 4x + x - 4x + 3x - 2 + 12 - 6  - 3  + 4 + 15

Evaluate

Perimeter = 8x + 20

Hence, the perimeter of the pool is 8x + 20

In (b), we have:

P = 8x + 20

Where P represents the perimeter of the pool

The cost of fencing the pool is the product of the perimeter and the unit cost per foot.

So, we have:

C = (8x + 20) * 3.47

Expand

C = 27.76x + 69.4

Hence, the cost of fencing the pool is 27.76x + 69.4

Read more about perimeter at:

https://brainly.com/question/24571594

#SPJ1

Answer:

First picture: SAS and not existent, so not congruent

Second picture: AAA does not exist, so not congruent

Third picture: SAS for both (yes)

Forth picture: AAS for both (yes)

Step-by-step explanation:

Sorry for no long explanation, but if you have any specific questions, feel free to ask in the comments

Hope this helps! If you found my answer helpful, please consider marking me brainliest. Thank you!

Step-by-step explanation:

1.77 would be closer to 2

Answer:

(2,8)

Step-by-step explanation:

Answer:  

Surface Area: 99.852

Volume: 71.592

Answer:

=23/30

Step-by-step explanation:

5/6-2/5

Multiply 5/6 by 5 and -2/5 by 6

25/30-12/30

25-12/30

=13/30

Then he adds another 1/3

=13/30+1/3

multiply 1/3 by ten

=13/10 + 10/30

=13+10/30

=23/30

5/6-2/5-1/3=23/30