What is the sum of an infinite geometric series if the first term is 156 and the common ratio is 2⁄3?

Let's consider the first number to be [tex]f[/tex] and the second number to be [tex]s[/tex]. Based on the information in the problem, we can create the following equations:

[tex]f + 2s = 1[/tex]

[tex]2f + s = 14[/tex]

Now, we can solve the equations through systems of equations. One way of doing this is by multiplying one of the equations so that there is a term in both equations which can be removed by addition or subtraction. In our case, we can multiply the entire first equation by 2 to get:

[tex]2f + 4s = 2/tex]

[tex]2f + s = 14[/tex]

Now, subtract [tex]2f[/tex] from both equations to get:

[tex]3s = -12[/tex]

[tex]s = -4[/tex]

Now that we have found [tex]s[/tex], "plug" it back into an equation to find [tex]f[/tex]:

[tex]f + 2(-4) = 1[/tex]

[tex]f - 8 = 1[/tex]

[tex]f = 9[/tex]

Our answers are s = -4 and f = 9.

Hey there!!

Let's take the first number as ' x '

Let's take the second number as ' y '

First number + twice the second number is 1

x + 2y = 1 ------------ ( 1 )

Twice the second number + second number is 14.

2x + y = 14 ----------- ( 2 )

Now let's get them all together...

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

x + 2y = 1 --- ( 1 )

2x + y = 14 --- ( 2 )

Now, let's multiply the first equation with 2 ...

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

2x + 4y = 2 --- ( 1 )

2x + y = 14 --- ( 2 )

Now, let's subtract the second equation from the second...

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

2x + 4y = 2 --- ( 1 )

- ( 2x + y ) = - ( 14 )

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

2x + 4y = 2 --- ( 1 )

-2x - y = -14 --- ( 2 )

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

3y = -12

Divide by 3 on both sides...

y = -4

The second number is -4.

We have the first equation x + 2y = 1

We got the y value, now substitute the value of y to get the value of x

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

x + 2y = 1

x + 2 ( -4 ) = 1

x - 8 = 1

Add 8 on both sides

x = 9

Hence, the second number is 9.

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

Hope my answer helps!!

Given problem is:

[tex](7.14\times10^{10})+(3.21\times10^{10})[/tex]

step by step solution:

we will add similar elements.

[tex]10^{10}(7.14+3.21)[/tex]

= [tex]10^{10} (10.35)[/tex]

Now converting [tex]10^{10}[/tex] in decimal form we get 10000000000 (10 zeroes)

Now multiplying 10.35 with 10000000000 we get 103500000000 (8 zeroes)

or we can change it to exponential form like [tex]1.035\times10^{11}[/tex]

11 because when you count from the extreme right end '0' and come counting to the left side, you skip 11 numbers till you reach the first number '1'. And when you put a decimal after 1st number, so the last '0' is at the 11th place, that is why it is [tex]10^{11}[/tex] .

[tex]x=1.\overline{34}\\\\x=1.343434...\qquad|\cdot100\\\\100x=134.343434...\\\\100x-x=134.343434...-1.343434...\\\\99x=133\qquad|:99\\\\x=\dfrac{133}{99}[/tex]

The right answer is 15t times 2.

The right answer is 15t times 2.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The garden club earned, $15 per hour by weeding neighborhood gardens for t hours.

A generous donor has agreed to double their earnings.

now,

hence, The right answer is 15t times 2.

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Answer:

[tex]\frac{g}{h}=2(g+h)+7[/tex]

Step-by-step explanation:

1. You have that the number [tex]g[/tex] is divided by the number [tex]h[/tex]. Then:

[tex]\frac{g}{h}[/tex]

2. The words "is the same" indicates that you must write an equals sign after the division. Then, it says that it is seven more than twice the sum of [tex]g[/tex] and [tex]h[/tex]. This means that the sum of these two numbers are multiplied by 2  and then you must add 7:

[tex]\frac{g}{h}=2(g+h)+7[/tex]

I believe the answer is 3.5

Answer:

x = 5

Step-by-step explanation:

First, we need to move all the x's onto one side:

-7x-3x+8x = -8-2

Then, we simplify:

-2x = -10

To find x, we need to divide each side by -2:

So then x = 5

Steps for solving for x.

Step 1. Add 6y to both sides

x = -30 + 6y

Step 2. Regroup terms

x = 6y - 30

Steps for solving for y.

Step 1. Subtract x from both sides

-6y = -30 - x

Step 2. Divide both sides by -6

y = -30 - x/6

The answer is the number 12. This is because if 12 is added to 24 it equals 36 and if 12 is multipled by 3 it is 36.

If a certain number is added to 24, the result is the same as if the number were multiplied by 3 the certain number is 12.

Let's assume the certain number is represented by "x."

According to the given information, if the number is added to 24, the result is the same as if the number were multiplied by 3. This can be written as the following equation:

x + 24 = 3x

Now, let's solve for "x":

Subtract "x" from both sides to isolate the "x" term on one side:

x + 24 - x = 3x - x

24 = 2x

Now, divide both sides by 2 to solve for "x":

x = 24 / 2

x = 12

Therefore, the certain number is 12.

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Answer:

25$

Step-by-step explanation:

4h+ 150= 250

subtract the 150 from 250 to get 100

4h =100

then divide 100 by 4

h=25

Answer:

25$

Step-by-step explanation:

$25 for each additional rental hour.

4h + 150 = 250

4h = 100

h = 25

Answer:

1/4

Step-by-step explanation:

3 feet = 1 yard

therefore in fraction form 1 yd over 4 yd

3 : 12 = [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex] in simplest form

we require the 2 measures to be in the same units

using 1 yard = 3 feet then 4 yards = 4 × 3 = 12 feet

ratio = 3 : 12 = [tex]\frac{1}{4}[/tex] as a fraction in simplest form

Answer:

Refer below

Step-by-step explanation:

5) 9x+2 = 119 (alternate angles of a parallel line)

Hence 9x = 117: x=29 degrees.

6) 12x-8 and 108 are supplementary

Hence 12x+100 = 180 Or 12x= 80 :

x = 20/3

7) 5x+7 = 8x -71

(since vertically opposite angles equal and corresponding angles equal)

3x= 78 or x = 26

8) 7x-61 = 4x-7:3x= 54 orx = 18

9) 9x+25 = 13x-19

4x = 44: x=11:  17y+5 = 13(11)-19

y -7

10) 9x-36 =180 : x = 24: 8y+17 = 6(24)-7

8y =120: y =15

11) 7x-23 =49+3x(exterior angle of triangle)

Or 4x = 72: x=18 : 3x =11y-1

y =5

12) 5x-38 = 3x-4

2x = 34 or x =17

7y-20 = 5(17)-38

= 47

y = 67/7

Fran's fudge recipe, originally calling for [tex]2\frac{1}{2}[/tex] cups of sugar, would require [tex]2\frac{9}{10}[/tex] cups after she increases the sugar by 2/5 of a cup. The process involves converting mixed numbers to improper fractions, finding a common denominator, and then adding the fractions together.

If Fran's fudge recipe calls for [tex]2\frac{1}{2}[/tex] cups of sugar and she increases it by 2/5 of a cup, we first need to find the common denominator to combine these two fractions. To do this, we express [tex]2\frac{1}{2}[/tex] cups as an improper fraction, which is 5/2 cups (since [tex]2\frac{1}{2}[/tex] = 5/2). Then, we add 2/5 of a cup to it.

Steps:

Convert 2 1/2 cups to an improper fraction: [tex]2\frac{1}{2}[/tex] = 5/2.

Add 2/5 cup to 5/2 cups: To add these, we need a common denominator, which is 10. So, we convert 5/2 to 25/10 and 2/5 to 4/10.

Add the two fractions: (25/10) + (4/10) = (29/10).

Convert 29/10 back to a mixed number: 29/10 = [tex]2\frac{9}{10}[/tex].

Therefore, Fran uses [tex]2\frac{9}{10}[/tex] cups of sugar in her fudge recipe after the increase.

First multiply 5 on both sides to get rid of the five on the bottom.

[tex]\frac{1-7n}{5*5}[/tex][tex]>10*5[/tex]

[tex]1-7n>50[/tex]

Subtract 1 from both sides of the inequality.

[tex]1-1-7n>50-1[/tex]

[tex]-7n>49[/tex]

Divide -7 on both sides, and flip the inequality sign since we are dividing by a negative.

[tex]\frac{-7n}{7}[/tex][tex]>\frac{49}{-7}[/tex]

[tex]n<-7[/tex]

The solution to the inequality is n<-7.

[tex]Solution, \frac{1-7n}{5}>10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-7\right)\end{bmatrix}[/tex]

[tex]Steps:[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}5, \frac{5\left(1-7n\right)}{5}>10\cdot \:5[/tex]

[tex]\mathrm{Simplify}, 1-7n>50[/tex]

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}, 1-7n-1>50-1[/tex]

[tex]\mathrm{Simplify}, -7n>49[/tex]

[tex]Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right), \left(-7n\right)\left(-1\right)<49\left(-1\right)[/tex]

[tex]\mathrm{Simplify}, 7n<-49[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}7, \frac{7n}{7}<\frac{-49}{7}[/tex]

[tex]\mathrm{Simplify}, n<-7[/tex]

The correct answer is n<-7

Hope This Helps!!!

1. 12*100 - 12*5

You would use the distributive property to get this equation (it is equivalent to the original one)

2. Um... There's no actual story for this problem; sorry I can't solve this problem

Answer:

1. 12*100 - 12*5

You would use the distributive property to get this equation (it is equivalent to the original one)

2. Um... There's no actual story for this problem; sorry I can't solve this problem

Step-by-step explanation:

the answer is 62 units because of the way the kite looks. a kite has 5 to 4 sides and if you divide that you will get sixty two units per unit.

The perimeter of kite ACBO is 62 units. Therefore, option C is the correct answer.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

From the given kite ACBO, OB=7 uints and OC=25 units.

Here, ∠OBC=90° (Angle between radius and tangent is 90°)

By using Pythagoras theorem,  

BC²=OB²+OC²

25²=7²+OC²

625=49+OC²

OC²=625-49

OC²=576

OC=24 units

So, perimeter=2(a+b), where a and b are adjacent sides

= 2(7+24)

= 2×31

= 62 units

Therefore, option C is the correct answer.

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Hey there!!

How do we find slopes ?

Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]

We are given with two co-ordinates :

(-1,8) and (3,-4)  

Hence, the slope is :

[tex]\frac{-4-8}{3+1}[/tex]

... [tex]\frac{-12}{4}[/tex] = -3

The slope is -3.

Hope my answer helps!

Let's solve your equation step-by-step'

X-2/5=7

Step 1: Simplify both sides of the equation.

x+-2/5=7

Step 2: Add 2/5 to both sides.

x+-2/5+2/5=7+2/5

x=37/5

Answer

x=37/5

Hi!

[tex]x-\frac{2}{5}=7[/tex]

[tex]x-\frac{2}{5}+\frac{2}{5}=7+\frac{2}{5}[/tex]

[tex]x=\frac{37}{5}[/tex]

Explanation: First you had to add 2/5 from both sides. Then simplify, and the answer is x=37/5 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day. -Charlie

Answer:

They place more emphasis on science.

Step-by-step explanation:

The enlightenment emerged in 18th-century, which brought ideas that were deeply influenced by reason, empiricism and classics.  It restructured the old Greek and Roman ideas to make new inventions, and was changing ideas due to reasoning. It was the idea behind the invention of sculpting, a new way of passing ideas or information to people more than through paintings.

Enlightenment initially started with assembling of ordinary materials by a process termed sculptural construction, did not mean exactly the same thing to everybody.

During the enlightenment, artists placed more emphasis on science.

Artists during the Enlightenment shifted from Rococo to Neoclassicism and used their works to convey political messages.

Artists during the Enlightenment played a crucial role in spreading Enlightenment concepts and inspiring rational thinking. The dominant artistic style shifted from Rococo to Neoclassicism, focusing on clarity, logic, and order. Artists like Jacques-Louis David depicted themes of democracy and political statements in their works.

The formula C = 0.35y efficiently calculates the total cost of y apples at $0.35 each. It demonstrates a straightforward linear relationship between cost and quantity.

To find the total cost (C) of y apples priced at $0.35 each, you can use the equation C = 0.35y. This formula multiplies the cost per apple ($0.35) by the number of apples (y) to give you the total cost. For instance, if you want to buy 10 apples (y = 10), the calculation would be C = 0.35 * 10, which equals $3.50.

This equation works because it represents a simple linear relationship between the cost and the quantity of apples. Each apple adds $0.35 to the total cost. Therefore, by multiplying the cost per apple by the number of apples, you get the overall cost.

Remember, this formula assumes a constant price per apple. If the price were to change, the equation would need to be adjusted accordingly. This calculation is useful for budgeting and understanding the cost implications of buying a specific quantity of apples at a given price.

Complete question:

What is the answer to y apples at $0.35 each

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Move all terms that don't contain c to the right side and solve.

Answer: c = 0

The linear equation for the total cost of buying and using the new iPhone with Verizon is total cost = $899 + ($65 * 24), which simplifies to $2459 for 24 months.

To find the linear equation for the cost of buying and using the new iPhone with Verizon, we need to consider the initial cost of the iPhone and the monthly plan cost. Let's assume the initial cost of the iPhone X is $899 and the monthly plan is $65. We can represent the total cost after 24 months as a linear equation.

The equation can be written as:

total cost = initial cost + (monthly plan cost * number of months)

Since we want to find the total cost after 24 months, we substitute the values into the equation:

total cost = $899 + ($65 * 24)

Simplifying the equation:

total cost = $899 + $1560 = $2459

Therefore, the total cost after 24 months would be $2459.

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Hello!

To find the answer to this question we first need to find the weekly average.

If we divide 4,320 by 9, we are given an average of $480 per week.

Since we are given the information that Robin works 50 weeks during the year, we can multiply that value by 50 which equal to $24,000.

Hope this helps.

Answer:A,C,D

Step-by-step explanation:

Took test