the first term of GP where second term is 2 and sum of infinity is8 it will be​

The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

for more such questions on logarithmic properties

https://brainly.com/question/30226560

#SPJ8

Answer:

A'(4,-4)

B'(6,2)

C'(8,8)

Step-by-step explanation:

we have to change the sign of y in reflection on x-axis and the sign of X in reflection on y-axis

Answer:

1/4

Step-by-step explanation:

3/12 ÷3= 3÷3=1 and 12÷3=4

Answer:

x = -3.5

Step-by-step explanation:

1(x-2) = -5.5

x-2 = -5.5

 +2    +2

x = -3.5

Answer:

\(\frac{8}{9}\)

Step-by-step explanation:

Given

Series: 0.8 + 0.08 + 0.008 + 0.0008 + ...

Required

Determine a rational number to represent the series

To do this, we simply get the sum to infinity of the series;

This is done as follows;

\(S = \frac{a}{1 - r}\)

Where a represent the first term

\(a = 0.8\)

r represent the common ratio

\(r = \frac{0.08}{0.8}\)

\(r = 0.1\)

Substitute these values in the above formula

\(S = \frac{0.8}{1 - 0.1}\)

\(S = \frac{0.8}{0.9}\)

Multiply the numerator and denominator by 10

\(S = \frac{8}{9}\)

Hence;

The number is \(\frac{8}{9}\)

Let be "x" the number mentioned in the exercise.

You need to remember that:

- "More than" indicates an Addition.

- The word "Times" indicates Multiplication.

- "Is" indicates that you must use this sign:

Then, knowing that, you can set up the following equation using the information given in the exercise:

Now you can solve for "x" in order to find the number:

Answer: do 2 x 0.6

Step-by-step explanation:

there y go

Answer:

1.) 20,160 cookies, 2.) 37,600 Letters to students in a different country 3.) 252.36 Exact form, Approximate form: 252

Step-by-step explanation:

The first question is written in standard form like this:

Standard Form: 315 x 64 = 20,160

Algebraically/Logical: 315 Packages x 64 Cookies = 20,160 Cookies in All

Therefore, Kenneth bought 20,160 Cookies

The second question is written like this:

Standard Form: 940 x 40 = 37,600

Algebraically/Logical Reasoning: 940 students x 40 letters = 37,600 letters written to students in a different country.

Note: This question has a random P 240, That will be erased so that is why the equation is 940 x 40

The third question is written like this:

Standard Form: 36 x 7.01 = 252.36

Approximate form: 36 x 7 = 252

Algebraically/Logical Reasoning: The standard form would explain it all but if I was answering this question I would round 7.01 to the one's place because there is no way you would get a decimal when trying to solve an even amount of cloths. So there are 36 squares in one table cloth, times that by 7 which is equal to 252 approximently.

Answer:

x=27°

Step-by-step explanation:

2x+72° = x+<PLM

<PLM = x+72°

3x = x+<PML

<PML = 2x

(x)+(x+72)+(2x)=180°

4x = 108°

x = 27°

Answer:

I believe the total area would be 144.5cm squared

Step-by-step explanation:

13x9=117

13-8=5

5x11=55

55÷2=27.5

27.5+117=144.5

sorry if this is not helpful

A triangular prism is a three-dimensional geometric shape that consists of two triangular bases and three rectangular faces connecting them. It is a polyhedron with six faces, nine edges, and six vertices.

The two triangular bases of a triangular prism are congruent and parallel to each other. The rectangular faces are perpendicular to the triangular bases, and their lateral edges connect the corresponding vertices of the triangular bases.

The triangular bases are identical and parallel to each other. Each base has three vertices, three edges, and one face.There are three rectangular lateral faces connecting the corresponding vertices of the triangular bases. Each lateral face has two edges and one face.

Learn more about triangular prism on:

https://brainly.com/question/27102803

#SPJ1

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

To know more about inequality visit:

brainly.com/question/11536194

#SPJ1

Answer:

5

Step-by-step explanation:

2/5 is the same thing as 2÷5 since / and ÷ both mean to divide. So therefore your blank would be 5.

Answer: y = (x - 1)² - 3

Step-by-step explanation:

y = (1-1)²-3
y=0-3
y=-3

Answer:

14 bananas

Step-by-step explanation:

42 divided by 3 = 14

1 x 14 = 14

(Left side - peaches)

(Right side - bananas)

3 - 1

6 - 2

9 - 3

12 - 4

15 - 5

18 - 6

21 - 7

24 - 8

27 - 9

30 - 10

33 - 11

36 - 12

39 - 13

42 - 14

We know that

• The company charges $19.95 plus $0.19 for each mile driven.

• Dana just has $50 to spend.

Based on the given information, we can define the following expression

Then, we solve for x

The difference in overall gain between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price is $239.50.

To determine the difference in overall gain or loss between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price, we need to calculate the selling prices of the stocks.

Stock A:

High price = $105.19

Low price = $103.25

Close price = $103.38

Stock B:

High price = $145.18

Low price = $143.28

Close price = $144.05

The investor purchased 50 shares of stock A at $90 per share and 75 shares of stock B at $145 per share.

To calculate the selling prices, we need to multiply the number of shares by the respective selling price.

Selling price of stock A at the high price: 50 shares \(\times\) $105.19 = $5,259.50

Selling price of stock A at the low price: 50 shares \(\times\) $103.25 = $5,162.50

Selling price of stock B at the high price: 75 shares \(\times\) $145.18 = $10,888.50

Selling price of stock B at the low price: 75 shares \(\times\) $143.28 = $10,746.00

Now, let's calculate the difference in overall gain or loss:

Difference in overall gain = Selling price at the high price - Selling price at the low price

= ($5,259.50 + $10,888.50) - ($5,162.50 + $10,746.00)

= $16,148.00 - $15,908.50

= $239.50

For similar question on selling stock.

https://brainly.com/question/13454463  

#SPJ8

If for every amount of $d , $0.20d is tipped, then for amount of $56, $11.6 will be tipped to the waiter

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.

If for every $d , $0.20d is tipped, then this means that the total amount spent is $56 and the amount Anthony's family tip the waiter is calculated as:

0.2 × 56

= $11.6

Therefore the waiter was tipped $11.6

learn more about rate from

https://brainly.com/question/25793394

#SPJ1

Answer:

A dinner bill of d dollars calls for a tip of 0.20d dollars. You want to find how much the family tipped the waiter for a bill of d=$56.

Evaluate the expression 0.20d for d=56.

0.20d

=

0.20(56)

=

11.2

The family tipped the waiter $11.20.

Answer: A

Step-by-step explanation:

For this problem, we would distribute the outer exponent to each exponent inside. Once we distribute, we multiply the exponents together.

\(2^\frac{12}{5} *9^\frac{4}{5}\)

Answer:

When we have exponents (being multiplied) in a parenthesis which also has an exponent, the exponent of the parenthesis gets multiplied by each one of the others. We have to distribute the outer exponent to each exponent inside, like:

\((a^n*b^m)^p = a^{n*p}*b^{m*p}\)

If there are numbers but no exponents (inside), it also happens the same, but as the exponent of the parenthesis gets multiplied by 1, we can just put the exponent, like:

\((a*b)^p=a^p+b^p\)

So, in our case we have what we have explained: two numbers, one of them with an exponent and the other without it in a parenthesis which also has an exponent, so we multiply that exponent by the ones of the numbers inside the parenthesis.

\((2^3*9)^\frac{4}{5}\) = \(2^{3*\frac{4}{5}}*9^\frac{4}{5}\) = \(2^\frac{12}{5}*9^\frac{4}{5}\)

So the answer is \(2^\frac{12}{5}*9^\frac{4}{5}\)

On solving the provided question, we can say that - Surface area of the following will be 20 sq unit sq.

A three-dimensional shape's surface area is the total amount of space that surrounds it. Additional distinctions between interface types include: The area that includes the base and curving section is referred to as the gross area. The curved area is the section of the curved portion that is devoid of a base. A plane is a two-dimensional object that occupies space. square units of measurement. The surface area of a three-dimensional object refers to the space it takes up on its outside surface.

Given plane:

\(-\sqrt{20} + 2y + z = 82\\ z = 82 + \sqrt{20} -2y\\\frac{dx}{dy} = \frac{d}{dy}(82 + \sqrt{20} -2y) \\= -2\)

Surface area =

\(\sqrt{1 + (\sqrt{20} )^2 + (-2)^2}\\ \sqrt{(1 + 20 + 2} \\5\)

5 X Area of the Porth

5 X 6

30 unit sq

To know more about surface area visit:

https://brainly.com/question/29298005

#SPJ4

Answer:

5.5

Step-by-step explanation:

The mean is the average of the numbers.

mean=(5+4+7+4+5+8+6+5)/8=44/8

=5.5

Answer:

14ab

Step-by-step explanation:

p = 2l + 2w

p = 2(4ab) + 2(3ab)

p = 8ab + 6ab

p = 14ab

Answer:

60

Step-by-step explanation:

Answer:

it is 60

Step-by-step explanation:

Answer:

the cost of the bench is $806

Step-by-step explanation:

853 minus 47 is 806

Answer:

D

Step-by-step explanation:

If you substitute the radius, 10, and the center of the circle, the origin (also known as (0,0) into the equation of a circle, you should get: \((x - 0)^{2} + (y - 0)^{2} = 10 ^{2} \)

Multiplying this out should leave you with D as your answer.

Answer:

6. -f         7. f= 6/8

Step-by-step explanation:

Hope dis helps!!

1. Patrick makes more per hour by $6.

2. Betthany makes more per hour by $5.25

3. Tommy makes more per hour by $ 1.25.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

The rate of Change of Critters and Co

Slope= Rise/ Run

        = 15/2

        = 7.5

So, the equation is y = 7.5x

and, rate of Change of Little Paws

= (52.50-35) / (6-4)

= 17.5 / 2

= 8.75

So, the equation is y = 8.5x + 5

and, rate of Change of The Waging Tail

= 8.25

1. Patrick makes more per hour by $6.

2. Betthany makes more per hour by $5.25

3. Tommy makes more per hour by $ 1.25.

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ1