The sixth term of an arithmetic
Sequence is 17 and the tenth Term
IS 33, Determine the first term and
Common difference.

According to estimates, there were 7,060,268,214 people on Earth as of August 16, 2012. Rounding to the nearest hundred million, 7,060,268,214 equals 7,100,000,000.

Find the digit that is 100,000,000 places away first. The next step is to check if the number that comes after the hundred million place is 5 or higher. Next, multiply the result by 100 million to the nearest billion. 200,000,000 is the reply. 4,000,000 or 5,000,000 may be the million closest to you.

Take a glance at the number in the right-hand column, the hundred thousands, to determine the nearest million. 5 appears in the column for "hundred thousands." It is standard practise to round up numbers that are five or more. This means that you should look at the digit in the ten thousand spot to round numbers out to the nearest hundred thousand. 1,000,000 is added as a rounding error.

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Answer:

He plans to kayak a total of 6.4 miles. Damon kayaks at an average speed of 1.6 miles per hour. How many hours will it take Damon to kayak the 6.4 miles? It will take Damon 4 ‾ hours to kayak 6.4 miles.

[tex] \frac{3x + 9}{6} = x - 3 \\ [/tex]

[tex]3x + 9 = 6(x - 3)[/tex]

[tex]3x + 9 = 6x - 18[/tex]

[tex]6x - 3x = 9 + 18[/tex]

[tex]3x = 27[/tex]

[tex]x = \frac{27}{3} \\ [/tex]

answer: [tex]x = 9[/tex]

12 rows had been completed before Elena started working.

What is meant by rows ?

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K is therefore equal to 1/2 since in the right-angled triangle, one angle is 45 and the perpendicular is 10 cm.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.

given

If you have an angle and its opposite side, you may calculate the hypotenuse by dividing the length of the opposing side by sin().

To find the length of the side next to the angle, you can also divide the length by tan().

Let the hypotenuse be AC=x

Now given AB=Kx

In △ABC

sin45 ∘ = AC / AB

1/2 = kx/x

K= 1/2

K is therefore equal to 1/2 since in the right-angled triangle, one angle is 45 and the perpendicular is 10 cm.

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Answer:

Todd spent 75, Matt spent 50 and Jeff spent 150

Step-by-step explanation:

Matt = y - 25

Jeff = 3(y - 25)

Todd = y

y - 25 + 3y - 75 + y = 275

5y - 100 = 275

5y = 275 + 100

5y = 375

y = 375/5

y = 75.......Todd therefore spent 75 dollars!!

I think it gets easy from here

final answer:y= - 1/97 - 6

to find slope, just do the opposite reciprocal of the given slope

to find y-intercept just substitute the given point in y=mx+b

hope this helps!

The set of ordered pairs that is a function is (b) (-9, 9), (-8, 1), (2, -4), (-2, 1)

The list of options represents the given parameter

All ordered pairs are relations but not all ordered pair are functions

For an ordered pair to be a function, the following must be true:

The y values on the ordered pair must have  different x values

Using the above as a guide,

This means that the ordered pair in option (b) represents a function

Hence, the ordered pair that is a function is (b)

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The log₂(7) is irrational, because if we assume that it is rational, we can reach a contradiction.

Assume that log₂(7) is rational. This means that it can be written as the ratio of two integers, a/b, where a and b are integers and b is not equal to zero.

Then, using the definition of a logarithm, we have: 2^(a/b) = 7

Multiply both sides by b, we have: 2^a = 7b

Now we have a problem, because 7b is not necessarily a power of 2. This means that our assumption that log₂(7) is rational leads to a contradiction, and therefore log₂(7) must be irrational.

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Answer:

I am so glad you were able to do it! Congrats on 100%

Step-by-step explanation:

That's great you got 100%!!!

Answer:

From the top of a 12 foot ladder, the angle of depression to the far side of a sidewalk is , while the angle of depression to the near side of the sidewalk

Step-by-step explanation:

Using simultaneous equations, the cost of one slice of pizza bought by Max's dad at the concession stand is $1.75.

Simultaneous equations are two or more equations solved concurrently or simultaneously.

Simultaneous equations are also called a system of equations.

                       Bottles     Slices of     Total

                     of Water       Pizza        Cost

1st purchase     5                8            $20.25

2nd purchase    1                3              $6.50

Let the cost of bottles of water = b and the cost of slices of pizza = p

Equation 1: 5b + 8p = 20.25

Equation 2: b + 3p = 6.50

Multiply Equation 2 by 5:

Equation 3: 5b + 15p = 32.50

Subtract Equation 1 from Equation 3:

5b + 15p = 32.50

-

5b + 8p = 20.25

7p = 12.25

p = 1.75

The cost of one slice of pizza (p) = $1.75

Check:

b + 3p = 6.50

b + 3(1.75) = 6.50

b + 5.25 = 6.50

b = 1.25

= $1.25

Thus, the cost of one slice of pizza is $1.75.

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In the production range of 2 to 3 combs, the opportunity cost of producing one more comb is d) 0.14 brushes.

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9)The value of x is 26 degrees

10)The value of x is 13 degrees

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Vertical angles are equal

2x+1=53

=> 2x=53-1 = 52

x=52/2 = 26 degrees

similarly,

5x+1=66

=> 5x=66-1 = 65

=> x=65/5 = 13 degrees

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Step-by-step explanation:

remember,

x^-n = 1/x^n

any negative exponent of 1.3 means we have to consider it as 1/1.3 with the positive exponent.

so, if the given temperature (x) is negative, 1.3 has a positive exponent and gets bigger and bigger the lower (smaller) x gets.

if the given temperature (x) is positive, 1.3 has a negative exponent and gets smaller and smaller the higher (bigger) x gets.

the domain is the interval or set of all valid x-values.

there is no need for any restriction for x.

so, the domain is all real numbers.

the question is : up to what temperature will there be heating ?

at 5°C ? yes, sure.

at 10°C ? yes, sure.

at 15°C ? some people still need heating.

at 20°C ? most likely not.

but f(20) = $0.042094266... ≈ $0.04

so, still a tiny little bit of heating is happening for the function, but in reality most likely not at all.

the information about such a limit is missing in the question. so, again no limit for x.

f(-8) means that x = -8.

f(-8) = 8(1.3)^--8 = 8(1.3)⁸ = 8×8.15730721 =

= 65.25845768

when the low outside temperature is -8°C, it would cost $65.26 to heat the building.

I don't know the answer options to the last part, but the interpretation certainly is in the context of the problem.

Point B on line AB, which is tangent to circle O, has a length of 12 units. The circle is intersected by the line AO from point A to the circle's centre at point C, and the line segment AC has a length of 8 units.

If you know the circumference C, you can calculate the radius of a circle using the formula r = C / (2 * ). If you know a circle's diameter, d, you can calculate its radius using the formula r = d / 2. The line AB crosses the circle at the precise locations P and Q. Here, the line AB is known as the secant of the circle.

Due to the fact that the endpoints of the line segment P Q are on the circle's circumference, it is known as the circle's chord.The two-headed arrow over AB designates a line that passes through points A and B. The name of a line that crosses two distinct points A and B is written as "line AB" or as.

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Answer:its b

Step-by-step explanation:yall dume

Trial Balance as of December 31, 20X1:

Account Debit Credit

Cash: 179,000

Equipment: 69,000

Accounts Receivable: 11,100

Accounts Payable: 69,000

Supplies: 35,000

Scott Hamilton, Capital: 179,000

Fee Income: 29,200

Telephone Expense: 590

Scott Hamilton, Drawing: 3,900

Salaries Expense: 9,900

Total: 368,190 368,190

Income Statement for the month ended December 31, 20X1:

Revenue: 29,200

Expenses:

Equipment: 69,000

Supplies: 35,000

Telephone Expense: 590

Salaries Expense: 9,900

Total Expenses: 114,490

Net Income: (85,290)

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Answer:

  y = 900(0.91^t)

Step-by-step explanation:

You want a function that describes the value of a $900 sound system that decreases in value by 9% per year.

When the amount of change is proportional to the amount, the amount is described by an exponential function:

  y = ab^x

where 'a' is the initial value, and 'b' is the "growth factor."

Here, the change is expressed as a "growth rate" of -9% per year. The growth factor is 1 added to the growth rate:

  b = 1 +(-9%) = 1 -0.09 = 0.91

The initial value is given as ...

  a = 900

So the function you want is ...

  y = 900(0.91^t)

__

Additional comment

The independent variable in this case is time, and the problem statement tells you to use 't' to represent it. The decay rate is given as a percentage per year, so the units of t will be years.

Let's first review the Sin function before talking about Sin 0. Therefore Sin 0 value is 0.

The Sine, Cosine, and Tangent functions in trigonometry are used to determine the angles and length of a right-angled triangle, respectively.

The relationship between the angle, perpendicular side, and hypotenuse side is defined by the sine function.

Alternatively, you can use sin theta, which is equal to the right-angled triangle's perpendicular to hypotenuse ratio. Sin theta is the angle produced between the hypotenuse and adjacent side.

Definition Of Sin In Relation To Sin 0.

Sin 0 denotes that (x,y) is where the value of the x coordinate is 1, and the value of the y coordinate is 0. (1,0). In this case, the hypotenuse has a value of 1, and the opposing side or perpendicular has a value of 0.

As a result, if we set the numbers in the sin ratio for = 0, the perpendicular side to be 1, and the hypotenuse to be 0, we obtain,

Sin 0 = 0/1

Sin 0 = 0

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(b) √29 is between 5 and 6. You can approximate it by finding the perfect squares that are closest to 29: 25 (5^2) and 36 (6^2). √29 is between 5 and 6 since 5^2 < 29 < 6^2

(c) √54 is between 7 and 8. You can approximate it by finding the perfect squares that are closest to 54: 49 (7^2) and 64 (8^2). √54 is between 7 and 8 since 7^2 < 54 < 8^2.

[tex]{3 }^{p} = \frac{1}{9} [/tex]

[tex]{3 }^{p} = 9 {}^{ - 1} [/tex]

[tex]{3 }^{p} = (3 {}^{2} ) {}^{ - 1} [/tex]

[tex]{3 }^{p} = 3 {}^{} {}^{ - 2} [/tex]

[tex]p = - 2[/tex]

The given statement that " Ricardo has an equally likely chance of spinning an odd number as spinning a number less than 4" is True.

When rolling a fair dice, the probability of getting an odd number is:

= Number of odd numbers / Number of sides on die

Number of odd numbers = 1, 3, 5

Probability of odd number:

= 3 / 6

= 1 / 2

Probability of number less than 4 :

= 3 / 6

= 1 / 2

Ricardo therefore has  an equally likely chance.

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Options for this question are:

The product of two sets is the set of ordered pair of elements from each set.

We know that the set is nothing but the collection of well-defined objects or elements or numbers.

The elements of sets are written in the curly brackets, seperated by comma.

A set is represented by a capital letter symbol.

For example., the set of natural numbers is denoted by N.

N = {1, 2, 3, 4, . . .}

As we know the Cartesian Product of sets M and N is defined as the set of all ordered pairs (x, y) such that x belongs to set M and y belongs to set N.

It is denoted as M × N = {(x,y) | x ∈ M and y ∈ N}

For example, consider a set P = {1, 2}

and set M = {3, 4, 5},

From the definition of the Cartesian Product of P and M,

P × M = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}

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The perimeter of the given polygon is about 16.4 units.

We want to find the perimeter of the polygon whose vertices are (-3, 2), (2, 2) and (-1, -3).

The perimeter will be equal to the sum of the distances between the vertices, and remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:

d = √( (x₂ - x₁)² + (y₂ - y₁)²)

The distances are:

between (-3, 2) and (2, 2)

d = √( (-3 - 2)² + (2 - 2)²) = 5

between (-1, -3) and (2, 2)

d = √( (-1 - 2)² + (-3 - 2)²)

d = √( 9 + 25) = 6

between (-1, -3) and (-3, 2)

d = √( (-1 + 3)² + (-3 - 2)²)

d = √29 = 5.4

Then the perimeter is:

5.4 + 6 + 5 = 16.4

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Negative numbers doesn't have real square roots since a square is either positive or 0.

Negative Square Roots Simplifying an expression involving the square root of a negative quantity is done by simplifying the quantity as if it was positive, and placing an i in front as a coefficient.

for example:-

The square root of -9 is 3i. But if you are talking about real numbers, then there would be no solution.

Square root

The square root of a number is defined as the value, which gives the number when it is multiplied by itself.

The √ symbol that is used to denote square root or nth roots.

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Answer: 25 degrees

Step-by-step explanation:

2x + 10 + 30 = 90

2x = 50

x = 25 degrees

A number that goes into a greater number with no remainders is called a factor.

A factor is an integer that divides into a greater number without any remainders.

For example, the number 6 is a factor of 18 because when 18 is divided by 6, the answer is 3 with no remainders. Similarly, the number 3 is a factor of 12 because when 12 is divided by 3, the answer is 4 with no remainders.

Factors are important in mathematics because they can be used to solve equations and determine the greatest common divisor (GCD) of two or more numbers. Factors can also be used to determine prime numbers and their multiples.

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Answer:

125, 216, 343, 512

Step-by-step explanation:

The next number in the sequence 1, 8, 27, 64 is 125.

This sequence follows the pattern of starting with the number 1, then finding the cube of each subsequent integer (the cube of a number is found by multiplying the number by itself twice, so the cube of 2 is 222=8). Therefore, the next number in the sequence would be 555=125.