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There's a fixed difference of 6 between terms (9 - 3 = 6, 15 - 9 = 6, and so on). The first term of the sequence is 3, so the [tex]n[/tex]-th term is

[tex]3 + 6(n-1) = 6n - 3[/tex]

If there are 24 terms in the sum, then the last term is 6×23 - 3 = 135.

Let [tex]S[/tex] be the sum,

[tex]S = 3 + 9 + 15 + \cdots + 123 + 129 + 135[/tex]

Reverse the order of terms:

[tex]S = 135 + 129 + 123 + \cdots + 15 + 9 + 3[/tex]

If we add up the terms in the same positions, we get twice [tex]S[/tex] on the left side, while on the right side we observe that each pair of terms will sum to 138.

[tex]S + S = (3 + 135) + (9 + 129) + (15 + 123) + \cdots + (135 + 3)[/tex]

[tex]2S = 138 + 138 + 138 + \cdots + 138[/tex]

and since there are 24 terms in the sum, the right side is the sum of 24 copies of 138. In other words,

[tex]2S = 24 \times 138[/tex]

and solving for [tex]S[/tex] gives

[tex]S = \dfrac{24\times138}2 = \boxed{1656}[/tex]

Answer:

y=23.6

Step-by-step explanation:

20+0.45×8

20+3.6

23.6

Answer:

b - read explanation if you are confused for future problems

Step-by-step explanation:

Inverse variation is when x*y = k whereas direct variation (may come up in future problems) is when y = x*k

Remember that k is always a set value while x and y are values that can change

In this case y*x = k so k = 18 (since y is 9 when x is 2)

So when  x = 8

8y = 18

y = 18/8 = 9/4

Answer:

Como faltar a la escuela. Por favor, ¿cuál es el significado?

Answer:

Pythagoras

Step-by-step explanation:

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Answer:

5sqrt3

Step-by-step explanation:

You can use trigonometry to figure out the answer

TOA is tan(any angle) = opposite/adjacent

Tan(30) = 5/x

tan(30) = sqrt3/3

x = tan inverse (30) multiplied by 5

x = 5sqrt3

Answer:

its 0

Step-by-step explanation:

you just gotta do the math correctly to get the answer. x & y are both values with different meanings. but in this case it's 0

The measure of the angle PUT is 13 degrees and the measure of the angle PQR = 21 degrees

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have triangles shown in the picture.

In the first triangle SUT:

PU is bisecting the angle SUT:

The measure of angle PUT:

Angle PUT = Half of Angle SUT

= 26/2

= 13 degrees

In the triangle SQR:

Angle SQP = Angle PQR

Angle SQP  = 21 degrees

Angle PQR = 21 degrees

Thus, the measure of the angle PUT is 13 degrees and the measure of the angle PQR = 21 degrees

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Answer:

C (The third answer). The square root of terms separated by addition and subtraction cannot be calculated individually.

Step-by-step explanation:

This problem can be thought similarly to: (x-2)²

A common mistake would to make the x squared and the -2 squared like x²+4, however, the problem should be solved like (x-2)(x-2) which equals to: x² - 4x + 4

In this question, if you square root an expression like ±√(b²-4ac), you cannot just take the square root of b² unless it was (b²)(-4ac).

The terms can only be divided individually if they are either multiplied or divided, but cannot if they are added or subtracted.

The solution to a given word problem by writing it as an equation is k = 253/232

The process of expressing word problems in mathematical forms takes a logical and chronological approach while taking the variables and arithmetic operations given into consideration.

From the given information, to express the word problem in mathematical form, we have:

Making k the subject of the equation, we have:

k = 253/232

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Answer: x = 44

Step-by-step explanation:

The exterior angles of a polygon add to 360 degrees so:

Answer:

x^2-2x-3

Step-by-step explanation:

(x+1)(x-3)

x(x-3)+1(x-3)

Answer:

The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 52 raised to the 3rd power is equal to 56.

Step-by-step explanation:

Answer:

5(a-12)

Step-by-step explanation:

5(a-12)

The algebraic expression that represents the number of new accounts that he will add in m months is x ≥ 7m.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Every month, a salesperson adds 7 new accounts.

Let m be the number of the month and x be the number of the accounts.

Then the inequality equation will be

x ≥ 7m

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It is important to multiply the dividend and the divisor by the same power of 10 to remove the decimal point.

When the numerator and denominator of improper fractions are in whole number form, it makes the division a lot easier.

For example;

what is the simplest form of 0.1/0.2?

To obtain the simplest form of the above function, we multiple the numerator and denominator by 10.

= (0.1 x 10)/(10 x 0.2)

= 1/2

Note: introducing factor of 10 to both numerator and denominator has not changed the function.

Thus, it is important to multiply the dividend and the divisor by the same power of 10 to remove the decimal point.

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The cost price of pawpaw is 40 and the cost if the basket of mangoes is 1250.

Based on the information given, the equations to solve the question will be:

30p + 100m = 2450 .... i

1.3 × 40p - 30 p + 1.3 × 100m = 855 ..... ii

30p + 100m = 2450

12p + 30m = 855

Solving simultaneously, the price of pawpaw is 40 and the price of mango is 12.5.

Therefore, the cost of 100 basket of mangoes will be:

= 12.5 × 100

= 1250

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The number of ways this can be done is 151200 if they choose 6 letters without replacement from 10 distinct letters.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Suppose we want to choose 6 letters without replacement from 10 distinct letters.

Number of letters = 10

Number of letters need to select = 6

Order is important.

A number of ways:

C(10, 6) = 10!/(10-6)!

= 10!/(4)!

= 151200

Thus, the number of ways this can be done is 151200 if they choose 6 letters without replacement from 10 distinct letters.

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This is about interpretation of graphs.

Option C is correct.

From the graph, we can see the 2 lines representing function f(x) and function g(x).

Now for us to find the value of x in g(x) = k⋅f(x), we need get a mutual x-coordinate where we can easily read their respective y-coordinate values.

We see that the best point for that is where x = -3.

For f(x), when x = -3, y = 1

For g(x), when x = -3, y = -3

we can rewrite them as;

x = -3, f(-3) = 1 and x = -3, g(-3) = -3

Let us plug in the relevant values into g(x) = k⋅f(x) to get;

-3 = k(1)

Thus; k = -1/3

Answer:

x = 34

Step-by-step explanation:

A straight line is 180 degrees

We can sum angles to form a straight line

x+12 + 100 +x = 180

Combine like terms

2x+112 = 180

2x+112-112 = 180-112

2x = 68

Divide each side by 2

2x/2 = 68/2

x = 34

answer:

=x+12+100+x =180

=x+x+12+100=180

=2x+112=180

=2x=180-112

=2x=68

=2/2x=68/2

=x=34

A consistent and independent system of equations describes the given system of equations.

The consistent and independent system of equations are given below.

A consistent equation is a system of linear equations that is consistently unbiased when it has precisely one solution. While this is the case, the graphs of the lines within the system move at exactly one point. In inconsistent, a system of linear equations is inconsistent if it has no solutions.

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Medical practitioners recommend losing around 365 pounds or 730 pounds per year.

An equation is an expression that shows the relationship between two or more numbers and variables.

Medical practitioners recommend losing around 1–2 pounds (0.5–0.9 kg) per week.

Hence for a year:

Amount of weight loss = (1 * 365) or (2 * 365)

Medical practitioners recommend losing around 365 pounds or 730 pounds per year.

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Step-by-step explanation:

We will need to use logs here...

First divide each side by 3

[tex]3(10)^x=30000[/tex]

[tex]10^x=10000[/tex]

Then take the log of each side

Keep in mind that [tex]log_{10} (10)[/tex] gets canceled out to leave x

[tex]log_{10} (10^x)=log(10000)[/tex]

Finally, log(10000) = 4 because [tex]10^4=10000[/tex]

[tex]x = 4[/tex]

Question:

2÷a=(5/2)÷(5/4)

Answer:

a = 1

Answer:

17x

Step-by-step explanation:

3x+4+4x+4+3x-4+3x-4+4x

Collect liketerms

Answer:

A) City A was 5°C and City B was 4°C

Step-by-step explanation:

let temperature of City A be x and City B be y

According to the conditions of the question

4x = 8 + 3y (first temperature)

x - 2y = -3 (second temperature)

x = -3 + 2y

4(x) = (-3 + 2y)×4

4x = -12 + 8y

But it's already given that 4x = 8 + 3y

So,

8 + 3y = -12 + 8y

8 + 12 = 8y - 3y

20 = 5y

y = 20/5

y = 4

That means City B temperature was 4°C

So Option A

If you want you can find x to find City A temperature

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Answer:

Step-by-step explanation:

1 km = 0.62 mi

So, to convert 6 km to mi, multiply 6 by 0.62.

6km = 6* 0.62

        = 3.72 mi

1 L = 0.26 gal

To convert 2.5 L to gallon, multiply 2.5 by 0.26.

2.5 L = 2.5 * 0.26

         = 0.65 gal

1 lb = 0.45 Kg

To convert 90 lb to Kg, multiply 90 by 0.45.

90 lb = 90 *0.45

        = 40.5 Kg