Find the 57th term of the arithmetic sequence -13,-29,-47,….

Answer:

Hello There!

According to the question,

Base=6

And

Height =4

Let's know the formula

[tex] \frac{1}{2} \times base \times height \\ so \\ \frac{1}{2} \times 6 \times 4 \\ [/tex]

simplify 2 with 6 then it will look like this

[tex] \frac{1}{1} \times3 \times 4 \\ \\ [/tex]

1 has no value so

[tex]3 \times 4 = 12 {ft}^{2} \\ [/tex]

So third option

[tex]a = 12 {ft}^{2} [/tex]

is correct.

[tex]\Large\textsf{Hope \: It \: Helped}[/tex]

Answer:

Area = 12 sq ft

Step-by-step explanation:

The formula to find the area of a triangle is

1/2 bh so we will replace the letters with their number value

1/2 (6x4)

1/2 x 24 = 12

So, 12 is your answer!

Answer:

0.14

Step-by-step explanation:

brainliest please

Answer:

x=41

Step-by-step explanation:

9²+40²=x²

81+1600=x²

1681=x²

√1681=√x²

41=x

Answer:

It'd be a rational number

Step-by-step explanation:

Real numbers are a set of numbers containing all of the rational numbers and all of the irrational numbers.

Types of numbers in the rational number "section" are decimals, whole, mixed, and fraction numbers whether they are negative or positive they are rational numbers.

Irrational numbers are numbers that cannot be expressed as the ratio of two integers. So they would be square root, pi and more.

Answer:

arrange them: -9x^3+2x^3-4x^2+x^2-6x-5x

the simplified is: -7x^3-3x^2-11x

Answer:

23 seconds later Erin will catch up

Erin will run 115 meters

Step-by-step explanation:

23+4x=5x

x=23

23 seconds later Erin will catch up

Erin will run 115 meters

Answer:

a.0.311

Step-by-step explanation:

Answer:

5 tacos for 2 guests would mean more for each person, while 2 tacos for 5 guests would mean less for each person

Answer:

Step-by-step explanation:

The progression of sums is ...

  1, 5, 15, 34, 65, ...

So, first differences are ...

  4, 10, 19, 31

Second differences are ...

  6, 9, 12, ...

Third differences are constant:

  3, 3, ...

This means the expression for Sn will be a cubic expression. If dn is the first of the n-th differences, then the equation can be written as ...

  Sn = S1 +(n -1)(d1 +(n -2)/2(d2 +(n -3)/3(d3)))

And this simplifies a little bit to ...

  Sn = 1 +(n -1)(4 +(n -2)(n +3)/2)

In simpler form, we have ...

  Sn = 1/2(n³ +n)

Then the two terms we're interested in are ...

  S7 = (1/2)(7³ +7) = 175

  S17 = (1/2)(17³ +17) = 2465

Each term Sₙ consists of the sum of a triangular number of terms, which are given by

[tex]T_n = \displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

The triangular numbers are given recursively for n ≥ 1 by

[tex]T_n = T_{n-1} + n[/tex]

starting with T₀ = 0.

For example,

• S₁ = 1 and

[tex]\displaystyle S_1 = \sum_{k=T_0+1}^{T_1} k = \sum_{k=1}^1 k = 1[/tex]

• S₂ = 2 + 3 and

[tex]\displaystyle S_2 = \sum_{k=T_1+1}^{T_2} k = \sum_{k=2}^3 k = 2 + 3[/tex]

• S₃ = 4 + 5 + 6 and

[tex]\displaystyle S_3 = \sum_{k=T_2+1}^{T_3} k = \sum_{k=4}^6 k = 4 + 5 + 6[/tex]

Then the n-th term of the sequence we're considering is

[tex]S_n = \displaystyle \sum_{k=T_{n-1}+1}^{T_n} k = \sum_{k=T_{n-1}+1}^{T_{n-1}+n} k[/tex]

Expanding this sum, we have

[tex]S_n = \left(T_{n-1}+1\right) + \left(T_{n-1}+2\right) + \left(T_{n-1}+3\right) + \cdots + \left(T_{n-1}+n\right)[/tex]

There are n terms on the right side, and hence n copies of [tex]T_{n-1}[/tex], and the rest of the terms make up the next triangular number [tex]T_n[/tex] :

[tex]S_n = nT_{n-1} + 1 + 2 + 3 + \cdots + n[/tex]

[tex]S_n = nT_{n-1} + \displaystyle \sum_{k=1}^n k[/tex]

[tex]S_n = nT_{n-1} + T_n[/tex]

We have a closed form for [tex]T_n[/tex], so we end up with

[tex]S_n = n \cdot \dfrac{(n-1)n}2 + \dfrac{n(n+1)}2 \implies \boxed{S_n=\dfrac{n^3+n}2}[/tex]

From here it's easy to find S₇ and S₁₇.

[tex]S_7 = \dfrac{7^3+7}2 \implies \boxed{S_7 = 175}[/tex]

[tex]S_{17} = \dfrac{17^3+17}2 \implies \boxed{S_{17} = 2465}[/tex]

Answer:

6/6 or 1

Step-by-step explanation:

bow tie method

[tex] = {8}^{3} \: \: cm ^{3} \\ = 512 \: \: {cm}^{3} [/tex]

Answer:

The volume is 512 cube centimetres.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

4 miles

Step-by-step explanation:

6*(1/6) = 1 hour

6*(2/3) = 4 miles

Answer:

4 miles

Step-by-step explanation:

You are finding the rate. The formula for this equation is Rate=Distance/Time.

Your distance is 2/3, and your time is 1/6.

You divide 2/3 by 1/6 to get your answer of 4

Answer:

d

Step-by-step explanation:

same explanation as before just replace the current values with the previous explanation

Answer:

After a quick stint of attempting to read the graphs I would speculate D

Answer:

don't know

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = -1(x + 2)(x - 3)(x - 3)(x + 0)(x + 0)(x + 1)(x + 1)(x + 1)

The 8 degree polynomial for the given roots can be written as  p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).

The roots of the polynomial are given as follows,

Number of roots at -2 = 1

Number of roots at 3 = 2

Number of roots at 0 = 2

And, number of roots at -1 = 3.

Now, the polynomial can be written using factor theorem as,

p(x) = x²(x + 2)(x - 3)²(x + 1)³

      = x²(x + 2)(x²- 6x + 9)(x³ + 3x² + 3x + 1)

      = x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x²

Hence, the polynomial for given roots can be written as p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

To know more about factor theorem click on,

https://brainly.com/question/13547729

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Answer:

The man traveled 20km by train.

Step-by-step explanation:

If x is the distance he traveled by train, you can write this equation to represent the situation:

[tex]10+x+2x=70[/tex]

Then, you can simply solve for x:

[tex]10+3x=70\\3x=60\\x=20[/tex]

The man traveled 20km by train.

[tex]10+(20)+2(20)=70\\10+20+40=70\\70=70[/tex]

Answer:

Dividend: Number on top

Divisor: Number on bottom

Quotient: Answer

Dividend ÷ Divisor = Quotient

Answer:0

Step-by-step explanation:

hey i'm in the six grade i'm not sure but pls try it

Answer:

x<=-12

Step-by-step explanation:

1/4x<=-3

*Multiply both sides by 4

x<=-12

and it's solved :)

Answer:

13 ft^2

Step-by-step explanation:

Area = Base * Height

= 3 * (4+1/3)

=3*(13/3)

=13

Answer:

Continuous

Step-by-step explanation:

Answer:

|-5| absolute be always + so 5

Answer:

[tex]5[/tex]

Step-by-step explanation:

Step 1:  Determine what absolute value does

Taking the absolute value of a number just returns how far a specific value is from 0.  So in this case we see a number -9 and although it's negative it's still 9 away from 0 therefore that would be the absolute value.

We are missing the absolute value of -5 or 5 so we know that taking the absolute value would just give us the distance from 0.  In this case that would just be 5.

Answer: [tex]5[/tex]

Answer:

Step-by-step explanation:

Answer:

1470 inches cubed

Step-by-step explanation:

Vol=length × width × height

But ALSO,

length × width = Area,

So we find another Volume equation,

Vol = BaseArea × height

This is the information you are given in the question.

Vol = 210 × 7

Vol = 1470 inches cubed

Answer:

x = 36

Step-by-step explanation:

3x+2x=180

5x=180

x=36

Answer:

x=36 degrees

Step-by-step explanation:

The distance Jen is from the base of the lighthouse is 86.6 meters.

Trigonometric ratio is used to show the relationship between the sides of a and angles of a right angled triangle.

Let d represent the distance Jen is from the base of the lighthouse.

Using trigonometric ratios:

[tex]tan(30)=\frac{50}{d} \\\\d=\frac{50}{tan(30)} \\\\d=86.6\ m[/tex]

The distance Jen is from the base of the lighthouse is 86.6 meters.

Find out more on Trigonometric ratio at: https://brainly.com/question/10417664