Solve the following equation for θ on the interval [0,360∘).

Find the 21st term in the arithmetic sequence.<br> 3, 7, 11, 15, 19, ...

NNADVOKAT [17]

The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.

<h3>What is the nth term of an arithmetic series?</h3>

The nth term of an arithmetic sequence is calculated by the formula

aₙ = a + (n - 1) · d

Here the first term is 'a' and the common difference is 'd'.

<h3>Calculation:</h3>

The given sequence is an arithmetic sequence.

3, 7, 11, 15, 19, ....

So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.

Thus, the required 21st term in the sequence is

a₂₁ = 3 + (21 - 1) × 4

⇒ a₂₁ = 3 + 20 × 4

⇒ a₂₁ = 3 + 80

∴ a₂₁ = 83

So, the 21st term in the given arithmetic sequence is 83.

Learn more about the arithmetic sequence here:

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5 0

11 months ago

Solve for x.<br> -x/3=2<br><br> x= -6<br> x= -1<br> x = 6

LenKa [72]

Answer:

x = -6

Step-by-step explanation:

Solve for x:

-x/3 = 2

Multiply both sides of -x/3 = 2 by -3:

(-3 (-x))/3 = -3×2

-3×(-1)/3 = (-3 (-1))/3:

(-3 (-1))/3 x = -3×2

(-3)/3 = (3 (-1))/3 = -1:

--1 x = -3×2

(-1)^2 = 1:

x = -3×2

-3×2 = -6:

Answer: x = -6

6 0

2 years ago

Choose the domain for which each function is defined

klemol [59]

Answer:

Part 1) $f(x)=\frac{x+4}{x}$ -----> $x\neq 0$

Part 2) $f(x)=\frac{x}{x+4}$ ----> $x\neq -4$

Part 3) $f(x)=x(x+4)$ ----> All real numbers

Part 4) $f(x)=\frac{4}{x^2+8x+16}$ ----> $x\neq -4$

Step-by-step explanation:

we know that

The domain of a function is the set of all possible values of x

Part 1) we have

$f(x)=\frac{x+4}{x}$

we know that

In a quotient the denominator cannot be equal to zero

so

For the value of x=0 the function is not defined

therefore

The domain is

$x\neq 0$

Part 2) we have

$f(x)=\frac{x}{x+4}$

we know that

In a quotient the denominator cannot be equal to zero

so

For the value of x=-4 the function is not defined

therefore

The domain is

$x\neq -4$

Part 3) we have

$f(x)=x(x+4)$

Applying the distributive property

$f*(x)=x^2+4x$

This is a vertical parabola open upward

The function is defined by all the values of x

therefore

The domain is all real numbers

Part 4) we have

$f(x)=\frac{4}{x^2+8x+16}$

we know that

In a quotient the denominator cannot be equal to zero

so

Equate the denominator to zero

$x^2+8x+16=0$

Remember that

$x^2+8x+16=(x+4)^2$

( $x+4)^2=0$

The solution is x=-4

so

For the value of x=-4 the function is not defined

therefore

The domain is

$x\neq -4$

6 0

2 years ago

Can some one help me please

frutty [35]

I believe The answer is B

6 0

2 years ago

HELP?<br><br> 7-15 please :) show work<br> thank you!

Alexus [3.1K]

Answer:

7. x = 3

Step-by-step explanation:

To find the value of x, use the triangle sum property. Every triangle has interior angles which add to 180 degrees. To solve, add the expressions and numbers together then set equal to 180. Then use inverse operations to solve for x.

7. 20x - 9 + 10x + 9 + 90 = 180 Subtract 90 from both sides.

20x - 9 + 10x + 9 = 90 Add -9 + 9 = 0

20x + 10x = 90 Add like terms 20x + 10x = 30x

30x = 90 Divide both sides by 30.

x = 3

Repeat this process for each problem.

7 0

2 years ago