Algebra 2 See image below for question, and requesting help! (20 points will be given!)

Which of the following expressions is equivalent to the expression x - 6?

svet-max [94.6K]

The second one. It is the same as the original.

8 0

3 years ago

Read 2 more answers

Sequence: 13, 11, 9, 7, .. an = an-1 a1 =

TiliK225 [7]

Answer:

a

n

=

−

2

n

+

15

Step-by-step explanation:

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

−

2

to the previous term in the sequence gives the next term. In other words,

a

n

=

a

1

+

d

(

n

−

1

)

.

Arithmetic Sequence:

d

=

−

2

This is the formula of an arithmetic sequence.

a

n

=

a

1

+

d

(

n

−

1

)

Substitute in the values of

a

1

=

13

and

d

=

−

2

.

a

n

=

13

+

(

−

2

)

(

n

−

1

)

Simplify each term.

Tap for more steps...

a

n

=

13

−

2

n

+

2

Add

13

and

2

.

a

n

=

−

2

n

+

15

4 0

3 years ago

A cylinder has a volume of 288 pi cubic meters and a height of 9 meters. What is the area of the base?

Pavlova-9 [17]

Answer:

The area of the base is about 32 square meters

Step-by-step explanation:

V = pi times r^2 times h which is the formula.

Since the volume is 288, and the height is 9 it is,

288 = pi times r^2 times 9,

288/9 = pi times r^2 times 9/9

32/pi = pi/pi times r^2

10.2 = r^2

The square root of 10.2 is about 3.19

Area formula is pi times radius, r^2

3.19 times 3.19 or 3.19^2 = 10.1761

10.1761 times pi is 31.96 which is about 32 square meters.

I hope this helps!

5 0

2 years ago

Read 2 more answers

Solve the Anti derivative.

Alex Ar [27]

Answer:

$\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C$

General Formulas and Concepts:

Algebra I

Factoring

Calculus

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration: $\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx$

Step 2: Integrate Pt. 1

[Integral] Factor fraction denominator: $\displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx$
[Integral] Integration Property - Multiplied Constant: $\displaystyle \frac{1}{9} \int {\frac{1}{x^2 + \frac{4}{9}}} \, dx$

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

$\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx$

Step 4: Integrate Pt. 2

[Integral] Substitute u-du: $\displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du$
[Integral] Trig Integration: $\displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C$
[Integral] Simplify: $\displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C$
[integral] Multiply: $\displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C$
[Integral] Back-Substitute: $\displaystyle \frac{1}{6}arctan(\frac{3x}{2}) + C$

Topic: AP Calculus AB

Unit: Integrals - Arctrig

Book: College Calculus 10e

7 0

2 years ago

Does the table show a direct proportional relationship? If so, what is the constant of proportionality?

lesantik [10]

Answer:

C. Yes, 3.5.

Step-by-step explanation:

If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality ( $k$ ) is described by the following expression:

$k = \frac{y}{x}$ (1)

Where:

$x$ - Input.

$y$ - Output.

If we know that $(x_{1}, y_{1}) = (13, 45.5)$ , $(x_{2}, y_{2}) = (14, 49)$ and $(x_{3}, y_{3}) = (15, 52.5)$ , then the constants of proportionalities of each ordered pair are, respectively: