Write a recursive formula and an explicit formula for the following arithmetic sequence.
5, 3, 1, -1, ...
A recursive formula is a1 = , an = |
(Simplify your answers. Use integers or decimals for any numbers in the expressions.)
An explicit formula is an =
(Simplify your answer. Use integers or decimals for any numbers in the expression.)

Answer:

i. 82°

ii. 14°

iii. 28°

iv. 47°

v. 58°

Step-by-step explanation:

The trigonometric functions are given as:

Sin θ = [tex]\frac{opposite}{hypotenus}[/tex]

Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Thus,

i. adjacent leg / hypotenuse = 0.139 = Cos θ

θ = [tex]Cos^{-1}[/tex] 0.139

  = 82°

ii. opposite leg / adjacent leg = 0.249 = Tan θ

θ = [tex]Tan^{-1}[/tex] 0.249

  = 14°

iii. opposite leg / hypotenuse = 0.469 = Sin θ

θ  = [tex]Sin^{-1}[/tex] 0.469

   = 28°

iv. adjacent leg / hypotenuse = 0.682 = Cos θ

θ = [tex]Cos^{-1}[/tex] 0.682

   = 47°

v. opposite leg / hypotenuse 0.848 = Sin θ

θ  = [tex]Sin^{-1}[/tex]  0.848

   = 58°

Answer:

Step-by-step explanation:

he volume of the topsoil is

28 ft by 21 ft by 5/15 ft = 245 cubic feet

There are 27 cubic feet in one cubic yard.

245/27 = 9.074074074.... = 9.074

Need 9.25 = 9 and 1/4 cubic yards

Answer:

60 minutes

Step-by-step explanation:

She painted 2/5 of the wall.

She still needs to paint 3/5 of the wall.

3 is 50% more than 2, so 3/5 is 1.5 times 2/5, so it will take her 1.5 times the time it took so far.

1.5 * 40 minutes = 60 minutes.

Answer: 60 minutes

Answer: x=3, elimination method

Step-by-step explanation:

x=3

-7x-2y=-13    ->  -7x-2y=-13

-(x-2y=11)      ->   -x+2y=-11

                        -----------------

                          -8x=-24

                              x = 3

elimination method

because you can easily eliminate one variable (y) using the elimination method

Answer:

Greater Than [The second choice]

Step-by-step explanation:

Step-by-step explanation:

[tex] {x}^{2} - 8x + 15 = 0 \\ (x - 3)(x - 5) = 0 \\ x = 3 \: or \: x = 5[/tex]

Answer:

7.0

Step-by-step explanation:

Tangents form right angles, so AOB is a right triangle.

Now using Pythagorean Theorem (A^2 + B^2 = C^2), plug in the values and solve inversely.

5^2 + B^2 = 8.6^2

25 + B^2 = 73.96

B^2 = 48.96

B = squareroot 48.96

B = 6.997 --> 7.0

Answer: r is 7

Step-by-step explanation:

ABO is a right triangle

[tex]a^{2} +b^{2} =c^{2} \\5^{2} +b^{2} =8.6^{2} \\25+b^{2} =73.96\\b^{2} =48.96\\b=6.997[/tex]

Answer:

x.......y

-8...-2

-1....1

0....0

1....-1

8...2

Answer:

-2

-1

0

1

2

Step-by-step explanation:

in order to find the y values you need to plug in the x values in the table into the function

the cube root of -8 is -2 (since this is a cube root instead of a square root we can have negative values in it because when we cube negative values we get negative values i.e. -2³=-8 ; -3³=-27)

the cube root of -1 is -1

the cube root of 0 is 0

the cube root of 1 is 1

the cube root of 8 is 2

Answer:1-5

Step-by-step explanation:Assuming the spinner is numbered 1–5 and has an equal chance of landing on any number, you have two independent probabilities, each 1 in 5.

Just multiply those: 1/5 * 1/5 = 1/25. You have a 4% chance of getting 2 twice.

Of course, if there’s anything special about spinning “2”, you’ll be keyed to watch for it after getting 2 the first time. Now there’s a 20% chance (1 in 5) you’ll spin it again, and you’ll be very excited that you got 2 twice in a row. Another way of saying that is that the probability of something that has already happened is 100%.

Answer:

Step-by-step explanation:

This is the proportional relationship:

We have x = 3, y = 24, then k is:

The table will look as:

Correct choice is C

Answer:

c

Step-by-step explanation:

Answer:

864

Step-by-step explanation:

144x6

Answer:

b

Step-by-step explanation:

Answer:

1.5 feet

Step-by-step explanation:

12/8 = 1.5 feet

Answer:

+8 and -8, 2nd answer from the right.

Answer:

a = 18 ft is the answer.

Step-by-step explanation:

a = ?

b = 24 ft

c = 30 ft

According to the Pythagoras theorem,

a² + b² = c²

a² + 576 = 900

a² = 900 - 576

a² = 324

a = 18 ft

∴ a = 18 ft is the length of the missing leg.

Answer:

18 feet

Step-by-step explanation:

The Pythagorean theorem is a formula that can be used to find the unknown side length of a right triangle when given the length of the other two sides. The general formula for the Pythagorean theorem is the following,

[tex]a^2 + b^2 = c^2[/tex]

Where (a) and (b) are the legs of the right triangle, or rather the sides adjacent to the right angle of the right triangle. Additionally, (c) is the hypotenuse or the side opposite the right angle of the right triangle.

Substitute in the given values and solve, let parameter (a) represent the unknown side of the triangle,

[tex]a^2 + b^2 = c^2\\[/tex]

Substitute,

[tex](24)^2 + a^2 = (30)^2\\[/tex]

Simplify,

[tex]576 + a^2 = 900[/tex]

Inverse operations,

[tex]576 + a^2 = 900\\-576\\\\a^2 = 324\\\sqrt{}\\\\a = 18[/tex]

Answer:

ummmm math?

Step-by-step explanation:

Answer:

361.09

Step-by-step explanation:

Explanation:

Calculate the standard error of the mean, SE, using this formula, where  is the standard deviation and n is the sample size.

For this situation, the sample size is 65, and the standard error of the mean is 44.8. Substitute these values into the formula, and solve for .

So the standard deviation is approximately 361.09.

The standard deviation is 361.09 if each sample contains 65 responses, and the standard error of the mean is 44.8.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

We have:

Melvin conducted a series of surveys asking political candidates about the number of constituents they mail literature to each sample contains 65 responses, and the standard error of the mean is 44.8.

As we know,

The standard error is given by:

SE = σ/√n

SE = 44.8

n = 65

44.8 = σ/√65

44.8√65 = σ

σ = 361.09

Thus, the standard deviation is 361.09 if each sample contains 65 responses, and the standard error of the mean is 44.8.

Learn more about the standard deviation here:

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The equation of the circle graphed below is (x + 2)² + (y - 3)² = 16.

To determine the equation of the circle graphed below, we need to use the standard form equation of a circle.

The standard form of a circle equation is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Given the graph, we can see that the center is located at (-2, 3), and the radius is 4 units. Therefore, we can substitute these values into the standard form equation as follows:(x - (-2))² + (y - 3)² = 4²(x + 2)² + (y - 3)² = 16

To lear more about : circle graphed

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Answer:

[tex](x +3)^2+(y-2)^2=4[/tex]

Step-by-step explanation:

The equation of a circle in standard form is:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

To determine the equation of the graphed circle, we need to find its center and radius.

The center of the circle is a single point that lies at an equal distance from all points on the circumference of the circle.

From inspection of the graphed circle, we can see that its domain is [-5, -1] and its range is [0, 4].  The x-coordinate of the center is the midpoint of the domain, and the y-coordinate of the center is the midpoint of the range.

[tex]x_{\sf center}=\dfrac{-5+(-1)}{2}=-3[/tex]

[tex]y_{\sf center}=\dfrac{0+4}{2}=2[/tex]

Therefore, the center of the circle is (-3, 2).

The radius of the circle is the distance from the center to all points on the circumference of the circle.  From observation, we can see that the radius of the circle is r = 2.

To determine the equation of the circle, substitute the center and radius into the standard formula.

[tex](x - (-3)^2+(y-2)^2=2^2[/tex]

[tex](x +3)^2+(y-2)^2=4[/tex]

Therefore, the equation of the graphed circle is:

[tex]\boxed{(x +3)^2+(y-2)^2=4}[/tex]

Answer:

I think it is either C or D

Step-by-step explanation:

I'm so sorry id didn't find the answer, i tried

Answer: you combine like terms to get 10x+9

Step-by-step explanation: 4+5+1 is 10 and 7+2 is 9.

Answer:

10x+9

Step-by-step explanation:

Answer:

C. 150

Step-by-step explanation:

It's right on Plato.

Answer:

5

Step-by-step explanation:

Answer:2/3

Step-by-step explanation:

The coordinates of point R' are given as follows:

(8,1).

The four translation rules are defined as follows:

The coordinates of points Q and Q' are given as follows:

Q(6,3), Q'(8,3).

Hence the translation rule is given as follows:

(x,y) -> (x + 2, y).

The coordinates of point R are given as follows:

R(6,1).

Hence the coordinates of point R' are given as follows:

(6 + 2, 1) = (8,1).

More can be learned about translation at brainly.com/question/29209050

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SAS, I guess (side angle side)

Step-by-step explanation:

Since AM=BC then AM+MB=MB+BN.

Therefore, AB=MN. So, the two triangle have one congruent angle, and the sides adjacent to it are congruent as well. Those triangle are thus congruent

Answer:

B. SAS (Side Angle Side)

Step-by-step explanation:

its right on E2020

ANSWER

-1,-1 is P

-4, -3 is R

-2,  -3 is Q

I think this is the answer hope it helps :)

Answer:he can buy at least 7 pairs of socks

Step-by-step explanation:

Answer: 10 miles

Step-by-step explanation:

Given

The length of the road is 1000 miles

Solve

1 : 100 = x : 1000 ⇔ Proportion Set Up

100x = 1000 ⇔ Cross Multiply

100x/100 = 1000/100 ⇔ Divide both sides by 100

x=10 ⇔ Simplify

Hope this helps!! :)

Please let me know if you have any questions