if radius equals 3 and the arc that bounds that sector is 40° what is the sector area and arc length equal?

The rule that can be used to find the next term of the sequence 27, 40, 53, 66, 79,... is given by: Option C: a_n = a_(n-1) + 13

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

[tex]a, a + d, a + 2d, ... , a + (n+1)d, ...[/tex]

Its nth term is

[tex]T_n = a + (n-1)d[/tex]

(for all positive integer values of n)

And thus, the common difference is

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

for all positive integer values of n

Here, the considered sequence is 27, 40, 53, 66, 79,...

We see that:

40-27=13

53-40=13

and so on, the difference between each consequtive pair of terms of this sequence is 13.

Thus, due to having common difference in consequtive terms, this is an arithmetic sequence.

For this series, we've got:

Thus, its nth term is given by:

[tex]T_n = a+(n-1)d= 27 +(n-1)13 = 13n + 14[/tex]

Since the options are using the notation [tex]a_n[/tex] instead of [tex]T_n[/tex], so we will use that too. Thus, nth term and (n-1)th terms are:

[tex]a_n = 13n + 14\\a_{n-1} = 13(n-1) + 14 = 13n + 1\\[/tex]

Thus, we can write nth term in the form of (n-1)th term as:

[tex]a_n = 13n + 14 = 13n + 1 + 13 = a_{n-1} + 13\\\\a_n = a_{n-1} + 13[/tex]

Thus, the rule that can be used to find the next term of the sequence 27, 40, 53, 66, 79,... is given by: Option C: a_n = a_(n-1) + 13

Learn more about arithmetic sequence here:

https://brainly.com/question/3702506

Answer:

c

Step-by-step explanation:

Answer:

F. 48.98 m

Step-by-step explanation:

What is circumference?

How does it apply here?

Solving

Step 1: Plug in your values.

Step 2: Simplify.

Therefore, the correct answer is F. 48.98 meters.

Answer:

C. y = 3/x + 1

Step-by-step explanation:

A linear function is, well, a line. The line goes on indefinitely without a stopping point.

In one of these functions, there is a line with a stopping point.

The function y = 3/x + 1 has a point that does not have a value, which is 0. 0 cannot be a value in a denominator. All of the other functions can be expressed at all values.

Graphical proof is attached. The function in green has a discontinuity at x = 0 and therefore is not linear.

Answer:

[tex]\Longrightarrow:\boxed{\sf{x=3}}[/tex]

Step-by-step explanation:

Isolate the term of x, from one side of the equation.

Use the distributive property.

Distributive property:

⇒ A(B+C)=AB+AC

2(x+10)

2*x=2x

2*10=20

2x+20=x+23

First, subtract by 20 from both sides.

2x+20-20=x+23-20

Solve.

Subtract the numbers from left to right.

23-20=3

2x=x+3

Then, you subtract by x from both sides.

2x-x=x+3-x

Solve.

[tex]\Longrightarrow: \boxed{\sf{x=3}}[/tex]

Answer:

Step-by-step explanation:

In this question we're given with an equation that is 2(x + 10) = x + 23 and we are asked to find the value of x .

Solution : -

[tex] \longmapsto \: 2(x + 10) = x + 23[/tex]

Step 1 : Solving the parenthesis on left hand side :

[tex]\longmapsto \:2x + 20 = x + 23[/tex]

Step 2 : Subtracting 20 on both sides :

[tex]\longmapsto \:2x + \bold{ \cancel{20}} - \bold{ \cancel{20} }= x + \bold{23 - 20}[/tex]

On further calculations , we get :

[tex]\longmapsto \:2x =x + 3[/tex]

Step 3 : Subtracting x on both sides :

[tex]\longmapsto \:2x - x = \bold{ \cancel{x} }+ 3 - \bold{ \cancel{x}}[/tex]

On further calculations, we get :

[tex]\longmapsto \: \red {\boxed{{x = 3}}}[/tex]

Now , we're verifying our answer by substituting the value of x in given equation :

Therefore, our answer is correct.

Answer:

day 26

Step-by-step explanation:

just multiply the numbers

Answer:

Complete the following statement.Of the three pools described, Model_______ needs the largest amount of water to be completely filled. B A C. 2. See answers.

2 answers

·

1 vote:

Answer: A Step-by-step explanation: It because of The Width and Depth

Missing: ___ ‎____ ‎drew ‎net ‎pyramid,

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume of cylinder = base area * height

height of the cylinder = Volume of the cylinder ÷ base area

                                   = 1205.76 ÷ 200.96

                                   = 6 in

Answer:

I think area will me 24 sq unit

AC=6

BD=8

1/2 × 8 × 6 = 24

[tex]f(x) = y = 2x +3\\\\\text{Replace x with y and then solve for y:}\\\\~~~~~~~x= 2y+3 \\\\\implies 2y = x-3\\\\\implies y = \dfrac{x-3}2\\\\\implies f^{-1}(x)= \dfrac{x-3}2[/tex]

Answer:

x = 8

Step-by-step explanation:

Theorem

When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Secant:  a straight line that intersects a circle at two points

Tangent: a straight line that touches a circle at only one point

Given:

⇒ x² = 16 · 4

⇒ x² = 64

⇒ x² = √(64)

⇒ x = ±8

As distance is positive, x = 8

Answer:

Tables 3,4 and 5

Step-by-step explanation:

Answer on quizlet.

Answer:

h

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

(24+2)/2 would be the expression.

PEMDAS so first complete the numbers in the Parantheseis:

(24+2)/2 = 26/2

Since there are no exponents or mulitplication, divide:

26/2 = 13

Hope this helps!

Answer:

2 hours

Step-by-step explanation:

You can express each person's total earning as the formula for a line. (y=mx+b) Use the amount per hour that can be earned as the slope (m) and the amount already earned as the y intercept (b)

Sophie: y=4x+7

Marcos: y=6x+3

Since y is the total amount of money saved and you know that both people need to earn the same amount of money, we know that y is the same in both equations so we can use substitution to substitute one of the equations in for y in the other equation like this:

4x+7=6x+3

From here, solve algebraically

Subtract 3

4x+4=6x

Subtract 5x

4=2x

Divide by 2

x=2

So they will have the same amount of money after 2 hours.

Answer:

30

Step-by-step explanation:

red : blue = 5:3

since difference between 5&3 is automatically 2....then just add 0 to 3

Answer:

5 pounds

Step-by-step explanation:

5 pounds is 80 ounces, which is greater then 75 ounces.

Answer:

40%

Step-by-step explanation:

147 - 105 = 42

42/105 = .4

.4 × 100 = 40%

Part I: Converting the terms into fraction form

Given equation:

First, let's convert the terms (that are in decimals) into fractions.

Replace the fraction forms in the equation:

Part II: Simplifying the division being performed

Since the expression in the parenthesis can't be simplified, we can open the parenthesis. Before we do that, we need to divide the expression by 9/10 (as division is third in BODMAS). This can be done by converting the divisor into it's reciprocal and changing the sign to a multiplication sign.

Since there is no other division being performed, we can simplify the distributive property (as multiplication is fourth in BODMAS).

Part III: Isolating "k" to determine it's value

Combine like terms as needed:

Subtract 7/10 both sides of the equation to isolate "x" and it's coefficient.

Cancel the denominators (as a/b = c/b ⇔ a = c)

Divide both sides by 25 to isolate "k"

Answer:

x ≈ 37.13°

Step-by-step explanation:

using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{13.4}{22.2}[/tex] , then

x = [tex]sin^{-1}[/tex] ( [tex]\frac{13.4}{22.2}[/tex] ) ≈ 37.13° ( to the nearest hundredth )

Answer:

                                                                            = length x width x height

[tex]r = \frac{Σ(X-X)(Y-Y)}{\sqrt{Σ(X-X)²} \sqrt{(Y-Y)²}}[/tex]

Where, X-mean of X variable

Y - mean of Y variable

Answer:

B) − 2/9

Explanation:

[tex]\hookrightarrow \sf \dfrac{11}{18} * -\dfrac{4}{11}[/tex]

join both fractions

[tex]\hookrightarrow \sf \dfrac{11*-4}{18*11}[/tex]

simplify by multiplying

[tex]\hookrightarrow \sf \dfrac{-44}{198}[/tex]

simplify the following

[tex]\hookrightarrow \sf -\dfrac{2}{9}[/tex]

[tex]\bold{Heya!}[/tex]

[tex]\sf{\frac{11}{18}(-\frac{4}{11})[/tex]

Apply rule :  [tex]\sf{a(-b) = -ab}[/tex]

[tex]\sf{\frac{11}{18}(-\frac{4}{11}) = -\frac{11}{18}[/tex] × [tex]\sf{\frac{4}{11}[/tex]

[tex]\sf{= -\frac{11}{18}[/tex] × [tex]\sf{\frac{4}{11}[/tex]

Cross - cancel common factor: [tex]\sf{11}[/tex]

[tex]\sf{= -\frac{4}{18}[/tex]

Factor the number: [tex]\sf{4 = 2}[/tex] × [tex]\sf{2}[/tex]

[tex]\sf{= -\frac{2 \: x \: 2}{18}[/tex]

Factor the number: [tex]\sf{ 18 = 2 \: x \: 9}[/tex]

[tex]\sf{= - \frac{2 \: x \: 2}{2 \: x \: 9}[/tex]

Cancel common factor: [tex]\sf{2}[/tex]

[tex]\sf{-\frac{2}{9}[/tex]

Hopefully This Helps ! ~

#LearnWithBrainly

[tex]\underline{Answer :}[/tex]

Jaceysan ~

Answer:

D. (f + g)(x) = -2x² - 2x + 8

Step-by-step explanation:

Given:

Find (f + g)(x):

⇒ [tex]f(x) + f(g)[/tex]

⇒ [tex]3x + 5 + ( -2x^{2} - 5x + 3 )[/tex]

⇒ [tex]3x + 5 - 2x^{2} - 5x + 3[/tex]

Combine like terms:

⇒ [tex]-2x^{2} + 3x - 5x + 5 + 3[/tex]

⇒ [tex]-2x^{2} - 2x + 8[/tex]

Answer: D. (f + g)(x) = -2x² - 2x + 8

Answer:

y=mx+b

Step-by-step explanation:

use that formula

Answer:

D. 50.

Step-by-step explanation:

50 trials . The greater the number of trials the closer will the experimental probability be to the theoretical.

[tex]\log_x (1)+\log_y (y)\\\\=\log_x x^0 + 1\\\\=0\cdot \log_x x +1\\\\=0+1\\\\=1[/tex]

Answer:

∠ MLK = 51°

Step-by-step explanation:

the secant- secant angle MLK is half the difference of the measures of the intercepted arcs , that is

∠ MLK = [tex]\frac{1}{2}[/tex] ( NJ - MK ) ← substitute values

4x + 3 = [tex]\frac{1}{2}[/tex] (170 - (5x + 8) ) ← multiply both sides by 2 to clear the fraction

8x + 6 = 170 - 5x - 8

8x + 6 = 162 - 5x ( add 5x to both sides )

13x + 6 = 162 ( subtract 6 from both sides )

13x = 156 ( divide both sides by 13 )

x = 12

Then

∠ MLK = 4x + 3 = 4(12) + 3 = 48 + 3 = 51°

Answer:

6

Step-by-step explanation:

10 runners

explanation:

1/4 x 10 = 2 1/2

Answer:

6 feet

Step-by-step explanation:

took the test and got it right

Answer:

6 feet

Step-by-step explanation:

(c) 6 feet

96

In this type of box plot, the two end lines are the absolute maximum and minimum values, each edge of the box is the lower and upper 25%, respectively from left to right, and the line in the box is 50%

So the answer here is the right edge of the box, or 96

Answer:

1/2 anwser is B

Step-by-step explanation:

rolled 2 fair number 500 times right? okay so the sum is a number of anytotal added up correct?

it was shown on the cubes each time ,so you can assume wit 42+10=52?2=x well then just divide that by 500! wich is 1/2