Find the measure of the third side. Round your answer to the nearest whole number. ​

The number that belongs to both sequences is 26.

The formula known as the nth term allows us to locate any term in a series. The letter "n" stands for "number."

By changing the term number's value, we can create a series that uses the nth term (n).

To find the 10th term we would follow the formula for the sequence but substitute 10 instead of ‘n‘; to find the 50th term we would substitute 50 instead of n.

We have two sequences, let's call one as A and the other as B.

The n-th term of sequence A is written as:

aₙ = 3*n^2 - 1

the nth term of sequence B is written as:

bₙ = 30 - n^2

We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)

Then we want to find:

aₙ = bₓ

where n and x are integer numbers.

Then we will heave:

3*n^2 - 1 = 30 - x^2

To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.

Let's isolate n.

3*n^2 = 30 - x^2 + 1

3*n^2 = 31 - x^2

n^2 = (31 - x^2)/3

n = √(  (31 - x^2)/3)

Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.

Then let's start with x = 1.

n(1) = √(  (31 - 1^2)/3) = √(30/3) = √10

We know that √10 is not an integer.

now with x = 2,

n(2) = √(  (31 - 2^2)/3)  = √( (31 - 4)/3) = √(27/3) = √9 = 3

then if x = 2, we have n = 3.

Both of them are integers, then we get:

a₂ = 3*(3)^2 - 1 = 27 - 1 = 26

b₃ = 30 - 2^2 = 30 - 4 = 26

Therefore, The number that belongs to both sequences is 26.

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Answer:

Step-by-step explanation:

Take the log of both sides:

log (5^2) = log 25, or

2 log 5 = log 25 or 2 log 5

Note that 5^2 = 25 is always true.

Answer:

7. .44

8. .009

Step-by-step explanation:

7. 44 ÷ 100 = .44

8. 9 ÷ 1000 = .009

The solution is Option B.

Noise is easily filtered out without damage to the original signal because a narrow range of values is expected

A digital signal encodes data as a sequence of discrete values. A digital signal can only have one value from a finite set of possible values at any given time. A signal which is a discrete function of time, i.e. non-continuous signal, is known as digital signal. Digital computers and digital phones are some of the examples of digital signals

The three types of digital signals are

Continuous-Time/Analog Signal

Discrete-Time Signal

Digital Signal

Given data ,

The digital signals are a more reliable way to encode and transmit information than analog signals

Because , while transmitting information through digital signals , they have less interference over long distances and digital signals offer better clarity

The digital devices only record pieces of sound waves, not full waves.

Now , Analog technology stores information as sound waves; digital technology stores it as strings of ones and zeroes.

Hence , noise is easily filtered out without damage to the original signal because a narrow range of values is expected

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Answer:

A. 6x - 4

Step-by-step explanation:

[tex]\sf 8-3(4-2x)[/tex]

Distribute:-

[tex]\sf 8+(-3)(4)+(-3)(-2x)[/tex]

[tex]\sf 8+-12+6x[/tex]

Combine Like Terms:-

[tex]\sf (6x)+(8+-12)[/tex]

[tex]\sf 6x+-4[/tex]

** + * - = -**

[tex]\sf 6x-4[/tex]

Therefore, option A. 6x - 4 is your answer!

_____________________

Hope this helps!

Have a great day!

Answer:

True

True

False

On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is 500

obtained is 400

so, percentage - 400/500 X 100 = 80%

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The ^ operator in logical mathematics means the OR operation . Therefore , the statement ∧ and ∠means that a or the negation of a is joined by the or operation .

These are known as logical operations as they are based upon logic.The meaning of the term logic is reasoning which means to resonate. The reasoning may be a legal opinion or mathematical confirmation.

We apply logic on expression to check whether they are true of false . Some of the mathematical logics are a negation, conjunction, and disjunction logical operations. The symbols used for them in mathematical logic is, ‘~’ for negation ‘^’ for conjunction and ‘ v ‘ for disjunction.

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Answer:

see explanation

Step-by-step explanation:

A

∠ UVX and ∠ WXV are alternate angles and are congruent , then

∠ UVX = ∠ WXV = 15°

∠ WVU = ∠ WVX + ∠ UVX = 24° + 15° = 39°

B

opposite sides of a parallelogram are congruent , then

UV = XW = 36

C

consecutive angles are supplementary , sum to 180° , then

∠ XUV + ∠ WVU = 180° , so

∠ XUV + 39° = 180° ( subtract 39° from both sides )

∠ XUV = 141°

D

diagonals bisect each other , so

YW = UY = 10

Answer:

hey guys!! answer is B!!

Step-by-step explanation

hope this helps!

Answer:

b give brainest

Step-by-step explanation:

The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.

Volume is the measure of the amount of 3-dimensional space occupied by an object or substance. It is usually measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in mathematics, physics, chemistry, and engineering, and is used to calculate the amount of material needed for a given project.

The volume of the box can be calculated by multiplying the area of the base with the height of the box. The area of the base is 58 cm² and the height of the box is x - 2 cm. Therefore, the volume of the box can be expressed as:
Volume = 58 cm² x (x - 2 cm)
     = 58 cm³
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.

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Answer:Answer:

the added person age is 26

Step-by-step explanation:

let the added person age is A

the six person mean is (23+19+12+21+13+A)/6=19

=> 88+A/6=19

=>A=(19×6)-88

there fore A=26

Answer:

39

Step-by-step explanation:

13 + 13 + 19 + 23 + 19 + x = 21

                       6

Combine like terms

(87 + x) / 6 = 21                  Multiply both sides by 6

(87 + x )  = 21 * 6

87 + x = 126                       Subtract 87 from both sides

x = 126 - 87

x = 39

The 6th person entering the room was 39

Based on the question above, Jessica sold 260 books and Josh sold 20 books.

Let x be the number of books Josh sold

We know that:

Jessica sold 13x books

Together they sold 280 books

So we can set up an equation:

x + 13x = 280

14x = 280

x = 20

Josh sold 20 books

Jessica sold 13 * 20 = 260 books

Therefore Jessica  = 260 books sold and Josh = 20 books sold.

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Its a solid and a cube

You were wrong with square because a square only has one face while a cube has 6.

You were also wrong with polygon because while polygons are 1-dimensional a cube is 3-dimensional

The following terms correctly describe the given object Square, Solid, Cube, Polygon.

Options A, B, C, D are correct.

A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.

Square is a figure in which all four sides are equal.

Solid is a three dimensional figure.

A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Polygon is two dimensional figure with straight lines.

The following terms correctly describe the given object Square, Solid, Cube, Polygon.

Options A, B, C, D are correct.

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Answer:

Step-by-step explanation:

To find the y-intercept, we can use the slope-intercept form of a linear equation which is y = mx + b, where m is the slope of the line, and b is the y-intercept.

Since the line passes through the points (2, -2.5) and (4, -2), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

To find the slope(m) we can use the rise over the run formula ,

m = (y2 - y1) / (x2 - x1) = (-2 - (-2.5)) / (4 - 2) = -0.5

then we can substitute the values in point-slope form

y - (-2.5) = -0.5 (x - 2)

And now we can use x = 0,

y = -0.5(0-2) -2.5 = 1.5

so the y-intercept of the line is 1.5

Answer:

sin (theta) = [tex]\frac{\sqrt{5} }{3}[/tex]

Step-by-step explanation:

cos = adjacent side/hypotenuse

Then, in a right triangle the adjacent = 2 and the hypotenuse = 3

By the Pythagorean theorem, 3^2 = 2^2 + opposite side^2

9 - 4 = 5

opposite side = [tex]\sqrt{5}\\[/tex]

sin (theta) = [tex]\frac{\sqrt{5} }{3}[/tex]

An easier way is to find sin(arccos (-2/3) = [tex]\frac{\sqrt{5} }{3}[/tex]

Note:  Remember that the sin is positive in the 2nd quadrant.

Answer:

3/14 chance first draw

Step-by-step explanation:

There are 14 jellybeans in all, you won’t be replacing so the probability will change with each draw.

Probability the 1st draw is red = 3/14.

Probability the 2nd draw is red = (3–1)/(14–1) = 2/13.

Probability the 3rd draw is red = (2–1)/(13–1) = 1/12.

3/14 x 2/13 x 1/12 = 6/2184 = 1/364 is approximately 0.27%, pretty rare.

Answer:

The initial fee

Step-by-step explanation:

Thats the fee to sort of set up the membership, the 15 is the monthly cost, and m is the months you use the membership. Make sense?

Answer:

y= 1200(0.92)^x

Step-by-step explanation:

Given data

Cost price= $1200

Rate of decrease= 8%

Let the time be x

The expression that describes an exponential function is

y= ab^x

for decrease b= 1-r

y= 1200(1-0.08)^x

y= 1200(0.92)^x

Hence the expression is

y= 1200(0.92)^x

Answer:

(a)  

∠(a) = 105°

(b)  ∠(b) = 75°

(c)  

∠(c) = 105°

Step-by-step explanation:

Complete Question

1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:

(a) Suppose a car is traveling west on 4th Street and turns onto King Avenue heading south. What is the measure of the angle created by the car's turning? Explain your answer.

(b) Suppose a car is traveling southwest on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.

(c) Suppose a car is traveling northeast on King Avenue and turns right onto 4th Street. What is the measure of the angle created by the car's turning? Explain your answer

Also find the attachment

Solution

(a)  

∠(a) + 75° = 180°

∠(a) = 180° - 75°

∠(a) = 105°

(b) As we can see the 3rd and 4th street are parallel thus the corresponding angle will be equal  

Thus, ∠(b) = 75°

(c)  

∠(c) + 75° = 180°

∠(c) = 180° - 75°

∠(c) = 105°

Answer:

Step-by-step explanation:

He added 18 on both sides instead of subtracting 18 on both sides

X+18-18<22-18

X<4

Answer: [tex]2\sqrt{11}\ ft[/tex], Irrational number

Step-by-step explanation:

Given

The square rug has an area of [tex]44\ ft^2[/tex]

The area of the square rug is [tex]\left( \text{Side length}\right)^2[/tex]

Suppose the side length is [tex]x[/tex]

[tex]\therefore x^2=44\\\Rightarrow x=\sqrt{44}\\\Rightarrow x=2\sqrt{11}\ ft[/tex]

As [tex]\sqrt{11}[/tex] is irrational, therefore, [tex]2\sqrt{11}[/tex] is not a rational number.

Answer: The answer is no, they are not proportional

Step-by-step explanation:

Let, third proportional is x 0.8 : 0.2 : : 0.2 : x = 0.8/0.2 = 0.2/x = x = 0.2 × 0.2/0.8 × 10 = 1/20 = 0.05 Hence, here third proportional is 0.05

The number of adult tickets purchased is 12.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let no. of adult = x

No. of children = 28 -x

So, 7. 25 * x + (28 - x) *4. 50  = 159

⇒2.75x +126=159

⇒2.75x =33

⇒x=33/2.75

x=12

Hence, the number of adult tickets purchased is 12.

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