2. Find the 20th term of an arithmetic sequence if its 6th term is 14 and 14th term is 6.
can anyone answer this ?​

Round to the nearest tenth , if necessary the value of x is 11.5.

What is right triangle ?

A right triangle is a type of triangle in which one angle is equal to 90 degrees. The side opposite this 90-degree angle is known as the hypotenuse, and the other two sides are known as the legs. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right triangles.

Triangle ABC is a right angle triangle,

We can apply the Pythagorean Theorem to get,

[tex]x^{2} +8^{2} = 14^{2} \\x^{2} = 14^{2}-8^{2} \\x^{2} = 196-64\\x^{2} =132[/tex]

x ≈ 11.5

So , Round to the nearest tenth , if necessary the value of x is 11.5.

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The equation is y=12x.

It takes 24 minutes for the rock climber to get to 288 feet.

The calculation is as follows:

here we know that

One hour = 60 minutes

so, by dividing 720 from 60 we get 12

here we assume  the time in minutes be x

So, the equation is

y = 12x

288=12x

288/12 = 12x/12

24 = x

So on solving the provided question we can say  that 3x³ is a polynomial as it have exponential power

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

here,

3x³ is a polynomial

as it have exponential power

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The ratio 5:73 represents A. The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Number of 8th grade baseball players = 5

Total number of athletes = 73

Therefore the ratio will be:

= 5 / 73

= 5:73.

The correct option is A

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There are 720 people (60 percent) attended a music festival on Friday night in Dawson Christian Academy.

A percentage is a figure or ratio that shows a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages. Additionally, you can indicate them by adding "percent" or "pct" after the number.

Given that Dawson Christian Academy have people to attend a music festival is 1200

out of these people to attend a music festival on friday is 60%

No. of people to attend a music festival on friday is 60% of 1200

⇒ (60/100)*1200

⇒ 0.60*1200

⇒ 720 people

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The width of the box is 4 inches wide

From the question, we have the following parameters that can be used in our computation:

Area = 20 square inches

Height = 5 inches

The width of the box can be calculated using the following equation

Width = Area/Height

substitute the known values in the above equation, so, we have the following representation

Width = 20/5

Evaluate the quotient

Width = 4

Hence, the width is 4 inches

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Complete question

The side of a box has an area of 20 square inches and a height of 5 inches. How many inches is the width of the box?

Answer:

-8/4 or -2

Step-by-step explanation:

First of all notice the graph is negative. Meaning that this will be a negative slope.

Now we can use rise over run, counting up 8 spaces, and to the left 4.

Since the graph is negative make the rise negative. -8/4.

To simplify this fraction divide -8 by 4, and receive an answer of -2.

-Hope this helped

An isosceles right triangle has a perimeter of 16 square centimeters since the hypotenuse is 8 length.

A boundary is a closed path that surrounds, delimits, or includes a two-dimensional shape or a one-dimensional length. The outermost part of a circle or an ellipse is called the perimeter. The perimeter calculation has numerous real-world applications. A shape's perimeter is the measurement of its edge's radius. Discover how to calculate the perimeter by adding together the lengths of the sides of various forms. The perimeter of any shape can be calculated by multiplying its side lengths. An object's perimeter is the region that surrounds it. A good illustration of this at your house is a closed-off garden. Its perimeter is the space encircling something. For a 50 by 50 foot yard, a 200 foot fence will be required.

given

AC (hypotenuse) = 8 cm. ,

AB^2+BC^2 = AC^2

x^2+x^2 = 8^2

2x^2 = 64

x^2= 64/2=32

x = 4.2^1/2 cm.

Perimeter = {8 +4.(2)^1/2+4.(2)^1/2}

= {8+8.(2)^1/2}

=8(1+2^1/2) cm.

Area =( base×altitude)/2= (4.2^1/2×4.2^1/2)/2 = 16sq.cm.

An isosceles right triangle has a perimeter of 16 square centimeters since the hypotenuse is 8 length.

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Answer:

(-1,0)

Step-by-step explanation:

See attached graph.  Use a free site such as DESMOS for graphing.

Answer:

Step-by-step explanation:the answer is d

Answer:

252 my guy

Step-by-step explanation:

238 after absolute value is 238

-28 after absolute value is 28

-14 after absolute value is 14, but theres a negative infront of the number

therefore:

238+28-14

= 252

The value of x in the equation 3x = 48 is 16 and for equation 4x = 64 is 16.  

What is equation ?

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

3x = 48

As it is multiplication we divide it by 3

3x / 3 = 48 / 3

x = 16

4x = 64

As it is multiplication we divide it by 4

4x / 4 = 64 / 4

x = 16

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I apologize for any confusion. Based on the information given, Brianna cannot use her sample data to form a valid inference about the town because it is not specified that her sample is random or representative of the entire population. Additionally, it is not clear what the population of the town is or how many people live in the town. The question is asking whether or not she can use her sample data to form a valid inference about the town based on the information given in the question. The answer is no, she cannot use her sample data to form a valid inference about the town.

It is possible to construct a triangle whose sides are 18 cm 24 cm and 30 cm because the sum of two sides are greater than three sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 18 cm 24 cm and 30 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 18 and 24

18 + 24 > 30

42 > 30

Now we add 18 and 30

18 + 30 > 24

48 > 24

Now we add 24 and 30

24 + 30 > 18

54 > 18

It is possible to construct a triangle whose sides are 18 cm 24 cm and 30 cm because the sum of two sides are greater than three sides.

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The formula of the image of a line is( l−p)/a = (m−q)/b = -2(ap+bq+c)/√a²+b²

What is the image of a line?

Typically, a little dash is used to identify a point's reflection, such as A'. This is said with a "prime." As a result, line AB's reflection is known as A'B'. The reflection is referred to as line AB's "image."

Here,

We have to determine the formula of the image of a line.

We concluded that

The mirror's "reflection" of the specified point P causes it to appear at an equal distance away on the opposite side of the line. To see this, move point P. According to tradition, the "image" of point P is the reflection of point P across the line, which is designated by the term P' (pronounced "P prime").

Hence, the formula of the image of a line is( l−p)/a = (m−q)/b = -2(ap+bq+c)/√a²+b²

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Answer:

1/128 or 0.0078125, round as needed

Step-by-step explanation:

✨calculator✨

Answer:

y = 3x + 2

Step-by-step explanation:

1. Work out the gradient of the line segment: change in y/change in x: -2 - -6/ -8 - 4 = 4/-12 = -1/3

2. Work out the gradient of the perpendicular bisector: the gradient of the line segment and the perpendicular bisector should multiply to get -1. This means that we can do -1 ÷ -1/3 to work out the gradient which is 3

4. Find the midpoint of the line segment: (-8 + 4) ÷ 2 = -2, and (-2 + -6) ÷ 2 = -4, so the midpoint is (-2, -4)

3. The equation will be in the format y = 3x + c and will go through (-2, -4), so we can substitute those values into the equation to find c:

The equation of the line is y = 3x + 2

Hope this helps!

Answer:

77.3

Step-by-step explanation:

Cos = Adjacent/Hypotenuse

Adjacent = 2.25 & Hypotenuse = 10.25

So that means...

Cos = 2.25/10.25

*When you type in the calculator type Cos-1 (2.25/10.25).

The answer is 77.319....

When you round it, it would become 77.3°.

Hope it's helpful.

The space left above the CD player of height 4 5/8 in. stacked on the amplifier of height 6 3/4 in. in the cabinet which has shelves of 12 1/2 in. apart calculated as mixed fractions is 1 1/8 inches.

A mixed fraction is a fraction that is specified using the value of the quotient (the whole number part) and a fraction consisting of the remainder divided by the divisor.

The distance between the shelves of the cabinet = 12 1/12 inches

The height of the amplifier on a shelve of the cabinet on top of which Katherine stacks the CD player = 6 3/4 inches

The height of the CD player placed on top of the amplifier = 4 5/8 inches

The dimensions of the distance between the shelves and the heights of the CD player and amplifier are specified in fractions.

The space left above the CD player can be found in fractions as follows;

The combined height of the CD player and the amplifier is therefore;

[tex]H = 4\frac{5}{8} +6\frac{3}{4} = (4 + 6) + \left(\dfrac{5}{8}+\dfrac{3}{4} \right)[/tex]

[tex](4 + 6) + \left(\dfrac{5}{8}+\dfrac{3}{4} \right)=10 + \left(\dfrac{5+2\times 3}{8} \right) = 10 + \dfrac{11}{8}[/tex]

[tex]10 + \dfrac{11}{8} = 10 + 1\dfrac{3}{8} = 11\frac{3}{8}[/tex]

The space above the CD player is therefore;

[tex]12\frac{1}{2} - 11\frac{3}{8} = 12 - 11 + \left(\dfrac{1}{2} - \dfrac{3}{8} \right) = 1 + \left(\dfrac{4 - 3}{8} \right)[/tex]

[tex]1 + \left(\dfrac{4 - 3}{8} \right) = 1\frac{1}{8}[/tex]

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The simplified expression of the radical is √10/3

From the question, we have the following parameters that can be used in our computation:

the square root of 40 and then divide by 6

This statement can be mathematically represented as

√40/6

Simplify the numerator

So, we have the following representation

2√10/6

Divide 2 and 6

√10/3

Hence, the solution is √10/3

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The geometric mean return of the given data set is 0.02.

The geometric mean return measures the compound rate of return over a period of time. It is calculated by taking the product of all the returns and then taking the nth root of the product, where n is the number of returns.

Formula: GMR = ((1+r1)(1+r2)…(1+rn))^1/n – 1

In this case, the data set is as follows:

r1 = 0.05

r2 = 0.03

r3 = -0.02

Using the formula above, the geometric mean return is calculated as:

GMR = ((1+0.05)(1+0.03)(1-0.02))^1/3 - 1

GMR = ((1.05)(1.03)(0.98))^1/3 - 1

GMR = (1.1394)^1/3 - 1

GMR = 0.0204

Therefore, the geometric mean return of the given data set is 0.02.

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Answer:

y= 3 2/4

Step-by-step explanation:

2 1/4 + 3 2/4 = 5 3/4

Answer: y= 7/2 = 3 1/2 = 3.5

Step-by-step explanation:

2 1/4 +y=5 3/4

Multiply both sides of the equation by 4.

2×4+1+4y=5×4+3

Multiply 2 and 4 to get 8.

8+1+4y=5×4+3

Add 8 and 1 to get 9.

9+4y=5×4+3

Multiply 5 and 4 to get 20.

9+4y=20+3

Add 20 and 3 to get 23.

9+4y=23

Subtract 9 from both sides.

4y=23−9

Subtract 9 from 23 to get 14.

4y=14

Divide both sides by 4.

y= 14/4

Reduce the fraction 14/4 to lowest terms by extracting and canceling out 2.

y= 7/2

​

The shape forms a pentagon. The value of y is  84°.

What is a polygon?

In geometry, a polygon is any closed curve made up of a series of line segments (sides) joined so that no two segments cross. Triangles (three sides), quadrilaterals (four sides), and pentagons are the simplest polygons (five sides).

The shape ABCDE forms a petagon.

The interior angle of a pentagon is 108°

The interior angle of a hexagon is 120°.

The ∠ABC is an angle of a regular hexagon, thus ∠ABC = 120°.

The ∠BCD is the angle of a regular hexagon, thus ∠BCD =120°.

The ∠BAE is an angle of a regular pentagon, thus ∠BAE=108°.

The ∠AED is an angle of a regular pentagon, thus ∠AED=108°.

The sum of all interior angle of a pentagon is 540°

Therefore,

∠ABC + ∠BCD + ∠BAE + ∠AED +∠EDC = 540°

120° + 120° + 108° + 108° + y = 540°

456° + y = 540°

y =  540° - 456°

y = 84°

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Perpendicular is an angle of 90° to a given line, plane, or surface means.

the equation is : y = ax+b

the equation is : y = ax+b

the slope is a : a×(1/4) = -1......( perpendicular to a line with a slope of 1/4) because

y=x/4 -2 means y = (1/4)x -2... the slope is : 1/4

but : a×(1/4) = -1 so : a = - 4 y= - 4x+b

the line that passes through (4, -1)

-1 =-4(4)+b

b = 15

the equation is : y = - 4x+15

Answer:A

Step-by-step explanation:

.

Reduced by 6%

In the first shift, they purchased 600 parts

the second time they purchased 564 parts

here the second year they purchased a percentage

-> second shift/first shift*100 of the first year

so it shows there is a reduction of 100-94 = 6%

As the second shift purchased 94 of them as compared to 100 in the first shift, So by this we can draw the inference that there is a drop of 6%.

Percent is the number out of 100 so here 36 parts are less than in the case of 600 which shows 6%. Moreover, the percentage gives a clear idea in terms of 100 which is more familiar as compared to their figures.

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The value of x in the triangle is 38 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

The exterior angle theorem can be used to find the angle x in the triangle.

Hence,

x + (180 - 84) = 134

x + 96 = 134

subtract 96 from both sides of the equation

x = 134 - 96

Therefore,

x = 38 degrees

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Answer: x=38

Step-by-step explanation:

x=38

Answer:

Product 1, because the function is exponential

Step-by-step explanation:

An exponential function, such as f(x) = 3^x, grows very quickly.

Answer: Product 1, because the function is exponential

Using the property of exponents, the value of x for the formula 3x=729 is 6.

The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal 23. Keep in mind that a number raised to the power of one is itself. Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself. For example, 6 is multiplied by itself four times, yielding 6 6 6 6. This is written as 64. The exponent is 4 and the base is 6.

Here,

3ˣ=729

3ˣ=3⁶

x=6

The value of x for expression 3ˣ=729 is 6 using property of exponents.

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Create an inequality where x represents the weight of the bobsled and y represents the weight of the three men. Graph the inequality below. Include proper labeling on each axis, units and shading.

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