a number increased by 6 is 30

(a) The expression of nth term of arithmetic sequence is [tex]a_n=1+(n-1)6[/tex] and (b) 4th term of the series  [tex]a_n=5n^2\\[/tex] is 80.

What is arithmetic sequence?

It is a sequence of numbers which have same difference between two consecutive numbers. The common difference can be any positive number or negative number or even it can be 0.

The six terms of the arithmetic sequence are as follows:

1,7,13,19,25,31

Calculate the common difference as follows:

7-1=6

13-7=6

19-13=6

Since it is an arithmetic sequence hence common difference is 6.

Hence, [tex]d=6[/tex].

Now, substitute value of the first term and the common difference in the following expression of the nth term.

[tex]a_n=a+(n-1)d\\a_n=1+(n-1)6[/tex]

Now, the nth term of another sequence is as follows:

[tex]a_n=5n^2\\[/tex]

Substitute n=4 in the above equation.

[tex]a_4=5(4)^2\\=80[/tex]

Hence, (a) the expression of nth term is [tex]a_n=1+(n-1)6[/tex] and 4th term of the series  [tex]a_n=5n^2\\[/tex] is 80.

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The difference of the polynomials [tex]2x^2[/tex] - 9x + 8 and [tex]6x^2[/tex] - 5x - 12 is -[tex]4x^2[/tex] - 4x 20

The first polynomial is given that

[tex]2x^2[/tex] - 9x + 8

The second polynomial is

[tex]6x^2[/tex] - 5x - 12

Here we have to find the difference, to find that we need to subtract the second polynomial from the second polynomial

Then,
[tex]2x^2[/tex] - 9x + 8 - ( [tex]6x^2[/tex] - 5x - 12 )

Open the bracket using the distributive property

[tex]2x^2[/tex] - 9x + 8 - [tex]6x^2[/tex] + 5x +12

Combine the like terms

[tex]2x^2[/tex] -  [tex]6x^2[/tex]  -9x +5x + 8 +12

Apply the arithmetic operations on like terms

-[tex]4x^2[/tex] - 4x 20

Hence, the difference of the polynomials [tex]2x^2[/tex] - 9x + 8 and [tex]6x^2[/tex] - 5x - 12  is   -[tex]4x^2[/tex] - 4x 20

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The function that includes all the ordered pairs in the given table is y = -x - 4

First choose two points

First point = (0, -4)

Second point = (2, -6)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (-6 - (-4) / (2 - 0)

= -6 + 4 / 2

= -2 / 2

= -1

Here at X = 0, the value of Y = -4

Therefore the y intercept of the line = -4

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Substitute the values in the slope intercept form

y = -1x - 4

y = -x - 4

Hence, The function that includes all the ordered pairs in the given table is y = -x - 4

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Answer: 5 hours.

Step-by-step explanation: First you need to subtract the $12 fee from the total to find out how many hours he paid for. 57-12=45. So if he paid $45 at $9 per hour, 45 divided by 9 equals 5.

Answer:

[tex]-12x+6[/tex]

Step-by-step explanation:

Take a look at the attachment,,,

Hope this helps! :)

Answer:

[tex]6 + 12x[/tex]

Step-by-step explanation:

The distributive property states that A(B + C) = AB + AC.

Therefore,

[tex]4 \left( \dfrac{3}{2} - 3x \right) = 4 \left( \dfrac{3}{2} \right) + 4(3x)[/tex]

Now we can simplify each term:

[tex]4 \left( \dfrac{3}{2} \right) + 4(3x)[/tex]

[tex]= \dfrac{12}{2} + 12x[/tex]

[tex]= 6 + 12x[/tex]

On October 24, 218 days after March 20, there will be 10 hours of sunlight.

The number of daily sunlight hours of a particular location is modelled by the trigonometric equation,

l(t) = 12 + 3.5sin (2[tex]\pi[/tex]/365t)

Here , L(t)= Number of sunlight hours in a day.

           t = Number of days after 20th March .

Now we are required to determime the day  during first 365 on which there are 10 sunlight hours ,that is, we need the value of "t" for which L(t) =10 hours. So in the given equation by putting L(t)= 10 and solving for t , follows as,

l(t) = 12 + 3.5sin (2[tex]\pi[/tex]/365t)

10 = 12 + 3.5sin (2[tex]\pi[/tex]/365t)

10-12 = 3.5sin (2[tex]\pi[/tex]/365t)

-2 =  3.5sin (2[tex]\pi[/tex]/365t)

-2/3.5 = sin (2[tex]\pi[/tex]/365t)

-0.574 = sin (2[tex]\pi[/tex]/365t)

For the inverse function of y = sin x

sin ⁻¹(y) =x + 2n[tex]\pi[/tex]

Now as we are required to calculate the day having 10 sunlight hours in first 365 days so putting n=0 we get,

t = -35.3521 or t =217.9422

Now t can not be negative as we want to find the day after march 20 having 10 sunlight hours. So neglecting t=-35.3521 . Now we get t=217.9422 .

Rounding off we get ,t=218 which is the required answer.

Hence, 218 days after march 20 i.e on October 24 it will have 10 sunlights.

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Answer:

7.07

Step-by-step explanation:

Draw a horizonal line and a vertical line to creat a right triangle.  The horizontal measurement would be 5 and so would the horizontal measurement.

Use the Pythagorean theorem

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]  The c side is the length that you are looking for

[tex]5^{2}[/tex] + [tex]5^{2}[/tex] = [tex]c^{2}[/tex]

25 + 25 = [tex]c^{2}[/tex]

50 = [tex]c^{2}[/tex]

[tex]\sqrt{50}[/tex] = [tex]\sqrt{c^{2} }[/tex]

7.07 = c  Rounded to the nearest hundredths

The linear function rule of the equation is y =  x + 18

From the question, the points on the line are given as

(2, 20) and (9, 27).

So, we have the following ordered pairs

(x, y) = (2, 20) and (9, 27).

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (2, 20) and (9, 27).

Substitute the known values in the above equation

So, we have the following equation

Slope = (27 - 20)/(9 - 2)

Evaluate the above quotient

Slope = 1

The equation is then calculated as

y = Slope(x - X) + Y

Substitute the known values in the above equation

So, we have the following equation

y = 1 * (x - 2) + 20

So, we have

y =  x + 18

Hence, the equation of the line is y =  x + 18

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The expansion of the series  ⁴∑ₙ = ₁ 3ⁿ ⁺ ¹ is; 9 + 27 + 81 + 243

We are given the summation formula of the series as;

⁴∑ₙ = ₁ 3ⁿ ⁺ ¹

At n = 1, we will input 1 for n and we have;

3¹ ⁺ ¹ = 3² = 9

At n = 2, we will input 2 for n and we have;

3² ⁺ ¹ = 3³ = 27

At n = 3, we will input 3 for n to get;

3³ ⁺ ¹ = 3⁴ = 81

At n = 4;

3⁴ ⁺ ¹ = 3⁵ = 243

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Answer:

positive

Step-by-step explanation:

The value of x is -8.

1).

N(-6,-8), O(5, 3), P(0, 9), and Q(x, 1).

slope between NO = y2 - y1 / x2 - x1

= 3 - (-8) / 5 - (-6)

= 3+8 / 5+6

= 11/11

= 1

slope between PQ = 1-9 / x-0

= -8/x.

Given lines are parallel so there slopes are equal

1 = -8/x

x = -8.

Therefore the value of x is -8.

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The fraction left for Mark to read is 17/20.

From the information illustrated, he wants to complete of the 160 pages book by the end of the week and Mark has read 24 pages so far.

The number of pages left will be:

= 160 - 24

= 136 pages

Therefore, the fraction of pages left will be:

= Number of pages left / Total pages

= 136 / 160

= 17/20

The fraction is 17/20.

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From the given data

a) Then the number of squares wide does the grid need to be so that the data fits on the graph is 7 blocks

b) If the grid is 20 squares tall, then the variable A can be replaced by 0.09 km

In the graph,

The x axis represents the Time since start in minutes and the y axis represents the distance from the start in kilometers.

In x axis each block represents 5 minutes

The maximum value of time taken in table = 35 minutes

Then the number of squares wide does the grid need to be so that the data fits on the graph = 35 / 5

= 7 blocks

Part b

If the grid is 20 squares tall

The maximum value of distance = 1.8 km

Then the value of A will be

1.8 / 20 = 0.09 km

Hence, from the given data

a) Then the number of squares wide does the grid need to be so that the data fits on the graph is 7 blocks

b) If the grid is 20 squares tall, then the variable A can be replaced by 0.09 km

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The equivalent expressions are (6^(-4) )^(-4), (6^(-2) )^(-8) and (6^8 )^2

Using exponent property, we have

[tex](a^{m})^{n} = a^{m*n}[/tex]

The given expressions is 6^16

From the question, we have

(6^0 )^16=6^(0×16)

⇒6^0 ≠ 6^16

(6^8 )^8=6^(8×8)

⇒6^64 ≠ 6^16

(6^(-4) )^(-4)=6^(-4x-4)

⇒6^16

(6^(-2) )^(-8)=6^(-2×-8)

⇒6^16

(6^(-1) )^16=6^(-1×16)

⇒6^(-16)≠6^16

(6^8 )^2=6^(8×2)

⇒6^16

Multiplication:

In mathematics, multiplying the numbers is used to find the product of two or more numbers. We frequently perform one of the basic mathematical operations. The simplest basic application is to use multiplication tables. Mathematicians multiply two integers to express the repetitive addition of one number to another. It is possible to contain natural numbers, fractions, integers, whole numbers, and other forms of numbers. M would either be added to itself 'n' times or subtracted from itself when M is multiplied by n.

Complete question:

Which expressions are equivalent to 6^16?

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Answer:

y= [tex]\frac{5}{2}[/tex]X +5

Step-by-step explanation:

Answer:

The angle is approximately 111.199 degrees.

Step-by-step explanation:

Cosine is adjacent over hypotenuse.

The hypotenuse is the longest side of the triangle.  

In this cos the hypoteneuse is a. However, we can only use cos on right triangles and on the angles that are not 90 degrees. In this case, p would be the 90 degree angle if we could use cosine.

In this case, you need the law of cosines, not cosine. The law of cosine says [tex]c=\sqrt{a^2+b^2-2 a b cosp}[/tex] where c is the side opposite to the angle, a and b are the sides adjacent to the angle, and p is the angle. The law of cosine works for all the triangles.

Plugging in the numbers:

[tex]5.3=\sqrt{3.6^2+2.8^2-2*3.6*2.8* cosp}\\5.3^2=20.8-20.16* cosp}\\7.29=-20.16*cosp\\cos^{-1}\frac{7.29}{ -20.16}=p\\p=111.198929[/tex]

Answer:

(3x+10)(x+1)

Step-by-step explanation:

This is the answer for 3x^2+13x+10.

I think you made an error while typing.

Hope this helps!

Answer:

yes

Step-by-step explanation:

every x value has at least one y value

The object moves at a speed of 25.352 m/s

The subject of a formula is the variable that is being worked out. It can be recognized as the letter on its own on one side of the equals sign. It is a variable which is expressed in terms of other variables involved in the formula.

Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.

In the question given, we have an equation;

s = d/t

d = 180m, t = 7.1s

s = 180 / 7.1

s = 25.352 m/s

The speed (s) of the object is 25.352 m/s

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The value of x that makes lines u and v parallel is 6. Option A is correct.

First, let us understand the angles formed by parallel and transversal lines:

The different types of angles are alternate exterior angles, alternate interior angles, corresponding angles, consecutive angles, etc.

From the picture attached,

If the lines u and v are parallel and a third line (transversal) is intersecting these lines at two distinct points,

Both the angles given in the picture will be equal in measure as these angles are alternate exterior angles if u and v are parallel.

20x + 10 = 130 degrees

20x = 130 - 10 degrees

x = 120 / 20 = 6

So, the value of x is 6.

Thus, the value of x that makes lines u and v parallel is 6. Option A is correct.

For question please check the below figure:

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The student that correctly used partial quotients to show 552 divided by 23 was Gavin.

The purpose of partial quotients is to facilitate division as by using partial quotients students can easily divide big numbers by using easy multiples first and then adding the multiplers to find the final divisiors. The recommended numbers to use are 5 or 10.

Based on the information provided, it can be conclude Gavin was better at applying this method because he used only easy multiples (10, 2) to make the number easier to divide, while Brianna completed the process only through to steps, which is not recommended when applying this method.

In conclusion, Gavin was the one who correctly used the method and calculated the result.

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The value of y in the  expression is y= - (x + 4) or,  y= (x -4)

Algebraic expression in mathematics is a phrase that include coefficients, unknown variables  operations, and constants

To solve for y in the equation 10x+5y=5x+20 we apply algebraic rule;

Step 1: Collect the like terms by moving the unknown 'ý' to the left side of the equation

5y =5x -10x+20

Step 2: Evaluate the the expression 5y =5x -10x+20

5y = -5x + 20

Step 3: Divide both sides by 5

[tex]\frac{5y }{5}[/tex] = [tex]\frac{-5x +20}{5}[/tex]  

y = -5x/5  + 20/5

y = - (x + 4) or,  y= (x -4)

Therefore, the value of y in the expression is y= - (x + 4) or,  y= (x -4)

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Answer:9072

Step-by-step explanation:

453.6 x 20 = 9072

Answer:

8 hours and 35 minutes. (8:35)

Step-by-step explanation:

8 hours and 35 minutes.

515 minutes.

The volume of the rectangular prism is 12 cubic inches

It is given that Each cube represent 1 unit

The base length of the rectangular prism = 4 inches

The base width of the rectangular prism = 3 inches

The height of the rectangular prism = 1 inches

The volume of the rectangular prism = The base length of the rectangular prism × The base width of the rectangular prism × The height of the rectangular prism

Substitute the values in the equation

The volume of the rectangular prism  = 4 × 3 × 1

= 12 cubic inches

Hence, the volume of the rectangular prism is 12  cubic inches

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Answer:

2/3

Step-by-step explanation:

the slope is rise over run so y/x

The money that the group will be able to donate with the savings from all 20 youth is $1400.

Let the daily pay plan for each youth = y.

Daily pay plan for 20 youths = 20y

Weekly pay plan = 7 × 20y = 140y

Assuming each youth saves $10 daily

Daily savings for 20 youth:

= 20 × $10

= $200

Weekly savings for 20 youth:

= 7 × $200

= $1400

If they used the early pay plan 140y to go swimming, they saved $1400 which they donated to the church.

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the answer for your question above is (-1,-1) or you could say option no.3

The commonly used technique in problem solving is means-end analysis

One typical heuristic is to define subproblems or subgoals. Means-ends analysis, which entails determining how to close the gap between a goal and the actual situation, is another frequently employed heuristic. You can divide a problem into smaller problems and deal with each one separately by using means-ends analysis.

Heuristic problem-solving entails what?

A problem-solving heuristic is a non-formal, speculative process that, in certain circumstances, produces a solution but not in others. The strategy can be either more or less successful than employing an algorithm because the results of applying a heuristic are unpredictable.

So,therefore the means-end analysis is commonly used technique in problem solving

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Answer:

[tex] \sf \: 2x + 2[/tex]

Step-by-step explanation:

Given expression,

→ (3x + 4) - (x + 2)

Let's simplify the expression,

→ (3x + 4) - (x + 2)

→ 3x + 4 - x - 2

→ (3x - x) + (4 - 2)

→ (2x) + (2)

→ 2x + 2

Hence, the answer is 2x + 2.