an=7+(n-1)2 is the general rule for the nth term of the arithmetic sequence 7,9,11,13,15 ... true or false ?

Answer:

6x^3(x+2)(x-7)

Step-by-step explanation:

1st step: factor out common term, 6x^3(x^2 - 5x - 14)

2nd step: Factor x^2 - 5x - 14, (x + 2)(x - 7)

3rd step: simplify, 6x^3(x+2)(x-7)

I am joyus to assist :)

Answer: Terminating decimal

Step-by-step explanation:

2 3/4 as a faction is 2.75

2.75 is a terminating decimal

To solve for r in the equation K = 8r - s, add s to both sides of the equation and divide both sides by 8, resulting in r = (K + s)/8.

To solve for r in the equation K = 8r - s, we need to isolate r.

We can start by adding s to both sides of the equation to get K + s = 8r.

Then, we divide both sides by 8 to solve for r.

The final equation is r = (K + s)/8.

Answer:

see explanation

Step-by-step explanation:

Given the range of f(x), find the domain by equating f(x) to each of the values in the range, that is

5x + 4 = 5 ( subtract 4 from both sides )

5x = 1 ( divide both sides by 5 )

x = [tex]\frac{1}{5}[/tex]

5x + 4 = 6 ( subtract 4 from both sides )

5x = 2 ( divide both sides by 5 )

x = [tex]\frac{2}{5}[/tex]

5x + 4 = 7 ( subtract 4 from both sides )

5x = 3 ( divide both sides by 5 )

x = [tex]\frac{3}{5}[/tex]

5x + 4 = 8 ( subtract 4 from both sides )

5x = 4 ( divide both sides by 5 )

x = [tex]\frac{4}{5}[/tex]

Thus

domain = { [tex]\frac{1}{5}[/tex], [tex]\frac{2}{5}[/tex], [tex]\frac{3}{5}[/tex], [tex]\frac{4}{5}[/tex] }

Answer:

See explanation

Step-by-step explanation:

A dog owner observes that from birth to age 14 weeks, the puppy’s weight can be modelled by the equation

[tex]w = 365\cdot (1.23)^t \ (0\le t \le  14)[/tex]

In this equation,

When w=4,000, then

[tex]4,000=365\cdot (1.23)^t\\ \\(1.23)^t =\dfrac{4,000}{365}=\dfrac{800}{73}\\ \\t=\log_{1.23}\dfrac{800}{73}\approx 11.5651[/tex]

This means that puppy will weight 4,000 grams nearly at the middle between 11th week and 12th week.

The angles of 115 degrees and (52+x) are the same, because they are alternate interior angles.

Answer:

62º + x = 115º

because AB and CD are parallel, which means 115º and 62+x are "alternate angles"

ALTERNATE ANGLES

Step-by-step explanation:

To finish the remainder of the 18-mile trail, it will take 3 hours and 41 minutes at a pace of 1 mile in 17 minutes.

To find out how many miles it will take to finish the trail, subtract the distance already covered from the total length of the trail. In this case, subtract 5 miles from 18 miles to get 13 miles remaining. Next, divide the remaining distance by the pace at which you walk, which is 1 mile in 17 minutes. So, if it takes 17 minutes to walk 1 mile, it will take 17 times 13 minutes to finish the rest of the trail. Finally, calculate the total time in minutes by multiplying: 17 times 13 equals 221 minutes, or 3 hours and 41 minutes to finish the trail.

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Answer:

15*10∧-5

Multiple 15 x 0,000001 = 0,000015.

3/8 multiplied by 4/5 forms the fraction 3/10

A fraction has numerator in top & denominator in bottom.

Given fractions are 3/8 & 4/5.

To multiply these two numbers, we have to multiply numerator of 3/8, i.e. 3 with numerator of 4/5, i.e. 4.

Also we have to multiply denominator of 3/8, i.e. 8 with denominator of 4/5, i.e. 5.

So, the new number be 3/8 × 4/5

                                     = (3×4)/(8×5)

                                     = 12/40 = 3/10

The required fraction is 3/10

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Answer:

$3

Step-by-step explanation:

By investing $2,000 Bobby will earn $60 interest

∴By investing $1 Bobby will earn =$(60/2000) interest

so,

By investing $100,

He will earn =$ {(60/2000 ) .100}  

                     =$3

If Bobby invests his money for one year at the same interest rate as his brother, then he will earn $3 amount.

Thus, option A $3 is correct.

Interest that Bobby will earn at same interest rate as his brother after 1 year of investment of $100.

If someone invests P amount for T years with simple interest rate R% per year, then the simple interest that that person will earn is given by:

[tex]SI = \dfrac{P \times R \times T}{100}[/tex]

Putting values of P, R and T of Bobby's brother's investment, we have:

[tex]60 = \dfrac{2000 \times 1 \times R}{100}\\\\6000 = 2000R\\\\R = \dfrac{6000}{2000} = 3\%[/tex]

At that rate, the SI for Bobby's $100 investment for 1 year is:

[tex]SI = \dfrac{100 \times 3 \times 1}{100} = \$3[/tex]

Thus, Bobby will get $3 as interest.

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Answer: Second option.

Step-by-step explanation:

Given the function f(x):

[tex]f(x) = x^2 - 2x + 8[/tex]

Find [tex]f(x -2)[/tex]:

[tex]f(x -2)=(x-2)^2 - 2(x-2) + 8[/tex]

Remember that:

[tex](a\±b)^2=a^2\±2ab+b^2[/tex]

Then, simplifying:

[tex]f(x -2)=x^2-2(x)(2)+2^2 - 2x+4+ 8\\\\f(x-2)=x^2-6x+16[/tex]

So the function g(x) is:

[tex]g(x)=x^2-6x+16[/tex]

Use the following formula to find the x-coordinate of the vertex of g(x):

[tex]x=\frac{-b}{2a}[/tex]

In this case:

 [tex]a=1\\b=-6[/tex]

Then:

[tex]x=-\frac{-(-6)}{2(1)}=3[/tex]

Substitute this value into the function g(x) in order to find the y-coordinate of the vertex. Since [tex]g(x)=y[/tex], you get:

[tex]y=3^2-6(3)+16=7[/tex]

Therefore, the vertex of g(x) is:

[tex](3,7)[/tex]

Answer:

Second one

Step-by-step explanation:

x + 6 = 33 ---> is 6 more than x ^^

x = 27

Final answer:

The sum of -2.5 and (-3.5) is -6.0, which is found by adding the absolute values of the numbers and giving the result a negative sign. The correct number line representation for this sum would show a leftward movement from -2.5 by 3.5 units to end at -6.0.

Explanation:

When calculating the sum of -2.5 and (-3.5), we follow the rule that when two negative numbers are added, the answer has a negative sign. Both numbers in the sum are negative, therefore, we add their absolute values and then give the result a negative sign. The calculation is as follows:

-2.5 + (-3.5) = -(2.5 + 3.5) = -6.0

The number line that shows this sum would start at -2.5 and move left (which indicates adding a negative number) 3.5 units, landing on -6.0.

Answer:

Im pretty sure its 13.137

        I hope this helps!

Answer:

[tex]13.13[/tex]

Step-by-step explanation:

We first we need to look at the equation:

381 ÷ 29

So we first have to look at how many times 29 goes into 38, since 29 is already in the tens place.

It only goes in once. Meaning that right now you have one as your tens place.

1

Now you need to subtract 29 by 38

==> 9

So drop down the one from 381 to get 91, then find out how many times 29 goes into 91

==> 3 times

So now 3 is your tens place

13

Now do 91 - 29

==> 62

62 left?!

That means we need to [tex]annex^{1}[/tex]  :

drop down 0 into 62 to get 620:

Find out how many times 29 goes into 620:

==> 13

13.13

annex = drop down 0 after a decimal

Answer:

10 years

Step-by-step explanation:

Answer:

The strategy to evaluate these expressions is called PEMDAS.

Step-by-step explanation:

[tex]15-[(3^2+6)\div5][/tex]

We're going to be following the rule of PEMDAS:

Keep in mind that multiplication/division and addition/subtraction are done from left to right.

In the first expression (written above), we'll first evaluate everything inside the brackets first (brackets are used when there are parentheses inside of it - but they serve the same function). There are parentheses in these brackets, so that will be the absolute first step in evaluating.

Solve for [tex]3^2+6[/tex] then rewrite the expression.

Now finish evaluating inside the parentheses by dividing 15 by 5.

The last step to evaluate the expression is to subtract 3 from 15.

[tex]4\times[50-3(1+3)^2][/tex]

Evaluate everything inside the the brackets. Start with the parentheses since that is first according to PEMDAS. Add 1 and 3 together then rewrite the expression.

Exponents are solved next after parentheses in PEMDAS, so evaluate the exponent.

Multiplication is done before subtraction, so multiply 3 and 16 together.

Finish evaluating inside the brackets by subtracting 48 from 50.

The last step in evaluating the second expression is to multiply 4 and 2 together, which gives us 8.

Answer:

-7.

Step-by-step explanation:

2- + (2+7)

First work out the parentheses   ( by order of operations PEMDAS)

= 2 - + 9  

= 2 - 9    (as - + = -)

= -7.

Answer: x=58

Step-by-step explanation:

We know that the entire angle equals 360 degrees

Let’s subtract 293 from 360

360- 293 = 67

Then let’s subtract 44 from 67 to get (x-35)

67 - 44 = 23

We now know that 23 = (x - 35), so let’s write and solve the equation for it

23 = x-35

Add 35 on each side

X = 58

Answer:

max showed less improvement!

Step-by-step explanation:

Max percentage improvement in the first exam = (6/30 × 100) %

= (600/30) %

= 20 %

Maria percentage improvement in the first exam = (30/60 × 100) %

= (3000/60) %

= 50 %

Hence, 20 % < 50 %

Final answer:

Max improved by 6 marks from his previous score, while Maria improved by 30 marks. Therefore, Max showed less improvement than Maria.

Explanation:

Max scored 6 marks higher than his previous score of 30, making his new score 36. Maria scored 30 marks more than her previous score of 60, taking her new score to 90. To determine who showed less improvement, we compare the amount of increase in their scores.

Max's improvement: 30 + 6 = 36

Maria's improvement: 60 + 30 = 90

Max improved by 6 marks, and Maria improved by 30 marks. Therefore, Max showed less improvement.

When comparing improvement, it's useful to look at the actual increase in marks gained, not necessarily the percentage improvement unless specifically asked. Here, the simple comparison of the additional marks scored determines who improved less. Though both students improved their scores, the difference in their points increased is a clear indicator of whose improvement was less significant.

Subtracting a number from x shifts the graph that may places tot he right

Subtracting a number at the end of the equation, shifts the graph that many units down.

The answer would be: Shift the graph of y = x^2 right 2 units and then down 10 units.

Answer:

Shift the graph of y = x^2 right 2 units and then down 10 units.

Step-by-step explanation:

The graph of y= x^2 can be transformed to the graph of the given equation: y = (x - 2)2 - 10. This can be done by shifting the graph of y = x^2 right 2 units and then down 10 units.

Answer:

[tex]200[/tex]

Step-by-step explanation:

This book has 500 pages in total.

We should split up the place values.

1 - 9

One only appears once.

1

10 - 19

One appears 11 times.

1 + 11

20 - 99

One only appears 8 times.

1 + 11 + 8

Add:

1 + 11 + 8

=> 20

Since the same is for  200-299, and so on. Let us add twenty four times.

20 * 4

=> 80

Looking back to 100-199, there are 120 ones.

Add:

120 + 80

=> 200

The total number of times that the digit 1 appears in the page numbers is: 200

In the first 99 pages there are:

1 one in the first 9 pages,

11 ones in pages 10-19 (one each for 10 and 12-19, and two for 11)

8 ones in pages 20-99 (21, 31, 41, 51, 61, 71, 81, and 91)

So we have 20 ones in the first 99 pages.

Likewise we have 20 ones in pages 200-299, 20 ones in pages 300-399, and 20 ones in pages 400-499. There are 0 ones on page 500.

For pages 100-199, there are 100 ones for the hundreds digits in addition to the 20 ones found in the tens and ones digits.

So we have a total of 20 + 120 + 20 + 20 + 20 = 200 ones on the page numbers.

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Answer:

The number of turbines is 74

Step-by-step explanation:

* Lets explain how to solve the problem

- Four 3 megawatt wind turbines can supply enough electricity

 to power 3000 homes

∴ The number of turbines is 4

∵ Each turbine give 3 megawatt

∴ The four turbines give ⇒ 4 × 3 = 12 megawatt

- This quantity give enough electricity to power 3000 homes

∴ The number of homes for the 12 megawatt is 3000

- We need to find how many turbines can cover enough electricity

  to power 55,000 homes, so we must to know the quantity of

  electricity that be enough to power 55,000 homes

* Lets use the cross multiplication to solve the problem

∵         megawatt    :     number of homes

                  12          :              3,000

                  ?            :            55,000

- By using cross multiplication

∴ [tex]?=\frac{(55,000)(12)}{3,000}=\frac{660,000}{3000}=220[/tex]

∴ The enough electricity to power 3000 homes = 220 megawatt

∵ Each turbine gives 3 megawatt

- Find the number of turbines divides the total megawatt by the the

  megawatt of one turbine

∴ The number of turbines = 220 ÷ 3 = 73.3

- If we take 73 only the electricity will not be enough to cover all

 homes, so we must to take 74 turbines

∴ The number of turbines is 74

To power 55,000 homes, approximately 74 wind turbines are required. Each turbine can power 750 homes, derived from the initial data where 4 turbines power 3,000 homes.

To determine how many 3 megawatt wind turbines are required to power 55,000 homes, we can use a simple proportion based on the given data.

We know that:

Now, we need to find out how many turbines are needed to power 55,000 homes:

Since we can't have a fraction of a turbine in practical terms, we would need 74 turbines to ensure all 55,000 homes are powered.

Hey!

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

Solution:

3x - 6 = -4

3x + (-6) = -4

3x + (-6) + 6 = -4 + 6 (Add 6 to both sides)

3x = 2 (Simplify)

3x/3 = 2/3 (Divide both sides by 3)

x = 2/3 (Simplify)

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

Answer:

x = 2/3

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

Hope This Helped! Good Luck!

Step-by-step explanation:

first 3(-x+5) you distribut

then you would get 15-3x+15=21+6x and u combine like terms which is 3x and 6x which is 9 and u get 15-9x+15=21tthen u sabtract 15x on both side and get 15-9=21 then u subtract 15 ok both side and get x = 0.7

Mistake in the Question:

The number 3 is not a fraction.

Answer:

Suppose if it is 3/8 then do the following:

Multiply

3

__ by an equivalent fraction that equals 1.

8

An equivalent fraction is equal to 1 such as 2 or 3

                                                                       __   __

                                                                        2     3

An equivalent fraction is the same as multiplying by 1 so the ratio does not change.

This fraction would be equal to a        where a is an integer.

                                                   __  = 1

                                                    a

Hence an example would be that

2     3        6

__ . __ =  __

2     8       16

Request: Please mark me as the brainliest.

Answer:

A

Step-by-step explanation:

Note that i² = - 1

Given

(7 - 5i)(2 + 3i) ← expand factors using FOIL

= 14 + 21i - 10i - 15i² ← collect like terms

= 14 + 11i + 15

= 29 + 11i → A

Answer:

A

Step-by-step explanation:

Answer: 21

Step-by-step explanation: 5*5=25-4=21

To find g(5), substitute the value of x as 5 in the function g(x) = x^2 - 4. Then, calculate the result to obtain g(5) = 21.

Given, the value of x is 5 and a function g(x) = x^2 - 4. To find g(5), we need to substitute the value of x as 5 in the function g(x) = x2 - 4.

So, on substituting the value of x, the answer becomes g(5) = 52 - 4. Here, 52 is the square of

On Calculating further, g(5) = 25 - 4 = 21.

Therefore, g(5) = 21. The answer obtained is 21.

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In mathematics, a horizontal line has a slope of 0, and its equation is always 'y = b', where 'b' is the y-coordinate of any point on the line. In this situation, since our line passes through the point (3,7), the equation of the horizontal line is 'y = 7'.

In the context of mathematics, a horizontal line is a line whose equation is in the form y = b where 'b' represents the y-intercept, or the y-coordinate of a certain point on the line. In this question, you are asked to find the point-slope form of a horizontal line passing through the point (3,7).

However, for a horizontal line, the point-slope form y = mx + b becomes y = b because m, the slope of a horizontal line, is 0. And the y-coordinate of any point on a horizontal line is the same.

So, since the line is passing through the point (3,7), the y-coordinate 7 is constant throughout the horizontal line. Therefore, the equation of the horizontal line through (3,7) would be y = 7.

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