Write down in terms of n, an expression for the nth term of the following sequences:
a) 12 10 8 6 4
b) 25 20 15 10 5

1.  m∠5 + m∠6 = 180° - Pair of linear angles

2. ∠ 2+ ∠ 3 = ∠ 6 - Exterior Angle Theorem.

3. m∠2 + m∠3 + m∠5 = 180° - Sum of angles of Triangle

The angles that are created outside of a triangle are its external angles. In other terms, the angle created between one of a triangle's sides and its neighboring extended side is the triangle's exterior angle.

Each exterior angle of the triangle and its corresponding interior angle will form a pair of linear angles i.e the Sum of an Exterior angle and its corresponding interior angle is 180°.

A triangle's exterior angle is equal to the sum of its two opposite interior angles. This property of the triangle is known as Exterior Angle Theorem.

Here we have

∠2, ∠3, and ∠5 are the interior angles of a triangle

∠1, ∠4, and ∠6 are exterior angles of the same triangle

Let's assume that the given triangle is ΔABC

Can be represented as given in the picture  

As we know the sum of angles in a triangle = 180°

=> m∠2 + m∠3 + m∠5 = 180°  will be true

If we observe the given picture,

From line BC, m∠5 + m∠6 = 180°   [ Pair of linear angles ]

From Exterior angle Property

=> ∠ 2+ ∠ 3 = ∠ 6.

Therefore,

The correct statements are

1.  m∠5 + m∠6 = 180° - Pair of linear angles

2. ∠ 2+ ∠ 3 = ∠ 6 - Exterior Angle Theorem.

3. m∠2 + m∠3 + m∠5 = 180° - Sum of angles of Triangle.  

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Answer:

The answer is A

Step-by-step explanation:

took the test.

The 99 percent confidence interval for the true mean length of the bolt is CI = (2.8712, 3.1288)

Confidence Interval is used to tell us the degree of certainty or uncertainty that is existent in a sampling method.

The general formula for confidence interval is;

CI = x' ± z(s/√n)

where;

x' is sample mean

z is z-score at confidence level

s is sample standard deviation

n is sample size

We are given;

sample size; n = 36

Sample mean; x' = 3 inches

standard deviation; s = 0.3 inches

confidence level = 99%

z at 99% CL = 2.576

Thus;

CI = 3 ± 2.576(0.3/√36)

CI = 3 ± 0.1288

CI = (2.8712, 3.1288)

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Answer:

17. VN ll OP

18. VN perp. TR

19. Yes because the both a straight line (m 180) and are not crossing at any point.

20. Yes because there crossing at an right angle.

Hope this helps!

Answer:

let width=x

length = x + 2ft

Area = 82ft^2

Area= length×width

=(x+2)x

=x^2 +2x=82

x^2+2x-82=0

Use Quadratic Equation to get x.

x = -10.1(reject, length cannot be minus value or 8.11)

x = 8.11

width = 8.11ft

length = 10.11ft

Check the picture below.  Let's recall is an isosceles, so it has twin sides and is a right-triangle.

[tex]x^2+(\sqrt{6x+16})^2\implies \sqrt{x^2+6x+16}\qquad \impliedby hypotenuse \\\\[-0.35em] ~\dotfill\\\\ x~~ = ~~\sqrt{6x+16}\implies \stackrel{\textit{squaring both sides}}{x^2=6x+16}\implies x^2-6x-16=0 \\\\\\ (x-8)(x+2)=0\implies x= \begin{cases} 8 ~~ \textit{\LARGE \checkmark}\\\\ -2 ~~ \bigotimes \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\underset{\textit{length of each side}}{\stackrel{\sqrt{(8)^2 + 6(8) + 16}}{{\Large \begin{array}{llll} 8\sqrt{2} \end{array}}}\hspace{5em}\stackrel{x}{\text{\Large 8}}\hspace{5em}\stackrel{\sqrt{6(8) - 16}}{\text{\Large 8}}}[/tex]

now, let's notice, the negative value is a legitimate value, however for this case is invalid since the lengths of the triangle can't be negative.

m = -[tex]\frac{17}{7}[/tex]

1. Combine like terms

-2m - 4m - 17 = 1m

-6m - 17 = 1m

2. Multiply by 1

-6m - 17 = 1m

-6m - 17 = m

3. Add 17 to both sides

-6m - 17 = m

-6m - 17 + 17 = m + 17

4. Simplify

Add the numbers:

-6m - 17 + 17 = m + 17

-6m = m + 17

5. Subtract m from both sides

-6m = m  + 17

-6m - m = m + 17 - m

6. Simplify

Combine like terms:

-6m - m = m + 17 - m

-7m = m + 17 - m

Combine like terms:

-7m = m + 17 - m

-7m = 17

7. Divide both sides by the same factor

-7m = 17

[tex]\frac{-7m}{-7}[/tex] = [tex]\frac{17}{-7}[/tex]

8. Simplify

Cancel terms that are in both the numerator and denominator:

[tex]\frac{-7m}{-7}[/tex] = [tex]\frac{17}{-7}[/tex]

m = [tex]\frac{17}{-7}[/tex]

Divide the numbers:

m = -[tex]\frac{17}{7}[/tex]

m = -[tex]\frac{17}{7}[/tex]

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

B. Sammy

Step-by-step explanation:

Kara, Sammy, Liz and Mark each took many samples from the same population of students. But the number of students in the Sammy's sample  is largest, hence their mean will have lest variation.

The automobile needs 26.5 gallons of gas to reach 890 miles.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, An automobile uses 17 gallons of fuel to go 570 mi.

∴ The automobile requires (17/570) gallons of gas to reach 1 mile.

∴ To reach 890 miles the automobile needs (17/570)×890.

= 26.5 gallons of gas.

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Answer: y= 2x - 5

Step-by-step explanation: lmk if u need explanation to solve

a) The probability that random guessing will lead to a passing score is of: 0%.

b) The probability that random guessing will lead to a perfect score is of: 3.35 x 10^-18.

c) The first version of the test is safer against examinees guessing to achieve a passing score.

The mass probability formula, giving the probability of x successes, is presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

For item a, considering that for 50 questions, all are guessed among five answer, the values of these parameters are given as follows:

n = 50, p = 1/5 = 0.2.

The probability of passing is given as follows:

P(X ≥ 35).

Using a binomial distribution calculator, with the given parameters, we have that:

P(X ≥ 35) = 0%.

For item b, the parameters are given as follows:

n = 25, p = 1/4 = 0.2.

Hence the probability of a perfect score is given as follows:

P(X = 25) = 0.2^25 = 3.35 x 10^-18.

For item c, we have that the first version is safer against examinees guessing to achieve a passing score, as:

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Answer:

By Pythagorean theorem: [tex]ET=\sqrt{113}[/tex]

By distance formula: [tex]ET=\sqrt{113}[/tex]

Step-by-step explanation:

The given rectangle has vertices R(-3,-4), E(-3, 4), C(4,4), and T(4-4).

The points have been plotted on the coordinate plane as shown in the attachment.

A. Using the Pythagoras Theorem;

[tex]ET^2=EC^2+CT^2[/tex]

We substitute the side lengths to obtain:

[tex]ET^2=EC+CT^2[/tex]

[tex]ET^2=49+64[/tex]

[tex]ET^2=113[/tex]

Take positive square root to obtain:

[tex]ET=\sqrt{113}[/tex]

B. The distance formula is given by:

[tex]d=\sqrt{(x_{2}-x_{1)^2+(y_{2}- y_{1} )[/tex]

The endpoints of ET are at E(-3,4) and T(4,-4).

Using the distance formula;

[tex]ET=\sqrt{4--3)^2+(-4-4)^2}[/tex]

[tex]ET=\sqrt{(7)^2} +(-8)^2[/tex]

[tex]ET=\sqrt{49+64}[/tex]

[tex]ET=\sqrt{113}[/tex]

Using fractions and mathematical operations, the number of students in the class are 53, the number of juniors are 21 and 16 seniors did not attend the field trip

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

A)

From the information given, 3/5 of the students are seniors

However, we know that he has 32 seniors currently

Let's use the concept of percentage here

3/5 = 0.6. Expressing this in percentage = 60%

This we can say 60% of the students are seniors

60/100 = 32/ x

x = total number of students

x = 32 / 0.6

x = 160/3 = 53 students

We have 53 students in the class

B) The number of juniors in the class are

53 - 32 = 21

C) The number of seniors that did not go will be

3/5 * 40 =  24

40 - 24 =  16

16 seniors did not go

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Step-by-step explanation:

we need to find the value of x for which C(x) = 2200.

2200 = 270ln(x + 1) + 1900

300 = 270ln(x + 1)

300/270 = ln(x + 1)

10/9 = ln(x + 1)

e^(10/9) = x + 1

x = e^(10/9) - 1 = 2.037731778... ≈ 2.0 acres

for an average intake of 2200 calories per day the number of acres of land owned is approximately 2.0.

Answer:

please download the attached file and let me know if you need any further information about addmition in roots international and if so how to make food with clay

Step-by-step explanation:

ok inshallah and a have of safe Earth’s warm and and

[tex]85(94 + 611) < 64(85 - 54)[/tex]

it same like before the end

Answer: 2/5 days

Step-by-step explanation:

4 / 5 = 2d

4 / 10 = d

2 / 5 = d

The f(x) = -ax²+18 function equation for his parabolic path. x=√8  is he reached, to the nearest tenth of a foot.

A function is an equation that has just one answer for y for every possible value of x. When utilizing a function, each input of a certain type receives exactly one output.

f(x) = -ax² + 18

f(2)= -a(2)²+18 = 12

-4a = 12-18

-4a = -6

  a = -6/-4

  a = 3/2

f(x) = (-3/2) x² + 12

f(0) = (-3/2) x² + 12

(3/2) x² = 12

x² = 8

x = √8

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The required percentage is 95%  data lies between the given data.

What is percentage?

Let X be the lengths of screws.

X~ Normal (μ = 5.5, σ = 0.1)

P[5.3 < X < 5.7]

= P[(5.3-5.5)/0.1 < (X-μ)/σ < (5.7-5.5)/0.1]

= P[-2 < Z < 2] Z is a standard normal variable.

= 2*P[Z < 2] - 1

= 2*0.97725 - 1, from standard normal table.

= 0.9545

P[5.3 < X < 5.7] = 0.95

Hence, the required percentage is 95%  data lies between the given data.

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12/√3 is  the direction of the vector v .

What does a basic math vector mean?

A thing with both magnitude and direction is called a vector.

                               A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector.

Normalize (make length 1) the vector v = <1, 1, -1>.

||v|| = √(1^2 + 1^2 + (-1)^2) = √3.  

So, the unit vector u is given by u = v/||v|| = <1, 1, -1>/√3.  

To find the rate of change of the potential in the direction of the vector v, you should calculate the   ∇f(6, 6, 5) and multiply by u.

=<df/dx, df/dy, df/dz>*u

= <4x-3y+yz, -3x+xz, xy> {at (6, 6, 5)} * u

= <36, 12, 36> · <1, 1, -1>/√3

= 12/√3.

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The complete question is -

Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 2x2 − 3xy + xyz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i + j − k.

Answer:

Step-by-step explanation:

SORRY CANT HELP YOU I AM ONLY IN 4 GRADE SO SORRY

The linear equation each graph is y = (1/5)x +3, y = 2x,  y = -3x+5 and y = (1/3)x +5 respectively

The equation of a line is of the form y = mx+c

Where m is the slope and c is the y-intercept

Graph 1

c = 3

m = 1/5 = 0.2

y = mx+c

Thus, the linear equation is y = (1/5)x + 3 or y = 0.2x + 3

Graph 2

c = 0

m = 2/1 = 2

y = mx+c

Thus, the linear equation is y = 2x+0 or y = 2x

Graph 3

c = 5

m = -3/1 = -3

y = mx+c

Thus, the linear equation is y = -3x+5

Graph 4

c = 5

m = 1/3 = 1/3

y = mx+c

Thus, the linear equation is y = (1/3)x+5 or y = 0.33x+5

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The monthly payment will be 1,228.18.

What is principle amount?

The amount you owe at any one moment is the primary amount. When you first took out the loan, it is exactly your loan amount. The principle amount drops as you make EMI payments, and when it hits zero, your loan is closed.

The total price of the home is $241,000.

The down payment will be 15% among the total price.

Rest amount will be paid by taking loan for 30 years.

The down payment amount is

15% of $241,000 = $ 241,000×15/100 = $36,150.

Hence the loan amount is going to be the rest amount, that is,

$(241,000-36,150) =$204,850.

So the principle amount, P= $204,850.

Interest rate= 5% implies

interest, R= 5/100 = 1/20 = 1/12×1/20 (monthly) = 1/240.

Number of years, N= 30 years = 30×12 months = 360 months.

Hence the monthly payment will be

[  P × R × (1+R)N ] / [ (1+R)N - 1 ] = $1,099.68.

So the principle amount, P= $204,850.

Interest rate= 6% implies

interest, R= 6/100 = 1/12×6/100 (monthly) = 1/200.

Number of years, N= 30 years = 30×12 months = 360 months.

Hence the monthly payment will be

[  P × R × (1+R)N ] / [ (1+R)N - 1 ] = 1,228.18

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Assuming that Susan types at a constant rate, the situation can be represented as a linear equation as:

n = 0.4t, where n represents the number of pages that Susan can type and t represents time in minutes in which Susan would type.

Number of pages Susan can type in 10 minutes = 4

The number of pages that Susan can type in 1 minute

= 4/10 = 0.4

Therefore, the number of pages that Susan can type in t minutes

= 0.4 × t = 0.4t

Hence, this can be represented in the form of a linear equation as

n = 0.4t

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The total commission Fred was paid for that month is $2570.5.

Given that, Fred sells new and used kayaks.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let the number of kayaks be x and the total amount of money Fred get paid per week be y.

A) An equation for the way Fred is paid.

So, equation is y =395.50 +12.5% of x

⇒ y=395.50 +0.125x

B) Last month, the total value of the kayaks he sold was $17400.

Here, x=17400

So, y=395.50 +0.125×17400

= $2570.5

Therefore, the total commission Fred was paid for that month is $2570.5.

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The reason why looking back is important in mathematical answers is that; Option D: Looking back allows a student to check that the answer is correct and makes sense in context of the problem.

We know that in mathematics, every problem has steps to solve it whether algebra, proportion, trigonometry, calculus, congruency, angles, logarithms, e,t,c

Now, since we know that every Maths problem has steps to solve them, then we can say that, in some instances, we definitely have to look back to be sure that the answer actually makes sense when we consider the solution being required.

Now, if we have to look back to check that the answer is actually correct and properly portrays the solution being demanded, then we can say that the appropriate option for looking back her is option D.

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The end behavior of the functions is obtained considering the limits of the functions as the input variable x goes to infinity.

For limits when x goes to infinity, only the term with the highest exponent of each of the numerator and of the denominator is considered, hence the functions are written as follows:

Applying the exponent properties, the equivalent expressions are given as the base x elevated to the subtraction of the exponents 2 and 3, hence:

Which is how the functions behave as x goes to infinity.

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The measure of the reference angle for the angle A = -319° is 41°

What is Reference Angle?

Every angle is measured from the positive part of the x-axis to its terminal line (the line that determines the end of the angle) traveling counterclockwise. For angles in the first quadrant, i.e., angles less than or equal to 90 degrees, the reference angle is equal to the original angle.

The reference angle is always positive

0° to 90°: reference angle = angle

90° to 180°: reference angle = 180° - angle

180° to 270°: reference angle = angle - 180°

270° to 360°: reference angle = 360° - angle

Given data ,

Let the reference angle be = R

Let the angle be represented as A

Now , the value of A is = -319°

And , The reference angle is always positive

So , the value of A = 319°

So , the angle lies in the first quadrant

Now , the reference angle is calculated by

R = 360° - A

Now , the value of the reference angle R = 360° - 319°

The value of R = 41°

Therefore,  the value of R = 41°

Hence , The measure of the reference angle for the angle A = -319° is 41°

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Using difference of squares, [tex]81x^6-25y^{10}=\boxed{(9x^3-5y^5)(9x^3 + 5y^5)}[/tex].

The graph that shows a dilation among the given graphs is; Graph F.

Dilation in graphs simply means each side is multiplied by the same

scale factor. What this means is that the ratio of each dilated side to their respective old sides before dilation must be the same scale factor.

We can see that the pre-dilated image has 2 units along the y - axis and 4 units across the x-axis. After dilation, it now has 4 units along the y - axis and 8 units across the x-axis. This means the scale factor in both axis are; 4/2 = 2 and 8/4 = 2. They are both the same scale factors and as such this graph shows a dilation.

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Answer:

m = -4

b =1

y = -4x+1

Step-by-step explanation:

We want to find the slope and y intercept

Given the two points ( -1,5) and ( 1,-3), we can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -3 -5)/( 1 - -1)

   = -8/( 1+1)

   = -8/2

   = -4

The y intercept is where it crosses the y axis

It crosses at 1

The slope intercept form of the line is

y = mx+b

y = -4x+1