Given two terms of each arithmetic sequence, find a₁ and d . a₃=32 and a₇ =-8

Yes, the results of dividing X by a negative value and dividing X by a positive value are different. If we divide X by a negative value, the result will be negative, and if we divide X by a positive value, the result will be positive.

For instance:

It is true that 8 > 2 is unequal.

Divide both sides by 2, then:

True inequality also exists when 4 > 1. Due to the fact that we divided by a positive number, the inequality symbol remained.

Let's begin once more with

8 > 2, and apply a -2 to both sides.

-4 > -1 is erroneous. The inequality is no longer valid if the inequality sign changes when both sides are divided by a negative integer. When dividing both sides by a negative integer, the inequality sign must be changed in order to maintain its validity.

8 > 2

Add a -1 to both sides.

True for -4 < -1.

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Answer:

you got this question right

# follow me please

The glide reflection  ( x + 5.5 , y ) is  that is reflected in the line that separates the left prints from the right prints.

A glide translation is what?

Now, let's assume that the initial position is (x , y) .

Since, the average stride length of a turkey is about 11 inches; also since the turkey has two legs, therefore, the average stride length between the two legs is as shown below:

average = 11/2  = 5.5

Thus, the glide reflection is ( x + 5.5 , y )

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Answer:

x>5

Step-by-step explain

+3 to 7

divide 2 from ten

Sn = a(1 - rⁿ)/(1 - r) is the formula for the sum of a finite number of terms in a geometric series, where is the number of terms, is the first term, and is the common ratio.

The sum of the finite geometric series Σ⁴ n=1 (1/2)ⁿ⁺¹ is 0.46875.

The equation be Sn = a(1 - rⁿ)/(1 - r), where s exists the total, a1 exists the series first term, and r exists the common ratio, is a general formula for estimating the sum of an finite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.

Let the sum of the finite geometric series be Σ⁴ n=1 (1/2)ⁿ⁺¹

Σ⁴ n=1 (1/2)ⁿ⁺¹ = (1/2)¹⁺¹ + (1/2)²⁺¹ +(1/2)³⁺¹ + (1/2)⁴⁺¹

simplifying the above equation, we get

= (1/2)² + (1/2)³ + (1/2)⁴ + (1/2)⁴⁺¹

= (1/4) + (1/8) + (1/16) + (1/32)

Where, the first term is a = 1/4

common ratio be r = 1/2

n th term be n = 4

Let the equation be Sn = a(1 - rⁿ)/(1 - r)

substitute the values in the above equation, we get

S4 = (1/4) (1-(1/2)⁴) / (1 - (1/2))

simplifying the above equation, we get

S4 = (1/4) (15/16) × 2 = 15/32 = 0.46875

Therefore, the sum of the finite geometric series Σ⁴ n=1 (1/2)ⁿ⁺¹ is 0.46875.

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Carter needs to ride 3.9 miles per day on an average to meet his target of riding 28.7 miles in a week.

We are given that:

The total number of miles that needs to be ridden by Carter = 28.7 miles

Now, he has already ridden 17 miles this week

So, the miles left to be ridden = 28.7 miles - 17 miles

Number of miles left = 11.7 miles.

Now, he has 3 more days to finish his target.

So, on an average, he should ride:

Average = 11.7 miles / 3 days = 3.8 miles per day

Therefore, Carter needs to ride 3.9 miles per day on an average to meet his target of riding 28.7 miles in a week.

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5a= -1 a=

[tex]\frac{b}{-3} = -15 b=

-14+c = -12.5 c=

Answer: 1/6

Step-by-step explanation:

[tex]\displaystyle\\\frac{2}{12} =\\\\\frac{2}{2*6}=\\\\\frac{1}{6}[/tex]

The solution of the equation is  (-3, 6).

-3c - 3y = -9

5c - 2y = -27

Therefore, using elimination method, the equation can be solved as follows:

multiply equation(ii) by 1.5(3  /2)

-3c - 3y = -9

7.5c - 3y = - 40.5

subtract equation(i) from equation(ii)

10.5c = - 31.5

divide both sides by 10.5

c = -31.5 / 10.5

c = -3

Therefore,

5c - 2y = -27

5(-3) - 2y = -27

-15 - 2y = -27

-2y = -27 + 15

-2y = - 12

divide both sides by -2

y = -12 / -2

y = 6

Therefore, the solution of the equation is  (-3, 6).

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Answer:

Step-by-step explanation:

A 270 degrees anticlockwise rotation is the same result as the rotation of the 90 degrees.

Answer:

hu7

h

Step-by-step explanation:

jjjuuuuyyytfgggggggg

There are 534 played games in total.

There are 24 teams, and each team plays 2 matches against each one of the other teams.

So, let's say that each team is called team 1, team 2, team 3, ..., team 24.

If we start with team 1, they will play 2 games with each one of the other 23 teams, so here we will have: 23*2 = 46 games.

Now we go to team 2, we already counted the 2 games that the played with team 1, so we only look at the remaining 22 teams, here we will have:

22*2 = 44 more games.

Now with team 3, there are 21 teams remaining, so here we add another 2*21 = 42 games

And so on, now we do that for all the teams and then add all the numbers of games, the total number of games will be given by:

N = 2*(23 + 22 + 21 + ... + 2 + 1) = 534

There are 534 played games in total.

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The standard form is y - 1/3x + 1 = 0 for line parallel to y=-3 x+4 through (0,-1)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that  y=-3 x+4

Here -3 is the slope and 4 is the y-intercept

To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = 1/3, x₁ = 0 and y₁ = -1

y - (-1) = 1/3(x - 0)

y + 1 = 1/3(x - 0

y = 1/3x -1

y - 1/3x + 1

We have the standard form y - 1/3x + 1 = 0 of a line  perpendicular to y = (2/3)x - 1 through (0,6)

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y = 3.5x is the equation that represents y, the total number of hours Tonya works in x days if she continues at the given rate.

Unitary method is a concept in which the value of a single unit is first found out and then multiplied by the necessary value to get the required answer.

Here, we are given that Tonya works 3.5 hours in 1 day.

The total number of days = x

and the total number of hours Tonya works in x days = y

If she works for 3.5 hours in 1 day, in x days she will work-

x x 3.5

= 3.5x hours

Thus, y = 3.5x hours

Hence, y = 3.5x is the equation that represents Tonya's situation.

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the two horizontal lines are parallel and intersected by the same third line at the same angle

Answer:

8

Step-by-step explanation:

Use the Pythagorean theorem:

a^2+b^2=c^2

(You have to count the distance of x and y, then plug those number in the formula)

0^2+8^2=c^2

64=c^2

square root it

8=c

You can also use the distance formula

square root of (x2-x1)^2+(y1-y2)^2

square root of (-3-(-3))^2+(-2-(-10))^2

=8

(I'm pretty sure, if it's wrong I'm sorry)

The Geometric mean of 36 and 48 is [tex]24\sqrt{3}[/tex].

Geometric Mean between two numbers is defined as the Square root of the product of those two numbers .

For Example ; let a and b be two numbers , their geometric mean will be

GM=[tex]\sqrt{a*b}[/tex]

In the given question

a=36 and b=48

Substituting the values in the Geometric mean formula we get .

[tex]GM=\sqrt{36*48} \\ \\ =\sqrt{1728} \\ \\=24\sqrt{3}[/tex]

Therefore , the Geometric mean of 36 and 48 is [tex]24\sqrt{3}[/tex].

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Answer :f(x) = -5x + 250

Step-by-step explanation:

* Lets  explain how to solve the problem

- In week 10 the manufacturer fixed 200 cars

- In week 15, the manufacturer fixed 175 cars

- the reduction in the number of cars each week is linear

- The form of the linear equation is y = mx + c, where m is the slope of

the line which represent the equation and c is the y-intercept

- The slope of the line m =

 where (x1 , y1) and (x2 , y2) are two points on the line

* Lets solve the problem

- Assume that the weeks' number is x and the cars' number is y

∴ (10 , 200) and (15 , 175) are two points on the line which represent

 the linear equation between the cars' numbers and the weeks

 numbers

∵ Point (x1 , y1) is (10 , 200) and point (x2 , y2) is (15 , 175)

∴ x1 = 10 , x2 = 15 and y1 = 200 and y2 = 175

- Use the rule of the slope above to find m

∴

- Substitute the value of x in the form of the linear equation above

∴ y = -5x + c

- To find c substitute x and y by one the coordinates of one of the

 two points

∵ x = 10 when y = 200

∴ 200 = -5(10) + c

∴ 200 = -50 + c

- Add 50 to both sides

∴ 250 = c

- Substitute the value of c by 250

∴ y = -5x + 250, where the number of cars seen each week is y and

 x is the number of the week

∵ f(x) = y

∴ f(x) = -5x + 250

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

The value of x is 18° and the value of the angles A and B are 73° and 107° respectively.

We are given the angle measurements as:

A = (6x - 35)°

B = (3x + 53)°

We need to solve for x and find the values of A and B

We know that co- interior angles are supplementary.

So, we get that:

A + B = 180°

Substituting the values of A and B in the above equation, we get that:

6 x - 35 + 3 x + 53 = 180

9 x + 18 = 180

9 x = 180 - 18

9 x = 162

x = 162 / 9

x = 18

So, we now get that:

A = (6x - 35)°

A = (6(18) - 35)°

A =(108 - 35)°

A = 73°

B = (3 x + 53)°

B = (3 (18) + 53)°

B = ( 54 + 53 )°

B = 107°

Therefore, we get that the  value of x is 18° and the value of the angles A and B are 73° and 107° respectively.

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The probability that they would spell TRAINS is 1/720.

Probability:

Probability refers the fraction of favorable event by the total number of event.

Given,

A bag contains one tile for each letter of the word TRAINS.

Here we need to find If we selected a permutation of these letters at random, what is the probability that they would spell TRAINS.

We know that,

There are 6 letters in the word and the number of arrangements is the permutation of 6 taken 6 at a time.

So, it is written in permutations as,

=> 6! = 720.

The total number of possible outcomes is 720 and there is only one favorable outcome which is TRAINS.

Therefore, the probability is written based on the formula as,

=> 1/720.

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Answer:

Graph attached

Step-by-step explanation:

Find algebraically y values for x = -2 and x = 2 and connect the two points by a line

Equation: y = 3x + 2

For x = -2, y = 3(-2) + 2 = -6 + 2 = -4

For x = 2, y = 3(2) + 2 = 6 + 2 = 8

So the two points are (-2, -4) and (2, 8)

The ladder can reach 21.17 feet high up of Denise's house.

Given,

The length of ladder Denise used to clean the outside of her second story windows = 24 feet

The distance between the base of the ladder and house = 13 feet

We have to find the height of the house which the ladder can reach:

For that we can use Pythagorean Theorem.

That is,

Hypotenuse² = Altitude² + Base²

Here,

Hypotenuse is the length of the ladder = 24 feet

Altitude is the height of the house ladder can reach = x

Base is the distance between base of the ladder and house = 13 feet

Therefore,

24² = x² + 13²

576 = x² + 169

x² = 576 - 169

x² = 407

x = [tex]\sqrt{407}[/tex]

x = 21.17

That is, the ladder can reach 21.17 feet high up of Denise's house

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For the linear equation C = kl, where c, cost is the local variable and it takes 49.4 cents more for a 30 min local call. The dependent variable is the price of a local call.

There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.

The equation representing the situation

C = kl

where c depicts the cost and l is the length of call.

The dependent variable is the price of a local call.

The term "mord more" denotes that we are searching for the price difference between a 4 minute call and a 30 minute call, or the price of a 26 minute call.

The cost for 26 minutes will be 49.4 cents.

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∠1 and ∠11 are corresponding angles.

The alternates interior angles are formed when the transversal line intersects the two  coplanar lines as the name the angles are interior to the figure and are alternative to each other as well.

Alternate exterior angles are at the opposite side of the transversal line and are at external to the figure or we can say that on outside boundaries of the figure.

These angles are the same side of any two of the parallel lines in the figure cut by the transversal line . They show a correspondence behavior with respect to each other.

When any of the two lines in figure are cut by a transversal line, then the pair of angles on any of the one side of the transversal  line and interior of  the two lines are called the consecutive interior angle.

According to given question ∠1 and ∠11 are corresponding angles.

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The complete question :

Identify pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

∠1 and ∠ 11

Answer: It is 32

Step-by-step explanation:

The final answer is 1/9

What is Simplify?
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/ fraction / problem in a simpler form. It makes the problem easy with calculations and solving.

Given the question:

2/9 . 4/8

Let's start the calculation:

2/9 x 4/8

2/9 x 1/2

=1/9

So, The final answer is 1/9

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The equation of the line shown is y = x + 1

The graph represents the given parameter

On the graph, we have the following points

(x, y) = (0, 1) and (1, 2)

The equation of the line is then calculated as

y = (y2 - y1)/(x2 - x1) * (x - x1) + y1

This gives

y = (2 - 1)/(1 - 0) * (x -0) + 1

Evaluate the difference

y = 1/1 * (x) + 1

Evaluate the product

y = x + 1

Hence, the equation of the line shown is y = x + 1

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