2. Use Structure Why do you multiply by a power
of 10 when writing a repeating decimal as a
rational number?

The statement is sometimes true.

The given statement is ' The geometric mean for two positive integers is another integer.'

Geometric mean of two integers is the square root of their product.

If a and b are two integers, then geometric mean = [tex]\sqrt{ab}[/tex]

Its value need not be an integer always. In some cases the statement fails.

For example, let a = 3 and b = 6

Then geometric mean = [tex]\sqrt{3 \times 6} = \sqrt{18}[/tex] = 4.24, which is not an integer.

Now if a and b are equal numbers, we will get an integer as the geometric mean. Because then their product will be a perfect square and taking square root, we get the same number as the geometric mean.

Also consider a = 9 and b = 4

Then their geometric mean = [tex]\sqrt{36}[/tex] = 6

So sometimes the statement is true but not always.

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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

As a single inequality, we can write the solution of the given compound inequality as → x ≥ 8.

There are two types of inequalities -

Strict inequalities : The inequalities that have < or > symbol between the L.H.S and R.H.S.

Slack inequalities : The inequalities that have ≤ or ≥ symbol between the L.H.S and R.H.S.

Given in the question are two inequalities as mentioned below -

-2x - 3 < -1   and   -2x - 3 ≤ -11

In this question → -2x - 3 < -1 is a strict inequality and -2x - 3 ≤ -11 is a slack inequality. We will solve them one by one.

Inequality - 1

- 2x - 3 < - 1

Add 3 on both sides -

- 2x - 3 + 3 < - 1 + 3

- 2x < 2

Multiply by -1/2 on both sides -

x > - 1

Inequality - 2

-2x - 3 ≤ -11

Add 3 on both sides -

-2x ≤ -8

Multiply by -1 on both sides -

2x ≥ 8

Divide by 2 on both sides -

x ≥ 8

Now, we have two inequalities -

x > - 1    and     x ≥ 8

We can write it as one equality -

x ≥ 8

Therefore, as a single inequality, we can write the solution of the given compound inequality as → x ≥ 8.

[Graph is attached at the end]

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Answer:

you got this question right

# follow me please

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 :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:

Answer: 1/6

Step-by-step explanation:

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

This is the explanation

Answer:

hu7

h

Step-by-step explanation:

jjjuuuuyyytfgggggggg

7 discs can he make from a metal post that measures 1/3 foot in length.

Using a tool with disks rather than teeth or shovels to cultivate or harrow the ground.

Samuel needs to make a 4/7-inch disc out of a foot is 4 inches

A metal post =1/3foot×(12 inch/1 foot)

= 12/3

=4

Samuel needs to make a 4/7inch disc out of1/3foot metal post.

One third of a foot is 4 inches

⇒4÷4/7

⇒ Is the same thing as

⇒4×7/4

The 4 cancel out so that’s how you get 7

⇒ 7

A moldboard or plow shovel that is occasionally used in place of a round, thin steel plate that is typically dished.

Therefore, Samuel cuts 4/7 discs of metal can be he make from a metal post that measure 1/3 foot in length is 7 discs.

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7 discs can he make from a metal post that measures 1/3 foot in length.

Using a tool with disks rather than teeth or shovels to cultivate or harrow the ground.

Samuel needs to make a 4/7-inch disc out of a foot is 4 inches

A metal post =1/3foot×(12 inch/1 foot)

= 12/3

=4

Samuel needs to make a 4/7inch disc out of1/3foot metal post.

One third of a foot is 4 inches

⇒4÷4/7

⇒ Is the same thing as

⇒4×7/4

The 4 cancel out so that’s how you get 7

⇒ 7

A moldboard or plow shovel that is occasionally used in place of a round, thin steel plate that is typically dished.

Therefore, Samuel cuts 4/7 discs of metal can be he make from a metal post that measure 1/3 foot in length is 7 discs.

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

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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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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Answer:

x>5

Step-by-step explain

+3 to 7

divide 2 from ten

Answer:      8.1 g/cm  

Step-by-step explanation:

Density is equal to mass divided by volume. You are given a mass of

64.7

grams. You can find the volume of the cube by doing height multiplied by width multiplied by the depth.

Because all of the sides of a cube are the same length, the volume just ends up being

(2 cm) = 8 cm

Now plug both of those numbers into your density equation

p= m/v = 64.7 g/8 cm = 8.1 g/cm

~Hope this helps ;0~

Answer:

[tex]2.11 \: \: gram \: per \: cm {}^{3}[/tex]

The density is 2.11 g/cm^3

Step-by-step explanation:

Density is the ratio of the mass of a body per volume. To find density we need mass and volume.

side given (l) =6 cm

Volume of the cube = l^3

= 6^3

= 6 * 6 * 6

= 216 cm^3

we have mass = 457 g

Now,

density= mass/volume

= 457/216

=2.11

Soo, the density is 2.11 g/cm^3

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)

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 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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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 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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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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Answer: S=93 m²

Step-by-step explanation:

Divide the figure into two rectangles:

1)

S=(3)(11+4)+(12)(4)

S=(3)(15)+48

S=45+48

S=93 m²

2)

S=(3)(11)+(4)(12+3)

S=33+(4)(15)

S=33+60

S=93 m²

5a= -1 a=

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

-14+c = -12.5 c=

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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Answer:

n = 8

Step-by-step explanation:

any term in a Fibonnacci sequence is found by adding the previous 2 terms.

that is x₃ = x₁ + x₂

using this to continue the sequence

1, 1, 2, 3, 5, 8, 13, 21, 34, 55 with a₁₀ = 55

so

x₈ + x₉ = x₁₀

compare to [tex]x_{n}[/tex] + [tex]x_{n+1}[/tex] = 55

with n = 8