126 diminished by
the product of two consecutive
integers

Negative powers of 10 helpful when writing and comparing small numbers.

Small numbers (numbers between 0 and 1) are written with a negative power of ten. The specific power of 10 indicates just how big or how small the number is. You can compare two numbers written in scientific notation by looking at their powers of 10. The number with the greater power of 10 will be the greater number.

When comparing small numbers, write these numbers in scientific notation (only one non-xero digit must be before point) and then

For example- 0.00003450000

                      3.45 x 10 -5

                      3.450000 x 10 -5

                       0.345 x 10 -4

                      0.3450000 x 10 -4

Hence it is prooved that negative powers of 10 helpful when writing and comparing small numbers.

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The sequence converges as the degree of the numerator and denominator are the same.

In this question we have the case of a rational equation representing a sequence, of which we must determine if the sequences converges and diverges. An useful form to prove the convergence of rational equations is using limit and algebra properties:

(5 · n - 1) / (n + 1)

[(5 · n - 1) / (n + 1)] · 1

[(5 · n - 1) / (n + 1)] · (n / n)

[(5 · n - 1) · n] / [(n + 1) · n]

[(5 · n - 1) / n] / [(n + 1) / n]

(5 - 1 / n) / (1 + 1 / n)

As n → + ∞, then 1 / n → 0 and the limit of (5 · n - 1) / (n + 1) is 5. Thus, the sequence converges as the degree of the numerator and denominator are the same.

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Answer:

x = 11

m<H = 39°

Step-by-step explanation:

m<G = 6x - 15

m<H = 3x + 6

complementary angles = angles that add up to 90

6x - 15 + 3x + 6 = 90

9x = 99

x = 11

m<H = 3x + 6, plug in 11 as x

3 * 11 + 6

= 33 + 6

m<H = 39°

Answer:

The number is 5.

Step-by-step explanation:

Given: If 6 is added to the square of a positive number, the sum is 31. Find the number.​

Step-by-step solution:

Step 1: Formula

We know that the square of a positive number plus 6 is equal to 31. In a formula, it would look like [tex]\sqrt{x}[/tex] + 6 = 31 where x replaces the positive number.

Step 2: Subtract 6

We need to get x by itself to find the number. Subtract 6 on both sides to cancel it out and move it to the left

so, [tex]\sqrt{x}[/tex] + 6 -6 = 31 -6 = [tex]\sqrt{x}[/tex] = 25

Step 3: Square Root of 25

The Square Root of 25 is 5. We know this because 5*5 = 25.

Therefore, the number is 5.

Answer:

82% or 23/28

Step-by-step explanation:

2+3+18=23

2+3+18+6=28

23/28=

Answer:

Options 2-5

Step-by-step explanation:

1. False, since the designs aren't identical.

2. True, both circles have a radius of 1.

3. True, you can translate the circles in Diego's design up to that they are all tangent to each other to make Elena's design.

4. True, both circles have diameter 10.

5. True, simlar logic to 2 and 4

The product of 2√5 and √2 is 2√10.

And, The result is an irrational number.

Here,

We have to find the product of 2√5 and √2.

And, also determine the result is a rational or irrational number.

What is Irrational number?

A number which cannot be written in the form of fraction p/q, is called an Irrational number.

Now,

The product of 2√5 and √2 is;

⇒ 2√5 * √2 = 2√5*2 = 2√10

Hence, The product of 2√5 and √2 = 2√10.

Since, √10 is an irrational number because it cannot be written in the form of fraction.

Hence, 2√10 is an irrational number.

Therefore, The product of 2√5 and √2 is 2√10.

And, The result is an irrational number.

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The correct question is this;

Find the product of 2√5 and √2 in simplest form. Also, determine whether the result is irrational or rational and explain

Answer:

Answers below

Step-by-step explanation:

To find per 20 miles

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 2 (to simplify)

= 1/2mile / 4 minutes x 40 (to get miles per 20 min)

=  20 miles / 160 minutes

_____________________________________________

To find per 15 miles

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 2 (to simplify)

= 1/2mile / 4 minutes x 30 (to get miles per 15 minutes)

= 15 miles / 120 minutes

_____________________________________________

To find miles per minute

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 8 (to get miles per minute)

= 0.125 miles / 1 minute

_____________________________________________

To find miles per hour

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 2 (to simplify)

= 1/2mile / 4 minutes x 15 (to get miles per hour)

= 7.5 miles / 60 minutes

The algebraic expression from the given statement is 8+x/4=x

Given the statement is the "eight more than the quotient of a number and 4 is equal to 2."

In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.

Lat us assume the number be x.

In the given statement the quotient of a number and 4 means x/4.

And eight more than the quotient of a number and 4 means 8 is the sum of quotient of a number and 4 and it can be written as

8+x/4      ......(1)

As given in the statement eight more than the quotient of a number and 4 is equal to 2 means we want to equate equation (1) with 2 and written as

8+x/4=2

Hence, the algebraic expression from the given statement "eight more than the quotient of a number and 4 is equal to 2" is 8+x/4=2.

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Answer:

y = -2

x = 9

Step-by-step explanation:

x - 7y = 23

8x - y = 74

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

Extra:

(x - 7y = 23) -8

-8x + 56y = -184

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

-8x + 56y = -184

8x - y = 74

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

55y = -110

÷55   ÷55

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

y = -2

x - 7y = 23

x - 7(-2) = 23

x + 14 = 23

   -14    -14

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

x = 9

I hope this helps!

Answer:

14

Step-by-step explanation:

To work out the lowest common multiple, we first:

7, 14, 21, 28...

14, 28...

The common multiples of 7 and 14 are 14, 28 etc, but the LEAST (or lowest) common multiple is 14.

Hope this helps.

Rawr!~ Allow me to help you today!

Answer:

[tex]V=\frac{2}{5}[/tex] cubic units!

Step-by-step explanation:

Step 1: Draw the carton (Carton is in the image)

Step 2: Calculate the volume V

[tex]V=LWH[/tex]

[tex]V=\frac{8}{3}[/tex] × [tex]\frac{1}{8}[/tex] ×[tex]\frac{6}{5}[/tex]

[tex]V=\frac{2}{5}[/tex] cubic units

I hope this helps you! <3

AshTheNeko

Answer:

The integers are 20 and 22

Step-by-step explanation:

Let the first even integer be x . Then the next consecutive even integer
= x  + 2
The relationship between these two integers is the difference of the squares = 84

This means
(x + 2)² - x² = 84

Use the relationship a² - b² = (a + b) (a -b)

Here a = x + 2 and b = x

So

a + b = (x + 2 ) + x = x + 2 + x = x + x + 2 = 2x + 2
a  - b = (x + 2) - x = x + 2 - x = x -x + 2 = 2

Therefore

(a + b)(a - b) in terms of x is
(2x + 2) x 2 = 4x + 4

We know this is 84

So 4x + 4 = 84

Subtract 4 on both sides:
4x = 84 -4

4x = 80

x = 20

So the next consecutive even integer = 22

The integers are 20 and 22

3/4*1/4 = 3/16

3/7*1/2 = 6/7

Answer:

f=-5

Step-by-step explanation:

the answer is 8

Step-by-step explanation:

just minus 11by 3

Answer:

If you're just looking for the area of the square, then it's 49m. If you want the surface area of the whole pyramid, it's 189.

Step-by-step explanation:

For just the square, it's easy: Multiply the side lengths. 7x7 is 49.

For the surface area, find the area of the square (49) and the four triangles. To find the areas of the triangles, multiply the base (bottom, here it's the side length of the square) by the height (in this case 10m) and divide by 2. 7x10=70 and 70/2=35. Now since there are 4 triangles, multiply that by 4. 35x4=140, and now add the area of the square; 140+49=189. I don't think you wanted the surface area though, but I hope this helps!

Answer:       5.1 x 10⁻¹ kg

To find the mass of water in the bottle, we can multiply the mass of one molecule by the number of molecules.

By using dimensional analysis, or by cancelling out units, we can figure out what to multiply or divide. Dimensional analysis uses fractions written with units. Dividing the same unit cancels out units we don't need.

To solve:

We are looking for the mass of H₂O in the bottle.

The units we need in the answer are:      [tex]\displaystyle{ \frac{kg}{bottle} }[/tex]

The question tells us:

Our equation puts the fractions in an equation, making them multiply to get the units we need.

[tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}\ =\ \frac{kg}{bottle}[/tex]

Why is this equation correct?

Remember that dividing the same unit will cancel them out. In the equation, we have H₂O in a numerator and H₂O in a denominator. So, H₂O will cancel out. In the end, we will only have kg in the numerator and bottle in the denominator.

Take the equation we wrote. Now that we know our equation gives us the right units, we only need the front part.

[tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}[/tex]

Cancel out H₂O:

[tex]=\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1} \ *\ \frac{(1.7*10^{28})}{1\ bottle}}[/tex]

Simplify the equation:

[tex]=\displaystyle{ \frac{(3 * 10^{-29})*(1.7*10^{28})\ kg}{1\ bottle}[/tex]

[tex]=\displaystyle{ \frac{3 * 10^{-29}*1.7*10^{28}\ kg}{1\ bottle}[/tex]

Use exponent rules to multiply 10⁻²⁹ with 10²⁸:

[tex]=\displaystyle{ \frac{3 *1.7*10^{28-29}\ kg}{1\ bottle}[/tex]

[tex]=\displaystyle{ \frac{3*1.7*10^{-1}\ kg}{1\ bottle}[/tex]

Multiply within the numerator to simplify:

[tex]=\displaystyle{ \frac{5.1*10^{-1}\ kg}{1\ bottle}[/tex]

∴ The mass of water in the bottle is 5.1 x 10⁻¹ kg.

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From the given equation 6.8x+8.8y+9.8=0 the value of x-intercept is -98/68 and value of y-intercept is -98 /88.

As given in the question,

Given equation :

6.8 x +8.8 y +9.8= 0

To get x -intercept substitute y =0 in the equation :

6.8 x+ 8.8 (0) + 9.8=0

⇒6.8x= -9.8

⇒x= 98 /68

To get y -intercept substitute x =0 in the equation :

6.8 (0)+ 8.8y + 9.8 =0

⇒8.8y= -9.8

⇒ y= 98 /68

Therefore, from the given equation 6.8x+8.8y+9.8=0 the value of

x-intercept is -98/68 and value of y-intercept is -98 /88.

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The least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².

So, given zeroes are -1, 3+3i.

Similarly,

So, the polynomial has the function: (x+1)x²

Therefore, the least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².

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Answer:√16 and 6.39 are rational numbers because they can be expressed as a ratio and a fraction.

So, The numbers on a distance of 2.2 units from −3 on a number line are

-3 - 2.2 and -3+2.2

= - (3+2.2)  and - (3-2.2)

= -5.2 and - 0.8

From the calculation below, the probability that a tourist will spend more than $250 on the 2 legs of the trip is 2/3.

From the question, the number of possible options available and their total amount is as follows:

Airplane and Van = $350 + $60 = $410

Airplane and Cab = $350 + $40 = $390

Bus and Van = $150 + $60 = $210

Bus and Cab = $150 + $40 = $190

Train and Van = $225 + $60 = $285

Train and Cab = $225 + $40 = $265

From the above, it can be observed that we have a total number of 6 different options available and 4 of the options are more than $250.

Therefore, we have:

Probability of spending more than $250 = Number of options that are more than $250 / Total number of different options = 4/6 = 2/3

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Answer:

20

Step-by-step explanation:

We need to determine what fraction of the container 6 gallons is. We know the difference between 2/5 and 7/10 is 6 gallons, so all we have to do is solve for 7/10 - 2/5. The common denominator is 10, as both 5 and 10 are factors of 10. 10/5 is 2, so we multiply the numerator of 2/5 by 2.

7/10 - 4/10 = 3/10

We now know that 6 gallons is 3/10 of the container. Now we solve.

10/3 = 3 1/3

So:

6 x 3 1/3 = 20

Answer:

20 gallons.-

Step-by-step explanation:

Let x be the number of gallons that the container holds.

The we have the equation

2/5 x + 6 = 7/10 x

Multiply through be 10

4x + 60 = 7x

3x = 60

x = 20.

The option yes, d = -2 is correct

The arithmetic sequence or progression is a sequence of numbers such that the difference between the consecutive terms is constant.

The formula of an arithmetic sequence is

           [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1)d

Here the sequence is 18, 16, 14, 12, 10...... which is in arithmetic sequence as there is a common difference between them.

Now we have to find the common difference between the two consecutive terms of the series,

common difference (d) = 16- 18 = 14 - 16 = -2

Therefore the series is an arithmetic sequence and the common difference between them is -2.

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0.61166117... is not an rational number as it has no regularly repeating digit or group of digits.

A rational number is one that can be stated mathematically as the ratio or fraction p/q of two integers, p and q, which must both be non-zero. Every integer, including 3/7 (3 = 5/1) and 7 is a rational number.

Boldface Q is typically used to represent the field of rationals, also known as the field of rational numbers, the set of all rational numbers, or "the rationals."

Real numbers are those that make sense. The rational real numbers are those whose decimal expansion either ends after a finite number of digits (for example, 3/4 = 0.75), or eventually starts to repeatedly repeat the same finite sequence of digits (for instance, 9/44 = 0.20454545).

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The claim made by Morehouse college make more sense as their ratio of winning a game than losing it is higher.

a) In home games, the Spelman college won 10 wins whereas Morehouse College won only 9 games.

So, Spelman College has a better team than Morehouse College in home games.

b ) In Away games, Morehouse College won 56 games whereas Spelman College only won 12 games. So, Morehouse College has a better team than Spelman College in Away games.

c ) In total, Spelman College has won 22 games and lost 23 games. The ratio of win is to lose is 22 : 23 that is it won 0.96 games against it lost 1 game. In total, Morehouse College won 65 games and lost 39 games. The ratio of win it to lose is 65 : 39 that is it won 1.67 games against the 1 game it lost.

So, the claim of Morehouse College makes more sense.

Therefore, we get that the claim made by Morehouse college make more sense as their ratio of winning a game than losing it is higher.

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