Let a and b stand for two different rational numbers. If |a| > |b| then what else must be true?

Answer:

4, 12, 36, 108  is set of geometric sequence.

Step-by-step explanation:

Given  : geometric sequence.

To find : Which set of numbers is a geometric sequence.

Solution : We have given geometric sequence.

In a Geometric Sequence each term is found by multiplying the previous term by a constant.

Like : {a, ar, ar², ar³, ... }, where , a = first term , r = common ration .

We can see sequence 4, 12, 36, 108 in form of  4 , 4*3 , 4 (3)² , 4( 3)³.

Here, common ration is 3.

Therefore, 4, 12, 36, 108  is set of geometric sequence.

The ages of  Edna, Ellie, and Elsa are 35, 36, 37 respectively.

For any integer say 'a', its consecutive integers will be → (a + 1), (a + 2), (a + 3), .... , (a + n).

Given is the sum of ages of Edna, Ellie, and Elsa is 108.

Assume that the age of Edna is x.

Then the ages of Ellie and Elsa will be (x + 1) and (x + 2) respectively.

From the question we can write -

x + (x + 1) + (x + 2) = 108

3x + 3 = 108

3x = 105

x = 35

So, we can write -

Age of Edna = 35

Age of Ellie = 36

Age of Elsa = 37

Therefore, the ages of  Edna, Ellie, and Elsa are 35, 36, 37 respectively.

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Answer:

A is the answer because $5 is the amount when Maysa started out, and $1 is the amount when Ethan started out. So it is A .

Step-by-step explanation:

Answer:

The answer is option A : 4 gallons.

Step-by-step explanation:

A recipe for 10 servings of raspberry sorbet calls for 2 cups of water, 1/1.2 cups of granulated sugar, and 4 cups of frozen raspberries.

Now 10 servings need = 2 cups of water.

And 320 servings will need = [tex]\frac{2}{10}\times320= 64[/tex] cups of water.

Now, 1 cup = 0.0625 gallons

So, 64 cups are = [tex]0.0625\times64=4[/tex] gallons

Therefore, answer is option A : 4 gallons.

Answer: 3 million barrels

Step-by-step explanation:

Given :- Total crude oil= 60 million barrels

Quantity of gasoline = 34% of total crude oil

[tex]=0.34\times60\text{ million barrels}\\=20.4\text{ million barrels}[/tex]

Quantity of diesel = 29% of total crude oil

[tex]=0.29\times60\text{ million barrels}\\=17.4\text{ million barrels}[/tex]

Clearly, Quantity of gasoline is more than Quantity of diesel

difference = Quantity of gasoline-Quantity of diesel

[tex]20.4\text{ million barrels}-17.4\text{ million barrels}\\=3\text{ million barrels}[/tex]

Therefore, The production of gasoline is 3 million barrels more than diesel last year.

3 million more barrels of gasoline then diesel were produced and this can be determine by using the arithmetic operations.

Given :

The quantity of Gasoline = 34% of total crude oil

                                           [tex]=\dfrac{34}{100}\times 60[/tex]

                                           = 20.4 million barrels

The quantity of Diesel = 29% of total crude oil

                                      [tex]=\dfrac{29}{100}\times 60[/tex]

                                      = 17.4 million barrels

Quantity of Gasoline - Quantity of Diesel = 20.4 - 17.4 = 3 million barrels

Therefore, 3 million more barrels of gasoline then diesel were produced.

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To solve such problems we must know about the system of equations.

The system of the equation will give a unique solution at point (7, 0).

2x-9y=14

as the value of x is already given in equation2, therefore, substituting the value of x in equation 1, we get,

[tex]2(6y+7)-9y=14[/tex]

[tex]-12y+14-9y=14\\ -12y-9y =14-14\\ -21y = 0\\ y =0[/tex]

[tex]x= - 6y + 7[/tex]

Substituting the value of y,

[tex]x= - 6(0) + 7\\ x= 7[/tex]

The system will give a unique solution at points x=7, and y=0, this can be verified by plotting the two equations on the graph.

Hence, the system of the equation will give a unique solution at point (7, 0).

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The value of the 4 in the number 5,679.04 is 4,000.

The value of the 4 in the number 5,679.04 is 4,000. In the given number, 5,679.04, the digit 4 is in the thousands place, which means it represents 4,000.

Final answer:

The value of the 4 in the number 5,679.04 is in the thousandths place.

Explanation:

Place value is a fundamental concept in mathematics that assigns a numerical value to each digit in a number based on its position. The rightmost digit represents the units, the next digit to the left represents tens, and so on.

For example, in the number 60, the digit 6 is in the tens place, indicating 6 tens or 60. Understanding place value is crucial for performing arithmetic operations and comprehending numerical relationships.

Thus,

The value of the 4 in the number 5,679.04 is 4,000.

In the given number, 5,679.04, the digit 4 is in the thousands place, which means it represents 4,000.

Answer:

20 and 400 and 70 and 100

The Standard form of number is,

⇒ 0.1588

We have to give that,

Scientific notation is,

⇒ 1.588 × 10⁻¹

Since Scientific notation is a way of writing very large or very small numbers.

For example; 230,000,000 can be written in scientific notation as

2.3 x 10⁸.

Hence, the Standard form of number is,

⇒ 1.588 × 10⁻¹

⇒ 1.588 / 10

⇒ 0.1588

Therefore, The solution is, 0.1588

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Answer: Using the graph to find the solution of the given equation, the solutions are:

Option A.) -4 and 2

Solution:

The solutions in the graph are the values of "x" where the curves intercept. In this case the curves intercept at x=-4 and at x=2, then the solution of the equation are -4 and 2