the high school marching band rehearses with either 6 or 10 members in every line.What is the smallest number of people who can be in the marching band?

Answer

a.22

b.11

c.10

d.25

The answer is C. 10

The factorization of given expression is 4(3a+2b).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given expression is 12a+8b.

In the given expression there are two terms 12a and 8b

Now, 12a=2×2×3×a and 8b=2×2×2×b

So, from both the terms common is 2×2=4

Thus, 4(3a+2b)

Therefore, the factorization of given expression is 4(3a+2b).

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To solve this problem, establish an algebraic equation that equates the sum of the lengths of the three pieces to the total length of the board. Solving this equation reveals that the first piece of wood is 5 inches, the second piece 20 inches and the third piece 25 inches.

This question represents a simple algebraic equation. Since the second piece is 4 times the length of the first piece and the third piece is 5 times the length of the first piece, the sum of these lengths should equal the total length of the board, which is 50 inches. Given that 'x' represents the length of the first piece, we can establish the following equation:

x + 4x + 5x = 50

This is because '4x' is the length of the second piece and '5x' is the length of the third piece. When you combine like terms, the equation simplifies to:

10x = 50

Upon solving this simplified equation, we find that 'x' or the length of the first piece of wood equals 5 inches. Therefore, based on the information provided, the length of the second piece would be 20 inches (4 times 'x') and the third piece would be 25 inches (5 times 'x').

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Final answer:

An even number is divisible by 2, while an odd number is not. Examples of even numbers are 8 and 10, while examples of odd numbers are 17 and 21.

Explanation:

An even number is a number that is divisible by 2, while an odd number is not divisible by 2.

For example, 2, 4, and 6 are even numbers because they can be divided by 2 without leaving a remainder. On the other hand, 3, 5, and 7 are odd numbers because they cannot be divided by 2 without leaving a remainder.

So, two examples of even numbers could be 8 and 10, while two examples of odd numbers could be 17 and 21.

9.125×10² is 100000 times the [tex]9.125\times10^{-3}[/tex].

We need to find what is the relationship between [tex]9.125\times10^{-3}[/tex] and 9.125×10².

The scientific notation helps us to represent the numbers that are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.

9.125×10² can be written as [tex]9.125\times10^{-3+5}=9.125\times10^{-3}\times10^{5}[/tex]

= [tex]9.125\times10^{-3+5}=9.125\times10^{-3}\times100000[/tex]

Therefore, 9.125×10² is 100000 times the [tex]9.125\times10^{-3}[/tex].

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Answer:

The correct answer is 1. 2d + 1 = 3d + 5

Step-by-step explanation:

Answer:

(4.55×10^13- 1.78×10^12)kg

=4.372×10^13kg

the iceberg is 4.372×10^13kg heavier than the rock.

or the iceberg is approximately 2.4 times heavier than the rock

Step-by-step explanation:

 6 1/2 - 3 2/3 =

13/2 - 11/3 =

39/6 - 22/6 = 17/6 = 2 5/6 qts left

Answer:

2 5/6

Step-by-step explanation:

The number of wrenches is 10 for which he paid $1.50, and $2.50. the number of wrenches is 5 for which he paid $4, and the number of wrenches is 6 for which he paid $3.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

We have:

Mr. Abernathy bought a selection of wrenches for his shop and paid $78.

Let's suppose:

The number of $1.50 wrenches is x

The number of $2.50 wrenches is also x

The number of $4 wrenches is x/2

The number of $3 wrenches is 1+x/2

Then linear equation becomes:

[tex]\rm 1.50x+2.50x+\frac{4x}{2} +3(1+\frac{x}{2} ) = 78[/tex]

[tex]\rm 3x+5x+4x +3(2+x ) = 156[/tex]

15x = 150

x = 10

The value of x = 10

=x/2 ⇒ 10/ 2 ⇒ 5

= 1+x/2 ⇒ 1+5 ⇒ 6

Thus, the number of wrenches is 10 for which he paid $1.50, and $2.50. the number of wrenches is 5 for which he paid $4, and the number of wrenches is 6 for which he paid $3.

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The correct answer is:

B . Division Property of Equality

Explanation:

The original equation is 4x = 20.  To solve this, we would cancel the 4.  Since the variable, x, has been multiplied by 4, we cancel it by dividing:

4x/4 = 20/4

x = 5

This is the division property of equality; we can divide both sides of an equation by the same number and preserve equality.

Answer:

Step-by-step explanation:

4 times (5 times 3) + (24 divided by 4)

4 times 15 + 6 (because 5 times three is 15, and 24 divided by 4 is 6)

60 + 6 (Multiplication first after parenthesis)

66 (The answer to 60 + 6)