Why do you subtract exponents when dividing powers with the same base?

Answer:

This may be perfectly expressed in a Rule of Three as:

If 1 yard is equal to 3 feet

15.4 yards are equal to x feet

1 yard-----3feet

15.4 yards------x

Then:

[tex]x=\frac{(15.4 yards)(3 feet)}{1 yard}[/tex]

[tex]x=46.2 feet[/tex]

Therefore the answer is 46.2 feet

Final answer:

Zero does not have an opposite because it is the identity element in addition; adding zero to any number yields that number without change. Zero's opposite is itself since 0 + 0 = 0. The concept of an 'opposite' is inapplicable for zero displacement or the null vector in vector algebra due to their lack of direction and magnitude.

Explanation:

The question is asking why zero does not have an opposite. In mathematics, zero is unique because it is the only real number that is neither positive nor negative. When we talk about the opposite of a number, we typically mean a number that, when added to the original number, yields zero. For any non-zero number, its opposite is the number with the same magnitude but a different sign. However, zero is the identity element for addition, which means that when you add zero to any number, you get the same number back without any change. Therefore, zero's opposite is itself, because 0 + 0 = 0.

In the context of displacement and vectors, an opposite might refer to direction rather than a notion of being negative or positive. For instance, a displacement of -100 m represents a movement of 100 m in the direction opposite of the chosen positive direction. However, zero displacement means no movement at all, so there can't be an opposite direction.

To elaborate on the concept, when dealing with vector algebra, the equivalent of zero is the null vector, which has no magnitude or direction. Therefore, it doesn't have an opposite because there is no direction or magnitude to invert or negate. Similarly, for an object making a round trip and returning to its starting point, there's zero displacement because its starting and ending points are the same, despite any distance traveled during its journey. This is another instance where zero's unique properties make the concept of an opposite meaningless.

The average time for each step in the assembly process is 3.75 minutes per step.

To find the average time for each step in the assembly process, we need to divide the total time taken by the number of steps. In this case, the assembly takes 3/4 hour, which is equivalent to 45 minutes. There are 12 steps in the process. So, to find the average time per step, we divide 45 minutes by 12:

Average time per step = 45 minutes / 12 = 3.75 minutes per step.

The number that is 70 percent of the number 70 will be 49.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Let the number be 'x'. Then the equation is given as,

x = 70% of the 70

Simplify the equation, then the value of the number is calculated as,

x = 70% of the 70

x = 0.70 × 70

x = 49

The number is 49.

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ2

90% = 0.90

4732000 x 0.90 = 4,258,800

The expression | 4/13 | evaluates to 4/13 because the absolute value of a positive number is the number itself.

The student's question asks to evaluate the expression | 4/13 |, which involves the use of absolute value. The absolute value of a number is the distance of that number from 0 on the number line, regardless of the direction. Therefore, the absolute value of any positive or negative number is a positive number, and the absolute value of 0 is 0 itself.

In this case, since 4/13 is a positive number, its absolute value is the same as the number itself. So the evaluation of the expression | 4/13 | is simply 4/13.

Question (1)

When the divisor is a decimal, what must we do?              

1) Multiply the divisor by 10, or 100, or 1000, etc., according to the number of decimal digits, so that it becomes a whole number.

 2)Multiply the dividend by the same power of 10.

Question (2)

When asked to add or subtract decimals, the most important step is to line up the decimal points. Step 1: Line up the decimal points so that similar place values are lined up. In other words, the tens place in both numbers should be lined up, the ones place in both numbers should be lined up, etc.

Question (3)

To multiply decimals: Set up and multiply the numbers as you do with whole numbers. Count the total number of decimal places in both of the factors. Place the decimal point in the product so that the number of decimal places in the product is the sum of the decimal places in the factors.

Answer:

perimeter of rectangle is 9/7 units.

Step-by-step explanation:

The perimeter of a rectangle is given by

Perimeter = 2(length + width)

Given that

[tex]length=\frac{1}{7}\\\\width=\frac{1}{2}[/tex]

Substituting these values in the above formula

[tex]P=2(\frac{1}{7}+\frac{1}{2})[/tex]

Add the fractions. The LCD is 14. So, multiply and divide by 14

[tex]P=\frac{2}{14}(\frac{1}{7}\times14+\frac{1}{2}\times14)\\\\P=\frac{1}{7}(2+7)\\\\P=\frac{9}{7}[/tex]

Thus, perimeter of rectangle is 9/7 units.