How do you work out 49.2 x 10.3

A number is said to be rational if it can be expressed as a fraction of two integers.

0.87 is a rational number

Let the number be x.

So, we have:

[tex]x = 0.87[/tex]

Express as a fraction with a denominator of 1

[tex]x = \frac{0.87}{1}[/tex]

Multiply the fraction by 100/100

[tex]x = \frac{0.87 \times 100}{1 \times 100}[/tex]

[tex]x = \frac{87}{100}[/tex]

The fraction cannot be reduced further.

87 and 100 are integers.

This means that 0.87 is rational.

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To solve the equation -3x = 15, you divide by -3 to get x = -5. To check, substitute -5 for x in the original equation to verify that the left and right sides are equal.

To solve the equation -3x = 15, we want to isolate x on one side of the equation. The algebraic property we will use here is the Division Property of Equality, which states that if we divide both sides of an equation by the same nonzero number, the two sides remain equal.

Step-by-Step Solution:

Now, let's check the answer to verify it's reasonable. Substitute x = -5 back into the original equation (-3x = 15) and see if the equation holds true:

One bag of sugar can make 19 batches of chocolate chip cookies.

To determine how many batches of chocolate chip cookies can be made with one bag of sugar, we need to divide the total amount of sugar in the bag by the amount of sugar used in each batch of cookies. Since the bag holds 23 3/4 cups of sugar, and the recipe uses 1 1/4 cups of sugar per batch, we can set up the following division:

23 3/4 ÷ 1 1/4 = (95/4) ÷ (5/4) = (95/4) × (4/5) = 95/5 = 19

Therefore, one bag of sugar can make 19 batches of chocolate chip cookies.

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A line is a straight, infinite, one-dimensional entity with no thickness or endpoints. It can be represented mathematically, intersects at points or can be parallel to other lines.

Given that,

To find the characteristic of a line.

Now, A line is a fundamental geometric concept characterized by several key properties.

Firstly, it is straight and extends infinitely in both directions.

Secondly, it has no thickness, meaning it is one-dimensional and can be represented by a mathematical equation or equation system.

Thirdly, any two points on a line can be connected to form a segment, making it possible to measure distances along the line.

Now, Additionally, a line has no endpoints, which distinguishes it from a line segment.

Lastly, lines can intersect each other at a single point or be parallel, maintaining a constant distance from one another throughout their lengths.

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The constant rate of change of $8 per hour signifies that for each hour that passes, the associated value increases by $8. To find missing values in the table, you add or subtract $8 per hour depending on whether you're looking forward or backward in time.

Since the constant rate of change in your table is $8 per hour, this means that for each hour that passes, the value in your relationship increases by $8. This value is akin to the concept of constant slope in the graph of a linear function, where the 'rise over run' (or change in y-values over change in x-values) remains the same.

To find the missing values in your table, start with the first known value and add $8 for each subsequent hour. If you're moving backwards (i.e., from a time later to an earlier time), you would subtract $8 for each hour.

For example, if you know that the value at 2 hours is $20, then the value at 3 hours would be $20 + $8 = $28. On the other hand, the value at 1 hour would be $20 - $8 = $12.

By applying this step-by-step process, you should be able to fill in the missing values in your table.

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To find out the miles on your uncle's car's odometer, you simply add the extra miles that the uncle's car odometer reads compared to your mother's car to the odometer reading of your mother's car. This gives a total of 24066 miles on your uncle's car's odometer.

The subject here is Mathematics, particularly simple addition and subtraction problems. According to the problem, your mother's car has read 22010 miles and her car's odometer reads 2056 miles less than your uncle's car. To find out the miles on your uncle's car's odometer, you will simply add 2056 to the reading on your mother's car's odometer.

So the equation would be: 22010 miles (Mother's car odometer) + 2056 miles = Uncle's car odometer.

When you add these two sums together, the total odometer reading for your uncle's car comes out to be 24066 miles.

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To find the total cost of shipping a 7-pound care package, you can use the formula: Total Cost = (Cost per pound * Number of pounds) + Flat fee. When applying this formula to the given scenario, the total cost to ship a 7-pound care package is $17.95.

To find the total cost of shipping a 7-pound care package, consider that it costs $0.85 per pound plus a flat fee of $12. You can create an algebraic expression to find the total cost:

Total Cost = (Cost per pound * Number of pounds) + Flat fee

Substitute in the values: Total Cost = ($0.85 * 7) + $12 = $5.95 + $12 = $17.95