Question

Measures 24 inches long and naterial is needed to cover one 576+ˣ²=900

Answer 1

Solving for x in the equation 576+x²=900 yields x=18. In practical applications, we use different units for measuring various objects and calculating volume involves multiplying length, width, and height.

Step-by-step explanation:

To solve the equation 576+x²=900, first subtract 576 from both sides to isolate the x² term, resulting in x²=324. Taking the square root of both sides gives us x=18, since the length cannot be negative in this context. This calculation determines the value of x that solves the equation given in the student's question.

When measuring real-world objects, such as the length of a pencil or the width of a chapter book, we often use inches or centimeters. For larger measurements, like the length of a table cloth or the area of a field, meters and square meters may be more appropriate. Moreover, to find the volume of a stack of objects, multiplying length by width by height is the correct approach, as shown in the volume formula: volume of stack = length x width x height.

Using the scale factor and knowing the side length of the first square, we can determine the side length of a larger square by multiplying the initial measurement by the scale factor. For example, if the side length of the first square is 4 inches, then the side length of the larger square is 4 inches x 2 = 8 inches.

Answer 2

To find the amount of material needed to cover one side of the suitcase, we can use the Pythagorean theorem to determine the width, since the length and diagonal form a right triangle. The width turns out to be 18 inches, and thus 432 square inches of material is required to cover one side of the suitcase.

Step-by-step explanation:

To cover one side of the suitcase, we need to calculate the area of that side. We have been given the length of the suitcase, which is 24 inches, and the length of the diagonal, which is 30 inches. Using the Pythagorean theorem (since the diagonal and the length form a right triangle with the width as the other side), we can find the width of the suitcase.

The Pythagorean theorem states that, in a right-angled triangle, a² + b² = c², where c is the hypotenuse (in this case, the diagonal of the suitcase) and a and b are the other two sides. Our equation is:

24² + b² = 30²

b² = 30² - 24²

b² = 900 - 576

b² = 324

b = √324

b = 18 inches

Now that we have the width (b), we can compute the area of the surface to be covered with material: Area = length × width.

Area = 24 inches × 18 inches = 432 square inches.

Therefore, 432 square inches of material is needed to cover one side of the suitcase.

Complete question:

A suitcase measures 24 inches long and the diagonal is 30 inches long. How much material is needed to cover one side of the suitcase?