7. If the diagonals of a square measure 24 meters,, №18011194, 06.05.2021 13:45

Mathematics

7. If the diagonals of a square measure 24 meters, what is the length of a side of the square?

Step-by-step answer

P Answered by Master

Step-by-step explanation:

the diagonal is the hypotenuse of a 45-45-right triangle

the two legs are the same measure so the Pythagoreant theorem

2x²=24 divide by 2

x² = 12 square root

$x = \sqrt{12} \\ \sqrt{4x3} \\2\sqrt{3}$

Mathematics

Match each cross section to its area. a cross section passing through the diagonals of opposite faces of a cube with edges that are 7 inches long and a diagonal that is approximately 10 inches a cross section parallel to the base of a cube whose edges are 8 inches long a cross section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism that is 24 inches wide, 7 inches long, and 12 inches tall and measures 25 inches along the diagonal of the base a cross section parallel to the base

Step-by-step answer

P Answered by PhD

77

FIRST.

64 square inches matches to a cross section parallel to the base of a right rectangle prism that is 3 inches long, 7 inches wide, and 11 inches tall

This is shown in the first figure below. A right rectangular prism where every edge connecting its base and the opposite face makes right angles with both faces. Since the tall is the side that measures 11 inches, then the base is formed by 3 inches long and 7 inches wide. Therefore, the area of this shape can be found as the area of a rectangle, which is:

$A_{cs}=L\times W \\ \\ A_{cs}=(3)(7) \\ \\ A_{cs}=21in^2$

SECOND.

64 square inches matches to a cross section parallel to the base of a cube whose edges are 8 inches long.

This is shown in the second figure below. A cube is a prism whose sides all have the same length and in this case is 8 inches. We name cross section is to the slice that cuts through a solid. If the cross section is parallel to the base of a cube, then it forms a square with length L=8in . Therefore, the area of this shape can be found as the area of a square, which is:

$A_{cs}=L^{2} \\ \\ A_{cs}=8^2 \\ \\ A_{cs}=64in^2$

Third.

7 square inches matches to a cross section passing through the diagonal of opposite faces of a cube with edges that are 7 inches long and a diagonal that is approximately 10 inches

This is shown in the third figure below. As you can see, the cross section passes through the diagonals of the base and the top of the cube that are two opposite faces. This form a rectangle having sides $L_{1}=7in \ and \ L_{2}=10in$ where:

$L_{1}: Edge \ of \ the \ cube \\ \\ L_{2}: Diagonal \ of \ the \ face$

So:

$A_{cs}=L_{1}\times L_{2} \\ \\ A_{cs}=7(10) \\ \\ A_{cs}=70in^2$

FOURTH.

300 square inches matches to a cross section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism that is 24 inches wide, 7 inches long, and 12 inches tall and measures 25 inches along the diagonal of the base.

This is shown in the fourth figure below. The cross section passes through the diagonals of the base and the top of the right rectangular prism. They are opposite to each other, so the shape of the cross section is a rectangle whose sides are $L_{1}=12in \ and \ L_{2}=25in$ where:

$L_{1}: Height \ of \ the \ cube \\ \\ L_{2}: Diagonal \ of \ the \ face$

So:

$A_{cs}=L_{1}\times L_{2} \\ \\ A_{cs}=12(25) \\ \\ A_{cs}=300in^2$

Match each cross section to its area. a cross section passing through the diagonals of opposite face

Mathematics

Match each cross section to its area. a cross section passing through the diagonals of opposite faces of a cube with edges that are 7 inches long and a diagonal that is approximately 10 inches a cross section parallel to the base of a cube whose edges are 8 inches long a cross section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism that is 24 inches wide, 7 inches long, and 12 inches tall and measures 25 inches along the diagonal of the base a cross section parallel to the base

Step-by-step answer

P Answered by PhD

77

FIRST.

64 square inches matches to a cross section parallel to the base of a right rectangle prism that is 3 inches long, 7 inches wide, and 11 inches tall

This is shown in the first figure below. A right rectangular prism where every edge connecting its base and the opposite face makes right angles with both faces. Since the tall is the side that measures 11 inches, then the base is formed by 3 inches long and 7 inches wide. Therefore, the area of this shape can be found as the area of a rectangle, which is:

$A_{cs}=L\times W \\ \\ A_{cs}=(3)(7) \\ \\ A_{cs}=21in^2$

SECOND.

64 square inches matches to a cross section parallel to the base of a cube whose edges are 8 inches long.

This is shown in the second figure below. A cube is a prism whose sides all have the same length and in this case is 8 inches. We name cross section is to the slice that cuts through a solid. If the cross section is parallel to the base of a cube, then it forms a square with length L=8in . Therefore, the area of this shape can be found as the area of a square, which is:

$A_{cs}=L^{2} \\ \\ A_{cs}=8^2 \\ \\ A_{cs}=64in^2$

Third.

7 square inches matches to a cross section passing through the diagonal of opposite faces of a cube with edges that are 7 inches long and a diagonal that is approximately 10 inches

This is shown in the third figure below. As you can see, the cross section passes through the diagonals of the base and the top of the cube that are two opposite faces. This form a rectangle having sides $L_{1}=7in \ and \ L_{2}=10in$ where:

$L_{1}: Edge \ of \ the \ cube \\ \\ L_{2}: Diagonal \ of \ the \ face$

So:

$A_{cs}=L_{1}\times L_{2} \\ \\ A_{cs}=7(10) \\ \\ A_{cs}=70in^2$

FOURTH.

300 square inches matches to a cross section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism that is 24 inches wide, 7 inches long, and 12 inches tall and measures 25 inches along the diagonal of the base.

This is shown in the fourth figure below. The cross section passes through the diagonals of the base and the top of the right rectangular prism. They are opposite to each other, so the shape of the cross section is a rectangle whose sides are $L_{1}=12in \ and \ L_{2}=25in$ where:

$L_{1}: Height \ of \ the \ cube \\ \\ L_{2}: Diagonal \ of \ the \ face$

So:

$A_{cs}=L_{1}\times L_{2} \\ \\ A_{cs}=12(25) \\ \\ A_{cs}=300in^2$

Mathematics

Look at the cups shown below (images are not drawn to scale): a cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches. how many more cubic inches of juice will cup b hold than cup a when both are completely full? round your answer to the nearest tenth. 18.8 cubic inches 21.9 cubic inches 25.1 cubic inches 32.6 cubic inches question 9(multiple choice worth 1 points) (03.02 lc) abcd is a rectangle. what is the value of x? rectangle with length 45 feet, width x feet, and diagonal 53

Step-by-step answer

P Answered by PhD

8) 18.8 cubic inches;
9) 28 feet;
10) 1.7 centimeters;
11) 13;
12) 10 centimeters;
13) it is incorrect because the length of the unknown side is the square root of 7,744;
14) square root of 18;
15) 12 miles;
16) 364 centimeters.

Mathematics

A new school randomly assigns a six-character student code to every prospective student. The school uses the characters 1, 2, 3, 4, 5, X, Y, and Z. If none of the student codes contain a repeated character, what is the total number of codes that can be randomly assigned?

Step-by-step answer

P Answered by PhD

The total nom of code that can be used is equal to 5+3 = 8

Mathematics

The ratio of tables to chairs at the furniture store is 1:6. There are 30 chairs. How many tables are there?

Step-by-step answer

P Answered by PhD

The solution is in the following image