Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 13 in. by 8 in.

Final answer:

The length of the median of the trapezoid with perpendicular diagonals of lengths 8 and 10 is 9 units. This is calculated using properties of the median and the Pythagorean theorem.

Explanation:

The question you've asked regarding the median of a trapezoid with perpendicular diagonals of lengths 8 and 10 can be resolved by recognizing a property of the median in a trapezoid. The median (also known as the mid-segment) of a trapezoid is parallel to the bases and its length is equal to the average of the lengths of the bases. Since the diagonals are perpendicular, they would form right triangles with the two bases and the median line, dividing the trapezoid into four right triangles.

Let's denote the lengths of the bases as a and b, and the median as m. We know the diagonals intersect at their midpoints, thus splitting each into segments of lengths 4 and 5. Now we can form two right triangles sharing the median as a common side. Applying the Pythagorean theorem, we get two equations: m² + 4² = a² for the first right triangle and m² + 5² = b² for the second right triangle.

Since the median is the average of the bases, we have m = (a + b) / 2. Using the equations above, after some algebraic manipulations, we find that a² - b² = 16. With more manipulation, eventually, we find that (a - b)(a + b) = 16, and, since m is the average, 2m = a + b. Hence, we derive that 2m - b = (a - b), which simplifies to give us m = 9. This gives us the length of the median of the trapezoid as 9 units.

Answer:

The correct option is D) 60°

Step-by-step explanation:

Consider the provided triangle.

From the provided figure it is given that one angle is 60° and we need to find the value of y.

As we know the sum of all interior angle in a triangle is 180°.

y°+y°+60°=180°

Now solve the above equation to find the value of y.

2y°+60°=180°

2y°=180°-60°

2y°=120°

y°=120°÷2

y°=60°

Hence, the value of y is 60°.

Thus, the correct option is D) 60°

Answer:

26 sq. units

Step-by-step explanation:

a-p-e-x

The area of the triangle is 26 sq.unit, the correct option is B.

A triangle is a polygon with three sides, angles and vertices.

The triangle is classified into various types on the basis of the angle and on the basis of the equality of the length of the sides, as obtuse , acute and right angled triangle and scalene, isosceles and equilateral triangle.

The triangle is shown in the figure has side 13 and height 4 units.

The area of the triangle whose base and height is given is calculated by using the formula:

Area = (1/2) * base * height

Substituting the value in the formula.

Area = (1/2) * 13 *4

Area = 13 * 2

Area = 26 sq.unit

To know more about Triangle

https://brainly.com/question/2773823

#SPJ5

Final answer:

To determine the angular size of an object with a diameter of 3 inches from 4 yards away, one can use the formula θ = d / D to calculate θ in radians, which is then converted to degrees, resulting in an angular size of approximately 1.19°.

Explanation:

To find the angular size of a circular object with a 3-inch diameter viewed from a distance of 4 yards, one can use the following formula for angular size θ (in radians): θ = d / D, where d is the diameter of the object and D is the distance to the object.

First, we convert the diameter and the distance to the same units. There are 36 inches in a yard, so 4 yards is 144 inches:

Then, we calculate the angular size in radians:

θ = d / D = 3 inches / 144 inches = 0.0208333...

This can be converted to degrees by multiplying with 180/π:

θ(in degrees) = 0.0208333... * (180/π) = 1.19° (approximately).

Thus, the angular size of the object is approximately 1.19° when viewed from a distance of 4 yards.

Answer:

Step-by-step explanation:

The first and second system have the same solutions, the are equivalent systems of equations. Let's calculate solutions to demonstrate it:

[tex]\left \{ {{4x - 5y = 2} \atop { 3x - y = 8}} \right.[/tex]

If we multiply the second equations by -5, we can eliminate one variable and find the first solution:

[tex]\left \{ {{4x - 5y = 2} \atop { -15x +5y = -40}} \right.\\-11x=-38\\x=\frac{38}{11}[/tex]

Now, we use this value to find the other solution:

[tex]3x - y = 8\\3(\frac{38}{11})-y=8\\\frac{114}{11}-8=y\\ y=\frac{114-88}{11}=\frac{26}{11}[/tex]

The solution of the first system is [tex](\frac{38}{11} ;\frac{26}{11} )[/tex]

[tex]\left \{ {{4x - 5y = 2} \atop { 10x - 7y = 18}} \right.[/tex]

We do the same process than we did before, but this time we have to multiply by [tex]-\frac{5}{7}[/tex]:

[tex]\left \{ {{4x - 5y = 2} \atop { -\frac{50}{7}x + 5y = \frac{90}{7} }} \right.\\\frac{28x-50x}{7}=\frac{-90+14}{7}\\-22x=-76\\x=\frac{38}{11}[/tex]

Then,

[tex]4x - 5y = 2\\4(\frac{38}{11})-5y=2\\\frac{152}{11}-2=5y\\ 5y=\frac{152-22}{11}\\y=\frac{130}{5(11)}=\frac{26}{11}[/tex]

The solution of the second system is  [tex](\frac{38}{11} ;\frac{26}{11} )[/tex]

Therefore, system 1 and system 2 are equivalent.

Mary grew 15 tomatoes. A simple algebraic equation was formulated and solved to determine the quantity: m + 3m - 6 = 54, where m represents the number of tomatoes grown by Mary.

Given that Jolene had 3 times as many tomatoes as Mary and birds ate 6 of Jolene's tomatoes, and together they have 54 tomatoes, we need to set up an equation to solve for the number of tomatoes Mary grew.

Let's denote the number of tomatoes Mary grew as m. Therefore, Jolene grew 3m tomatoes. Since birds ate 6 of Jolene's tomatoes, we have 3m - 6 for the number of tomatoes left with Jolene. The equation representing the total number of tomatoes then becomes m (Mary's tomatoes) + (3m - 6) (Jolene's remaining tomatoes) = 54. Simplifying this equation:

m + 3m - 6 = 54

4m - 6 = 54

4m = 60

m = 15

Therefore, Mary grew 15 tomatoes.

To solve this problem, the first thing we can do is to take out 7 tan (x) from the whole equation, this results in simplification:

7 * tan (x) * (tan (x)^2 - 3) = 0 

Therefore the initial roots are taken from:

tan (x) = 0

Calculating for x:

x = 0, pi

The other roots can be taken from:

(tan (x)^2 - 3) = 0 

Calculating for x:

tan (x)^2 = 3

tan (x) = ± sqrt (3)  

x = pi/3 , 2pi/3 , 4pi/3 , 5pi/3 

Therefore the solutions are:

0 , pi, pi/3 , 2pi/3 , 4pi/3 , 5pi/3 

Answer:3y is the answer

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

In the triangle with B = 36°, a = 41, c = 20, b ≈ 45.3, C ≈ 29.5, A ≈ 114.5.

To solve the triangle, we can use the Law of Sines and the fact that the sum of angles in a triangle is 180 degrees.

Given:

[tex]- Angle \( B = 36° \)[/tex]

[tex]- Side \( a = 41 \)[/tex]

[tex]- Side \( c = 20 \)[/tex]

First, we need to find angle [tex]\( A \)[/tex]. We can use the fact that the sum of angles in a triangle is 180 degrees:

[tex]\[ A = 180 - B - C \][/tex]

We can find angle [tex]\( C \)[/tex] using the Law of Sines:

[tex]\[ \frac{\sin C}{c} = \frac{\sin B}{b} \][/tex]

Solving for [tex]\( C \):[/tex]

[tex]\[ \sin C = \frac{c \times \sin B}{b} \][/tex]

[tex]\[ \sin C = \frac{20 \times \sin 36°}{b} \][/tex]

[tex]\[ \sin C = \frac{20 \times 0.5878}{b} \][/tex]

[tex]\[ \sin C = \frac{11.756}{b} \][/tex]

Now we can find angle [tex]\( C \)[/tex] using the inverse sine function:

[tex]\[ C = \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]

Now, we can substitute [tex]\( C \) i[/tex]nto the equation for [tex]\( A \)[/tex] and solve for [tex]\( b \):[/tex]

[tex]\[ A = 180 - B - C \][/tex]

[tex]\[ A = 180 - 36 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]

[tex]\[ A = 144 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]

Since we know all three angles of the triangle, we can find [tex]\( b \)[/tex] using the Law of Sines again:

[tex]\[ \frac{\sin A}{a} = \frac{\sin B}{b} \][/tex]

[tex]\[ \sin A = \frac{a \times \sin B}{b} \][/tex]

[tex]\[ \sin A = \frac{41 \times \sin 36}{b} \][/tex]

[tex]\[ \sin A = \frac{41 \times 0.5878}{b} \][/tex]

[tex]\[ \sin A = \frac{24.0678}{b} \][/tex]

Now, we can find [tex]\( b \)[/tex] using the inverse sine function:

[tex]\[ b = \frac{24.0678}{\sin A} \][/tex]

Finally, we'll use the given values and calculate the closest option:

[tex]\[ A \approx 144 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]

[tex]\[ b \approx \frac{24.0678}{\sin A} \][/tex]

[tex]\[ c \approx 20 \][/tex]

B = 36°

[tex]\[ a = 41 \][/tex]

After the calculation, the closest option is:

[tex]\[ b \approx 45.3, \ C \approx 29.5, \ A \approx 114.5 \][/tex]

Complete Question:

Solve the triangle.

B = 36°, a = 41, c = 20

choices:

b ≈ 27.5, C ≈ 115.5, A ≈ 28.5

b ≈ 45.3, C ≈ 25.5, A ≈ 118.5

b ≈ 45.3, C ≈ 29.5, A ≈ 114.5

b ≈ 27.5, C ≈ 25.5, A ≈ 118.5

The point of intersection of lines represents the common solution of the system of linear equations. The solution of linear equations given in the graph is (0,2).

Linear equation represents a line on the graph. The system of linear equations represents couple/s of linear equations or lines.

The solution of system of linear equations means the common point satisfying the different linear equations.

Graphically, the point of intersection of two lines represents the common solution of these two lines or simply the solution of the system of linear equations.

So, the point of intersection from the given graph is (0,2).

Therefore, the solution of linear equations given in the graph is (0,2).

For more details, refer to the link:

https://brainly.com/question/16515610

Answer:

A is correct!

Step-by-step explanation:

Answer: Cylinder.

Step-by-step explanation: Lip-gloss tubes may have different shapes, but the usual form of a lip-gloss tube is, as the name says, a tube.

This means that it has a circular base and a circular top, and a given height that connects the base and the top, the geometrical shape that has this shape is called a cylinder.

1st minute = 0.46

 additional minutes = 0.37

6.75 -0.46 = 6.29

6.29/0.37 =17

 17 +1 = 18 total minutes