A rectangular prism has a volume of 60 in³. what is the least possible surface area of the prism?

and

A rectangular prism has a volume of 24 m³. What is the least possible surface area of the prism?

The logarithmic graph for the function loga(x) represents relationships similar to that of a log-log plot such as exponential relationships. Understanding properties of logarithms and principles of graphing can help interpret this function. Unlike linear equations, these graphs have a unique shape that are not straight lines.

The graph of the logarithmic function f(x) = loga(x) can be understood using logarithmic properties and graph principles. The log-log plot reveals that logarithmic graphs represent exponential relationships such as the decay of radioactivity or the relationship between light's frequency and wavelength. The logarithmic scale is advantageous in graphing large ranges of values.

There are a few principles to note about logarithms for this. For instance, the logarithm of a number with an exponent is equal to the exponent multiplied by the logarithm of the number. Similarly, the logarithm resulting from dividing two numbers is the difference between the logarithms of the two numbers. These properties can be helpful in interpreting the logarithmic graph.

Our graph, however, is not a straight line as in the case of linear equations which have a uniform slope, a y-intercept and x as the horizontal axis. Logarithmic graphs have unique characteristics determined by the base and the values of x.

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Final answer:

The hypotenuse of a right triangle inscribed in a circle is referred to as the diameter of the circle.

Explanation:

The hypotenuse of a right triangle inscribed in a circle is referred to as the diameter of the circle.

This can be explained using the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the hypotenuse of the right triangle represents the diameter of the circle.

For example, if the lengths of the legs of the right triangle are represented by a and b, then the length of the hypotenuse (diameter) represented by c can be calculated as c = √(a² + b²).

The term that describes the hypotenuse of a right triangle inscribed in a circle is the diameter. This is based on Thales' theorem, which states that the hypotenuse of a right triangle inscribed in a semicircle is the diameter of the circle.

The hypotenuse of a right triangle inscribed in a circle is described by the term diameter. When a right triangle is inscribed in a circle, the hypotenuse always corresponds to the diameter of that circle. This is because, according to the Thales' theorem, a right angle in a semicircle suggests that the side opposite the right angle of an inscribed triangle (the hypotenuse) must be the diameter of the circle. Furthermore, the relationship between the sides and the hypotenuse of a right triangle is given by the Pythagorean theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

Answer:

To decompose this shape I would draw a vertical line from the vertex that is pointing outside to the vertex that is pointing inside. By doing this the vertical line will give me 2 congruent parallelograms. Yes it's that simple

Step-by-step explanation:

The inequality that can be used to find how many $2.50 fruit packs can be purchased for $15.00 is 2.50f ≤ 15, where f represents the number of fruit packs. Therefore, you can purchase up to 6 fruit packs with $15.00.

To find how many $2.50 fruit packs can be purchased for $15.00, we can use the inequality:

2.50f ≤ 15

where f represents the number of fruit packs.

To solve the inequality, we divide both sides by 2.50:

f ≤ 6

Therefore, you can purchase up to 6 fruit packs with $15.00.

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Answer:

21.5

Step-by-step explanation:

took test 100% 4.08 Quiz: Finding the Volume of Rectangular Prisms and Problem Solving

Both Judy and Edith are correct. They each ate one-sixth of the lemon pie.

Judy and Edith are discussing how much of the lemon pie they each ate. Judy claims that they each ate one-sixth of the pie, while Edith says they ate two-sixths. To determine who is correct, let's break it down:

Therefore, both Judy and Edith are correct. They each ate one-sixth of the lemon pie.

Answer:

old quetstion xd

Step-by-step explanation:

Given:

[tex] \angle A=(12x-5)^{\circ}\\ \\ x=9 [/tex]

Solution:

Substitute 9 for x in the expression for angle A.

[tex] \angle A=12(9) -5=108-5=103^{\circ}\\ \\ [/tex]

An obtuse angle is an angle of greater than 90° and less than 180°, so..

[tex] \angle A \; is \; equal \; to \; 103^{\circ} \; and \; it \; is \; an \; Obtuse \; Angle! [/tex]

Answer:

The answer is

D (2 1/2)/(1/4)

And 10

Oranges are needed to make 2 1/2 cups of juice

Step-by-step explanation:

From the given expression

We can solve the problem

If we state it out Mathematically

Step one

1 orange will give 1/4 cup of juice

x orange will give 2 1/2 cups of juice

Step two

By cross multiplication we have

x=( 2 1/2)/(1/4)

Let's convert the mixed fraction

2 1/2

to proper fraction we have 5/2

x=( 5/2)/(1/4)

x=5/2*4/1

x=20/2

x=10

Answer:

(A) 24 [tex]mm^{3}[/tex]

Step-by-step explanation:

Length of the first piece = 8 - 6 = 2 mm

Width of the first piece = 1 mm

Height of the first piece = 6 mm

Volume of the first piece = 2 × 1 × 6= 12[tex]mm^{3}[/tex]

Length of the second piece = 6 mm

Width of the second piece = 1 mm

Height of the second piece = 6 - 4 = 2 mm

Volume of the first piece = 6 × 1 × 2= 12[tex]mm^{3}[/tex]

Volume of the entire solid = 12 + 12 = 24 [tex]mm^{3}[/tex]

Mary is 15 years old and Jose is 3 years old. This is determined by setting up a system of linear equations based on the relationship of their ages and solving for their individual ages.

The question involves solving a system of linear equations to find the ages of Mary and Jose. Let's denote Mary's age as M and Jose's age as J. According to the problem, Mary is five times older than Jose, so we have M = 5J. Additionally, the sum of their ages is 18, which gives us a second equation: M + J = 18.

To solve for both ages, substitute the first equation into the second to get: 5J + J = 18. Combining like terms, we get 6J = 18. Dividing both sides by 6 gives us J = 3. This means Jose is 3 years old. To find Mary's age, we substitute J back into the first equation: M = 5(3), resulting in M = 15, so Mary is 15 years old.

To solve this problem, set up a system of equations where Mary's age is M and Jose's age is J. Use substitution method to solve the system. Mary is 15 years old and Jose is 3 years old.

To solve this problem, we can set up a system of equations. Let's assume that Mary's age is M and Jose's age is J. We are given two pieces of information: 1) Mary's age is 5 times Jose's age, so we can write the equation M = 5J, and 2) the sum of their ages is 18, so we can write the equation M + J = 18.

Now we have a system of two equations with two variables:

We can solve this system by substitution or elimination. Let's use the substitution method. From equation 1, we know that M = 5J. We can substitute this value of M into equation 2 and solve for J:

5J + J = 18

6J = 18

J = 3

Now that we know J, we can substitute this value into equation 1 to find M:

M = 5(3) = 15

Therefore, Mary is 15 years old and Jose is 3 years old.

Here is your answer, my good sir, or maiden.

Answer:

The answer is 1/6 yard

Step-by-step explanation:

The length, width, and height of a cube are equal. Each cubic block must have the same length, width, and height:

Length of tank= 1/6 yard = 1/6 yard = 3 x 1/6 yard

Height of tank: 2/6 yard = 2 x 1/6 yard

width of tank= 1/6 yard

Because the length and height of the tank are multiples of the width, the length of each cubic block should be equal to the width of the tank:

= 1.6 yard