The perimeter of a face of a cube is 16 mm. What is its volume?1.64 mm3
2.128 mm3
3.512 mm3
4.4096 mm3

Answers

Answer 1

Answer: 16 is divided by 4 because square has 4 sides
16:4= 4mm
then you search the volume
4 x 4 x 4= 64mm3

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Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. When he starts his shift, the water level shows 4 gallons, or 128 cups of water. As the shift progresses, he records the level of the water every 10 minutes. After 2 hours, he uses a regression calculator to compute an equation for the decrease in water. His equation is W –0.414t + 129.549, where t is the number of minutes and W is the level of water. According to the equation, after about how many minutes would the water level be less than or equal to 64 cups

Answers

The correct answer is:

t ≥ 158.33, or rounded, t ≥ 160.

Explanation:

The equation we're given is
W = -0.414t + 129.549, which an be written as
-0.414t + 129.549 = W.

We are asked to find the amount of time it would take for the water level to be less than or equal to 64 cups. Plugging this information in, we have:

-0.414t + 129.549 ≤ 64

To solve this, we first cancel 129.549 by subtracting from both sides:
-0.414t + 129.549 - 129.549 ≤ 64 - 129.549
-0.414t ≤ -65.549

Now divide both sides by -0.414:
-0.414t/-0.414 ≤ -65.549/-0.414
t ≥ 158.33

(When we multiply or divide both sides of an inequality by a negative number, we must flip the inequality symbol.)

Which of the following best defines density?A.
A measure of the volume of a given substance

B.
A number between 0 and 1 that defines how thick a substance is

C.
A measure of how much mass a given volume of a substance will have

D.
A measure of the mass of a given substance

Answers

Answer:

Density = mass/volume

Step-by-step explanation:

The mass per unit volume of a given substance is called its density. It can be represented by d or ρ. Mathematically, it is given by :

density=mass/volume

The SI unit of mass is kg and the SI unit of volume is m³. So, the SI unit of density is kg/m³.

So, the statement that defines density is "A measure of how much mass a given volume of a substance will have". Hence, the correct option is (c).

Density is mass per unit volume, therefore the correct answer is C. A measure of how much mass a given volume of a substance will have

What type of solutions do the methods for solving systems of equations find and how does this relate to setting the equations equal to each other?

Answers

A system of equations is a set of two or more equations that share two or more unknowns. The solutions to a system of equations are all the values that make all of the equations true, or the points where the graphs of the equations intersect. We can solve a system of linear equations through graphing, substitution and linear combination. Systems of nonlinear functions, such as quadratic or exponential equations, can be handled with the same techniques.

Final answer:

Methods to solve systems of equations typically find the values of variables that satisfy all equations in the system, relating this to setting equations equal to each other. Common methods include substitution, elimination, and graphing for linear equations, and factoring, using the quadratic formula, or completing the square for quadratic functions.

Explanation:

Methods for solving systems of equations often result in finding the values of variables that satisfy all equations in the system simultaneously. This is directly related to setting the equations equal to each other because when we equate two or more equations, we are essentially looking for their common solutions or intersection points. For instance, consider two equations y = b + mx and y = ax^2 + bx + c, linear and quadratic respectively. In order to ascertain their intersection points or common solutions, you would have to set them equal to each other, thus leading to a new equation, ax^2 + bx + c = b + mx.

The process of solving systems of equations underlies various natural phenomena and engineering processes; knowing the methods to handle these equations is crucial. For linear equations, common methods include substitution, elimination, and graphing. For quadratic functions, solutions can often be found using factoring, using the quadratic formula, or, if necessary, completing the square.

In the context of real-world applications, understanding how systems of equations function can play a part in everything from kinematic problem-solving to interpreting rates of change in scientific or technological processes. Such knowledge, then, is indispensable to anyone seeking to manage these processes effectively.

Learn more about Systems of Equations here:

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Between which two square roots of integers could you find Euler's number (2.7182818284...)?

Answers

The square root of 7 is roughly 2.6
The square root of 8 is roughly 2.8

Hence Euler's number is between $√(7)$ and $√(8)$ .

between the square roots of 7 and 8

e^2 = 7.38 roughly

Evaluate the following y^2-5y+2

Answers

If y = 3, then you substitute 3 into wherever it says y.

So the original:
y² - 5y + 2

becomes:
3² - 5×3 + 2.

which is:
9 - 15 + 2.

9 - 15 = -6
-6 + 2 = -4.

-4 is the answer.

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!What are the equations for the vertical and horizontal asymptotes of the function?

Answers

Answer: (A) vertical asymptote: x = 2, horizontal asymptote: y = 1

Step-by-step explanation:

$f(x) = (1)/(x-2)+1$

Vertical Asymptote is the restriction on the x-value. The denominator cannot be zero, so x - 2 ≠ 0 ⇒ x ≠ 2

The restricted value on x is when x = 2 which is the vertical asymptote

Horizontal Asymptote (H.A.) is the restriction on the y-value. This is a comparison of the numerator (n) and denominator (m). There are 3 rules that will help you: