alice leaves her house and walks to school she walks 45 meters south and 336 meters east. how far is Alice from her house?

In mathematics, a plane is a two-dimensional surface with no definite beginning or end, extending infinitely in all directions. The properties of a plane, such as the loss of the usual 1/² dependence, are abstract and not physically tangible. Examples of motion, like an airplane passenger's movement or the effect of wind on a plane's trajectory, can help visualize concepts related to planes.

When considering the concept of a plane in mathematics, it is important to understand its properties. A plane is a flat, two-dimensional surface that extends infinitely in all directions. It does not have a definite beginning or end, meaning there is no bounded border that marks where it starts or stops. This idea can be difficult to conceptualize because it is abstract and not something we encounter in the physical world. In terms of geometry, we often approach problems involving planes by considering a portion of the plane that is relevant to the problem. For example, the concept of an infinite plane becomes intriguing as it affects the mathematical properties, such as the loss of the usual 1/² dependence encountered in finite plane calculations. To illustrate motion in a plane, one might analyze the average velocity of an object, such as an airplane passenger moving from the front to the back of an airplane or the influence of wind on a plane's trajectory relative to the ground. These scenarios involve physical planes and motions, but they help to visualize the movements within the mathematical context of planes.

The area of a piece of wood with a length of  [tex]\( \frac{5}{12} \)[/tex]  foot and a width of  [tex]\( \frac{2}{3} \)[/tex]  foot is [tex]\( \frac{5}{18} \)[/tex] square feet.

To find the area of a rectangular piece of wood with a length of [tex]\( \frac{5}{12} \)[/tex] foot and a width of [tex]\( \frac{2}{3} \)[/tex] foot, we use the formula for the area of a rectangle

[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]

Given that the length is  [tex]\( \frac{5}{12} \)[/tex]  foot and the width is  [tex]\( \frac{2}{3} \)[/tex]  foot, we plug these values into the formula:

[tex]\[ \text{Area} = \frac{5}{12} \times \frac{2}{3} \][/tex]

To multiply fractions, we multiply the numerators together and the denominators together:

[tex]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[ \text{Area} = \frac{5 \times 2}{12 \times 3} \]\[ \text{Area} = \frac{10}{36} \][/tex]

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

[tex]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[ \text{Area} = \frac{10 \div 2}{36 \div 2} \]\[ \text{Area} = \frac{5}{18} \][/tex]

So, the area of a piece of wood with a length of  [tex]\( \frac{5}{12} \)[/tex]  foot and a width of  [tex]\( \frac{2}{3} \)[/tex]  foot is [tex]\( \frac{5}{18} \)[/tex] square feet.

Answer: D) 25π

Step-by-step explanation:

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The cost of 1 bicycle is $48 by using the system of equations.

Word problems are a mathematical interpretation by using variables, numbers, and arithmetic operations to solve real-life problems.

From the given information:

We have a system of equations, and we can solve for the cost of1 bicycle

Using the Elimination method:

4U + 3B = 268

-2U + 3B = 110

2U + 0    = 158

U = 158/2

U = 79

The cost of 1 bicycle = 4(U) - 268

= 4(79) - 268

= 316 - 268

= $48

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Answer:

$48

Step-by-step explanation:

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To find the total amount Jeremy earned from mowing lawns, we set up the equation x - $17 = $75 where x is the total earnings. Solving the equation, we find that Jeremy earned a total of $92.

The amount of money Jeremy earned mowing lawns can be found by setting up a simple algebraic equation. We know that after paying $17 for gas, he had $75 leftover for camp. Therefore, we can write the equation as:

Total Earnings - Gas Cost = Money for Camp

Let x represent the total amount Jeremy earned. The equation will then be:

x - 17 = 75

Now, we solve for x:

x = 75 + 17

x = 92

Jeremy earned a total of $92 from mowing lawns.

Answer:

C)  

late spring.

Step-by-step explanation:

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To find 60% of 33, first write 60% as a decimal by moving the decimal point two places to the left to get .60.

Next, the word "of" means multiply, so we are are going to multiply.

(.60) (33) = 19.8

Therefore, 60% of 33 is 19.8.

Answer: So, the possible number of additional senators who must vote in favor of the treaty in order to radify it is given by

[tex]19\leq x\leq 52[/tex]

Step-by-step explanation:

Since we have given that

Number of states = 50

Number of senators from each of the 50 states = 2

Total number of senators would be

[tex]50\times 2\\\\=100[/tex]

Since [tex]\dfrac{2}{3}[/tex] of the senators present must approve the treaty.

[tex]\dfrac{2}{3}\times 100\\\\=66.67[/tex]

Number of senators have voted in favor of a treaty = 48

So, remaining senators would be

[tex]67-48\\\\=19[/tex]

Let x be the number of senators needed.

So, Inequality would be

[tex]x\geq 19[/tex]

Now, [tex]100-48=52[/tex]

[tex]x\leq 52[/tex]

So, the possible number of additional senators who must vote in favor of the treaty in order to radify it is given by

[tex]19\leq x\leq 52[/tex]

In mathematics, a line segment can grow from a) zero-dimensional points or b) one-dimensional line segments but cannot grow from a three-dimensional object due to differences in properties such as volume.

In the field of mathematics, a line segment can grow from a zero-dimensional point and a one-dimensional line segment. The process of a line segment growing from a point involves extending out in a certain direction from the zero-dimensional point. When we say a line segment can grow from a one-dimensional object, it means an existing line segment can be extended to become a longer line segment.

A line segment cannot 'grow' from a three-dimensional object because a line segment is a one-dimensional entity, and dimensional objects have 'volume,' a property which a line segment does not possess.

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To factor the expression x³ - 2x² - 9x + 18, use the grouping method to factor out a common binomial factor.

To factor the expression x³ - 2x² - 9x + 18, we can first look for any common factors. Since there are no common factors among all the terms, we will use the grouping method to factor the expression.

Step 1: Group the terms in pairs.
(x³ - 2x²) - (9x - 18)
Step 2: Factor out the greatest common factor from each pair.
x²(x - 2) - 9(x - 2)
Step 3: Notice that we now have a common binomial factor of (x - 2).
(x² - 9)(x - 2)

Therefore, the factored form of the expression x³ - 2x² - 9x + 18 is (x² - 9)(x - 2).

The student is looking to factor the polynomial expression x^3 - 2x^2 - 9x + 18. This process typically involves finding whether factors like binomials divide the polynomial without a remainder, using methods like grouping, trial and error, or the Rational Root Theorem, followed by long or synthetic division.

The student has asked to factor the expression x^3 - 2x^2 - 9x + 18.

To factor this expression, we can follow a systematic approach, which often starts with looking for common factors or applying techniques such as grouping, trial and error, or the use of the Rational Root Theorem. In this case, we may not see an immediate common factor, so we might try to group terms or apply synthetic division or the Rational Root Theorem to identify potential roots of the polynomial.

A factor of a polynomial is a binomial (or another polynomial) that divides the original polynomial without leaving a remainder. If we find such a factor, we can then divide the original polynomial by this factor to simplify the expression further. For example, if we discover that (x - 3) is a factor, then we can divide the polynomial by (x - 3) to find the other factors.

Unfortunately, without performing the actual factoring process or having additional information, we cannot factor this specific expression purely based on the question provided. If we had one root or factor given, we could use long division or synthetic division to further factor the expression, and then possibly factorize it completely into the product of binomials or another polynomial.

The solution to the equation 3.2 - 4d = 2.3d + 3 is d = 0.0317.

The given equation is,

3.2 - 4d = 2.3d + 3

Combine like terms by adding 4d to both sides of the equation:

3.2 - 4d + 4d = 2.3d + 3 + 4d

3.2 = 6.3d + 3

Move the constant term (3) to the other side of the equation by subtracting 3 from both sides:

3.2 - 3 = 6.3d + 3 - 3

0.2 = 6.3d

Divide both sides of the equation by 6.3 to isolate the variable d:

0.2/6.3 = 6.3d/6.3  

d = 0.0317

So, the solution to the equation 3.2 - 4d = 2.3d + 3 is d = 0.0317.

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