The length of a rectangle parking area is three times the width.The perimeter is 280 yd.Find the length and width of the parking are.

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

$57.60

Step-by-step explanation:

40% of $96.00 is $38.40

$96.00 - $38.40 = $57.60

The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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Answer:

parallel

Step-by-step explanation:

If two coplanar lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel

========================================================

Explanation:

This is due to the converse of the corresponding angles theorem.

Ignoring the "converse" part for now, the corresponding angles theorem says that if two lines are parallel, then the corresponding angles are congruent.

The converse swaps the order. The converse says that if two corresponding angles are congruent, then the lines are parallel.

Corresponding angles are the angles that are in the same configuration of the four-angle set up. For instance, both angles could be in the upper right corner for each X shape.

Check out the image below to see an example of what I mean.

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

It looks like you are trying to solve some math problems and are looking for help filling in some information on a geometry reference sheet. Here are the answers to the questions you provided:

A Median:

Originates at the vertex of the triangle.

Connects the vertex to the midpoint of the opposite side.

Divides the side into two equal parts.

To solve for x in the equation 2x + 1 = 0, you can subtract 1 from both sides to get 2x = -1. Then divide both sides by 2 to get x = -1/2.

To solve for x in the equation 3x - 31 = 0, you can add 31 to both sides to get 3x = 31. Then divide both sides by 3 to get x = 31/3 = 10 1/3.

An Altitude:

Originates at the vertex of the triangle.

Connects the vertex to the line containing the opposite side.

Divides the opposite side into two equal parts.

To solve for x in the equation 10x + 9 = 6x + 21, you can subtract 6x from both sides to get 4x + 9 = 21. Then subtract 9 from both sides to get 4x = 12. Finally, divide both sides by 4 to get x = 3.

Without more context, it is not possible to solve for x in the equation (pa + 53)*(5x + 2) = 0. Please provide more information about the problem you are trying to solve.

Step-by-step explanation:

The quotient of  10⁻⁴/10² is 10⁻⁶

Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.

For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.

Division law states that:

10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ

In this case have:

10⁻⁴/10² = 10⁻⁴⁻²   (Division law)

10⁻⁴/10² = 10⁻⁶

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Answer:

To solve 2^x = 32, we need to find the value of x that satisfies the equation.

We can rewrite 32 as a power of 2 by noting that 2^5 = 32. Therefore, we have:

2^x = 2^5

Since the bases of the powers are equal, we can equate the exponents:

x = 5

So the solution to 2^x = 32 is x = 5.

To rewrite this equation in a logarithmic form, we can use the definition of logarithms:

log(base 2)32 = x

Here, the logarithm with base 2 of 32 is equal to x.

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The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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Answer:

D) 19

Step-by-step explanation:

-7 + 19 = 12

Answer:

b. y = 4x + 3

Step-by-step explanation:

slope intercept form is y = mx + b

where m equals the coefficient before x and b is the y intercept

so, your answer has to be y = m(aka 4)x + b(aka 3)

or,

y = 4x + 3

Answer:

w= -9/8

Step-by-step explanation:

-1/3w -3/5 = 1/5w

+1/3w            +1/3 w

-3/5=1/5w+1/3w

Make common denominators to combine like terms of the right

-3/5=1/5w+1/3w

         *3       *5

-3/5=3/15w+5/15w

-3/5=8/15w

multiply both sides by the reciprocal of 8/15 which is 15/8

-3/5*15/8=8/15w*15/8

\(\frac{-3}{5}\)*\(\frac{15}{8}\) ----> cross reduce 5 in the denominator becomes 1 and 15 in the numerator becomes 3

\(\frac{-3}{1}\)*\(\frac{3}{8}\) -----> now multiply across

w= -9/8

Answer: -6/7

Step-by-step explanation:

-1/2w-3/5=1/5w

-w/2 - 3/5=w/5

Collect like terms

w/5 + w/2=-3/5

(2w + 5w)/10=-3/5

7w/10=-3/5

Cross multiply

7w x 5=-3 x 10

35w=-30

Divide both sides by 35

35w/35=-30/35

w=-6/7

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

a)The probability of the computer breaking down during the next month is 0.27

b) The probability that the time between two consecutive breakdowns is longer than 2 weeks is 0.135

c)The probability that the time between two consecutive breakdowns is longer than 2 weeks (or 0.5 months) is 0.778

d)The probability of having zero breakdowns in a 2-week period is 0.607.

e)The probability that X is greater than 2 is 0.25.

a) The number of breakdowns in a month can be modeled as a Poisson distribution with parameter

λ=2,

since we are given the average rate of breakdowns per month.

Therefore, the probability of the computer breaking down during the next month is:

P(X = 1) = (e^-λ) * (λ^1) / 1! = (e^-2) * (2^1) / 1! ≈ 0.27

(b) We can use the exponential distribution with parameter

λ=2

to model the waiting time between two consecutive breakdowns in weeks.

The probability that the time between two consecutive breakdowns is longer than 2 weeks is:

P(X > 2)

= e^(-2*2)

≈ 0.135

(c) We can convert the waiting time between two consecutive breakdowns in weeks to months by dividing by 4, since 4 weeks constitute a month.

Therefore, the waiting time between two consecutive breakdowns in months can be modeled by an exponential distribution with parameter

λ=2/4

=0.5.

The probability that the time between two consecutive breakdowns is longer than 2 weeks (or 0.5 months) is:

P(X > 0.5)

= e^(-0.5*0.5)

≈ 0.778

(d) We can model the number of breakdowns per week by a Poisson distribution with parameter

λ=2/4

=0.5,

since there are 4 weeks in a month.

The probability that the time between two consecutive breakdowns is longer than 2 weeks is equivalent to the probability of having zero breakdowns in a 2-week period.

Therefore, we need to find:

P(X = 0)

where X is the number of breakdowns in a 2-week period

P(X = 0)

= e^(-0.5*2) * (0.5^0) / 0!

≈ 0.607

(e) We can also model the waiting time between two consecutive breakdowns in weeks using a geometric distribution,

where X is the number of weeks until the next breakdown.

The probability that the time between two consecutive breakdowns is longer than 2 weeks is equivalent to the probability that X is greater than 2.

Therefore, we need to find:

P(X > 2) = (1 - p)^2

where p is the probability of a breakdown in a given week

p = 2/4 = 0.5

since the computer breaks down on average 2 times per month

P(X > 2) = (1 - 0.5)^2 = 0.25

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The solution of the expression is,

⇒ x = - 1 and x = 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Solve the expression,

x² – 3x − 2 = x + 3

Now, We can simplify as;

x² – 3x − 2 = x + 3

x² – 3x − 2 - x - 3 = 0

x² - 4x - 5 = 0

x² - 5x + x - 5 = 0

x (x - 5) + 1(x - 5) = 0

(x + 1) (x - 5) = 0

x = - 1

x = 5

Thus, The solution of the expression is,

⇒ x = - 1 and x = 5

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So, each farmer pays the following amounts: The first farmer pays 738.40 euros. The second farmer pays 443.04 euros. The third farmer pays 418.56 euros

Proportion refers to the equality of two ratios. In other words, when two ratios are set equal to each other, they form a proportion. A proportion is typically written in the form of two fractions separated by an equals sign, such as a/b = c/d. Proportions are commonly used in mathematics to solve problems involving ratios and proportions, such as finding missing values or scaling up or down a given quantity.

Here,

To find out how much each farmer pays, we need to determine the proportion of the total rent that each farmer owes based on the number of sheep they have. First, we need to find the total number of sheep:

120 + 72 + 68 = 260

The first farmer has 120 sheep, which is 46.15% of the total number of sheep (120/260). Therefore, the first farmer owes 46.15% of the rent:

0.4615 x 1600 = 738.40 euros

Similarly, the second farmer has 72 sheep, which is 27.69% of the total number of sheep (72/260). Therefore, the second farmer owes 27.69% of the rent:

0.2769 x 1600 = 443.04 euros

The third farmer has 68 sheep, which is 26.15% of the total number of sheep (68/260). Therefore, the third farmer owes 26.15% of the rent:

0.2615 x 1600 = 418.56 euros

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Complete question:

The rent of 1600 euros for a piece of land is divided among three farmers who graze their sheep there. As they do not have the same number of sheep, they decide to pay proportionally according to the number of sheep each has. If the first one has 120 sheep, the second 72, and the third 68. How much does each one pay?

Answer:

it will rotate 7.5 degrees

Step-by-step explanation:

Let's say that the price of one tablecloth is "x" and the price of one centerpiece is "y", we know that

Also

Then we must solve a system of equations

We have multiple ways to solve that system of equations, we just want to find the value of "x", then, let's do a substituition method to solve it for x.

Then

The price of one tablecloth is $2.5

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

x = 40 which is Thomas's age

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

12 colors times 2 possibilities of with or without air conditioning is 24.

24 times two possibilities of with or without automatic transmission is 48.

48 times two possibilities of with or power windows is 96.

96 times two possibilities of with or CD player is 192.

The original price of the meal deal if they would have exactly enough money to buy two of the meal deal is $4

let

x = cost of the meal

Both = 2x - 3

3/4x + 1/2x = 2x - 3

(3+2)x / 4 = 2x - 3

5/4x = 2x - 3

5/4x - 2x = - 3

(5-8)x/ 4 = -3

-3/4x = -3

x = -3 ÷ -3/4

= -3 × -4/3

= 12/3

x = $4

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The integral test compares an infinite sum to an improper integral and is the test that can only be applied when we are considering a series whose terms are all positive.

1) For a series ∑n=1∞aₙ to converge, the nth term an must satisfy aₙ→0

 as n→∞.

Therefore, from the algebraic limit properties of sequences,

lim k→∞a k = lim k→∞(S k−S k−1)=limk→∞S k−lim k→∞S k−1 = S−S = 0.

Therefore, if  ∑n=1∞aₙ converges, the nth term an→0 as  n→∞. An important consequence of this fact is the following statement:

If aₙ↛0 as n→∞,∑n=1∞aₙ diverges

The integral test compares an infinite sum to an improper integral. It is important to note that this test can only be applied when we are considering a series whose terms are all positive.

2) The sum of the areas of the rectangles is less than the sum of the area of the first rectangle and the area between the curve f(x)=1/x2 and the x -axis for x≥1

Since the area bounded by the curve is finite, the sum of the areas of the rectangles is also finite.

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The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

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