In triangle ABC, segment DE is parallel to segment AC and thus, triangle BED is similar to triangle BCA.


A. ) use the ratios of the lengths of corresponding sides to create a proportion


B. ) Solve for x

The lowest point should be used for measurement. To acquire a correct reading, students must read the meniscus at eye level. In order to read the meniscus at eye level, students need first set the graduated cylinder on the table and then stoop.

A measuring cylinder, often referred to as a graded cylinder, a cylinder measuring cylinder, or a mixing cylinder, is a piece of lab apparatus used to gauge the quantity of fluids, chemicals, or solutions used during a typical lab session. Compared to common laboratory flasks and beakers, graduated cylinders offer higher precision and accuracy. The graduated cylinder is a scientific tool that employs the metric system rather than the American standard system, so measurements are made in millilitres rather than ounces. The volume of an object or quantity of liquid is measured using a graduated cylinder, a common piece of laboratory glassware. It is a glass cylinder with side markings resembling those on a measuring cup, as its name suggests.

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Answer:

Step-by-step explanation:

It is 20% because there is 5 squares. So we need to make this a fraction. So the fraction would be 1/5.  So we then have to find a multiple  for 1/5 because it is out of 100. So 20x5=100. So we have to multiply the top and the bottom part of the fraction by 20. So 5x20=100 and 1x20=100. So then we get 20/100. So the top number is your percent. So 20% is your answer. Good luck.

Answer:

The team sold 91 hats.

Step-by-step explanation:

$3,094 ÷ %34 = 91

The following, find 2 solutions and 2 non solutions is \(x=\frac{30-5 y}{2}\)

What is non solutions?

Ideal solutions are those that follow Raoult's law throughout the whole concentration range. A solution is said to as a non-ideal solution if it violates Raoult's law.

\($$2 x+5 y=30$$\)

\(Move $5 y$ to the right side\)

\($$2 x=30-5 y$$\)

\(Divide both sides by 2\)

\($$\frac{2 x}{2}=\frac{30}{2}-\frac{5 y}{2}$$Simplify$$x=\frac{30-5 y}{2}$$\)

Non solutions, in the plural, refer to anything that falls short of offering a fix for a problem. These batteries also lose their charge, rendering them useless for solving the more significant issue of storing and utilizing renewable energy.

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Answer:

I think the equation is y= -1/3x+1

Solutions: (0,1)(-6,3)

y-int= 1

Slope= 3-1/(-6)-0 = 2/-6= -1/3

y=-1/3x+1

32 + 40 二

(6 + 3) = 12 (4+

Answer:

4+ what?

Step-by-step explanation:

Answer:

  2048/3 π cubic units

Step-by-step explanation:

You want the exact volume of a sphere with radius 8 units.

The volume of a sphere is given by the formula ...

  V = 4/3πr³

  V = 4/3π(8³) = 2048/3·π . . . . cubic units

The volume of the sphere is 2048/3·π cubic units.

__

Additional comment

That's (682 2/3)π.

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Answer:

m∠FXD = 36°

EG = 10

m∠FZG = 24°

Step-by-step explanation:

In triangle XYZ, G is the incenter of the triangle.

Since, m∠FXG = 18°

And m∠FXD = 2(m∠FXG)

                     = 2 × 18°

                     = 36°

Since, point G is equidistant from all sides (Property of incenter of a triangle)

Therefore, DG = EG = GF = 10

Since, m∠X + m∠Y + m∠Z = 180°

2(m∠FXG) + m∠DYE + 2(m∠FZG) = 180°

2(18)° + 96° + 2(m∠FZG) = 180°

2(m∠FZG) = 180° - 132°

m∠FZG = 24°

Answer:

Below

Step-by-step explanation:

Losing 27 % of value each year means it retains 73% each year

  we need to multiply 20 000 x  .73 x .73 x .73     ....  .73     (twelve times )

                  or   re-written as   20 000 * .73^12 = value =$ 458.04

Answer:

1) James brother is 10-x years old

2) James was 3 years ago x-3 years old

3) James brother was 3 years ago 7-x years old

4) 3(x-3)=7-x

5) James is 4 years old, his brother is 6 years old

Step-by-step explanation:

3) 10 - x - 3 = 7 - x

5) 3* James age 3 years ago = James brothers age 3 years ago

<=> 3*(x-3) = 7-x

<=> 3x - 9 = 7 - x

<=> 4x = 16

<=> x = 4

Answer:

\( \sqrt[3]{1000} = 10\)

So the radius of the sphere is 10/2 = 5 inches.

The volume of this sphere is

(4/3)π(5³) = 500π/3 cubic inches.

Answer:

9 years old

look at the comment section.

The age of john is 9 years.

Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division, with an objective to find the values.

An algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/). An example of an algebraic expression is 5x + 6. Here 5 and 6 are fixed numbers and x is a variable.

Given:

John is 3 years older than Mary.

Five years ago he was four times as old as Mary was then.

let the age of mary be x

John's age= x+ 3

Five years age,

Mary's age= x-5

john's age = x-2

So,

x-2= 4( x-5)

x- 2 = 4x- 20

-3x= -18

x=3

Hence, john's age= 9 years

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answer:

338 out of 520

step by step:

13 out of 20 dont favor mystery

13:20

? :520

520÷20=26

13×26= 338

338 students out of 520 do not favor mysteries

Step-by-step explanation:

x - 5x = -74 - 14

-4x = -88

x = 22

Answer:

x = 5x - 74

-4x = -88x

x = 22

Given the series: $00 Σn²e^{-n²} $In order to use the integral test, we have to check if the sequence $a_n = n^2e^{-n^2}$ is decreasing and non-negative. Therefore, the smallest value of $n$ that will ensure that the error for the series is accurate to 4 decimal places is\($n = 8$.\)

To check if\($a_n$\)is decreasing, we have to calculate its derivative:$a_n' = \(2ne^{-n^2} - n^3e^{-n^2} = n(2 - n^2)e^{-n^2}$\)Since \($2-n^2 < 0$ for all $n \geq 2$\), we have\($a_n' < 0$ for all $n \geq 2$\), which means \($a_n$\)is a decreasing sequence.

Now, to check if $a_n$ is non-negative, we simply notice that \($n^2 \geq 0$ and $e^{-n^2} > 0$, so $a_n$\) is non-negative for all\($n \geq 1$\).

Therefore, the integral test applies and we can check convergence by evaluating the following integral:\($$\int_0^\infty x^2e^{-x^2}\,dx$$\)

We can evaluate this integral using a u-substitution:\($u = x^2,\quad du = 2x\,dx$$$$\int_0^\infty x^2e^{-x^2}\,dx = \frac{1}{2} \int_0^\infty e^{-u}\,du = -\frac{1}{2}e^{-u}\Big|_0^\infty = \frac{1}{2}$$\)

Since the integral converges, the series converges as well.4) In order to find the value of n that will ensure that the error for the series in the last problem 3 is accurate to 4 decimal places, we have to use the following error bound formula for alternating series:

\($$|R_n| \leq a_{n+1}$$where $a_{n+1}$\)is the first neglected term. In our case, the series is not alternating, so we have to use the Cauchy error bound formula instead:\($$|R_n| \leq \frac{M}{(n+1)^p}$$where $M$\) is an upper bound for \($|f^{(p+1)}(x)|$ for all $x$\) in the interval of convergence, and $p$ is the smallest integer such that $f^{(p)}(x)$ is not defined at $x=a$.

Since we know that the series converges, we can use the fact that $a_n$ is decreasing to find an upper bound for \($|R_n|$:$$|R_n| \leq \sum_{k=n+1}^\infty a_k$$$$|R_n| \leq \int_n^\infty x^2e^{-x^2}\,dx = -\frac{1}{2}e^{-x^2}\Big|_n^\infty = \frac{1}{2}e^{-n^2}$$\)

Now we need to find the smallest $n$ such that \($\frac{1}{2}e^{-n^2} \leq 0.0001$:$$\frac{1}{2}e^{-n^2} \leq 0.0001$$$$e^{-n^2} \leq 0.0002$$$$-n^2 \leq \ln(0.0002)$$$$n^2 \geq -\ln(0.0002)$$$$n \geq \sqrt{-\ln(0.0002)} \approx 7.441$$\)

Therefore, the smallest value of $n$ that will ensure that the error for the series is accurate to 4 decimal places is\($n = 8$.\)

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In the Subgame Perfect Equilibrium of a Stackelberg model, firm 1 chooses a number, and firm 2 chooses a function. Therefore, option (d) is the correct answer.

The Subgame Perfect Equilibrium (SPE) is a solution concept in game theory that analyzes strategic decision-making in sequential games. In a Stackelberg model, firm 1 acts as the leader and sets its output level first, followed by firm 2 as the follower, who observes firm 1's output before making its decision.

In the Subgame Perfect Equilibrium of this model, firm 1 chooses a number (output level) while firm 2 chooses a function (strategy). This implies that firm 1's decision is made independently as a quantity, and firm 2, observing firm 1's choice, formulates its strategy based on that information.

Therefore, option (d) is the correct answer: Firm 1 chooses a number, and firm 2 chooses a function in the Subgame Perfect Equilibrium of a Stackelberg model.

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Answer:

Solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles.

If you attempted the problem four times and all recorded scores were 0%, it suggests that your attempts did not yield the correct solution. To solve the equation t = r + 7kw, we need to have specific values or information about the variables involved. Without any additional details, it is not possible to provide a numerical solution.

To improve your chances of solving the equation successfully, consider the following steps:

Review the equation: Make sure you understand the structure and the relationship between the variables. In this case, t is equal to the sum of r and 7 times the product of k and w.

Check for errors: Review your calculations and ensure there are no mistakes in your algebraic manipulations. Double-check your arithmetic operations and signs.

Seek assistance: If you're having difficulty solving the equation, consider reaching out for help. Consult a teacher, tutor, or someone knowledgeable in the subject matter. They can guide you through the problem-solving process and clarify any misunderstandings.

Practice and persistence: Continue practicing similar equations to improve your problem-solving skills. Persistence and practice are key to mastering mathematical concepts.

Remember, solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles. Keep practicing and seeking assistance, and you will improve your problem-solving abilities over time.

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Answer:

Solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles.

If you attempted the problem four times and all recorded scores were 0%, it suggests that your attempts did not yield the correct solution. To solve the equation t = r + 7kw, we need to have specific values or information about the variables involved. Without any additional details, it is not possible to provide a numerical solution.

To improve your chances of solving the equation successfully, consider the following steps:

Review the equation: Make sure you understand the structure and the relationship between the variables. In this case, t is equal to the sum of r and 7 times the product of k and w.

Check for errors: Review your calculations and ensure there are no mistakes in your algebraic manipulations. Double-check your arithmetic operations and signs.

Seek assistance: If you're having difficulty solving the equation, consider reaching out for help. Consult a teacher, tutor, or someone knowledgeable in the subject matter. They can guide you through the problem-solving process and clarify any misunderstandings.

Practice and persistence: Continue practicing similar equations to improve your problem-solving skills. Persistence and practice are key to mastering mathematical concepts.

Remember, solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles. Keep practicing and seeking assistance, and you will improve your problem-solving abilities over time.

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Answer:

This algebraic problem can be solved by setting up a system of equations. For example, let x be the number of pounds of 3-inch nails that Toni buys, and y be the number of pounds of 2-inch nails that Toni buys. We know that x + y = 5 (since Toni believes a total of 5 pounds of pins) and that 0.99x + 1.39y = 6.15 (since that is the total cost of the nails). We can solve for one of the variables using one equation and then substitute that value into the other equation.

Solving for x in the first equation: x + y = 5

x = 5 - y

Substituting this into the second equation: 0.99(5 - y) + 1.39y = 6.15

4.95 - 0.99y + 1.39y = 6.15

4.95 = 0.4y + 6.15

-1.2 = 0.4y

y = -3

Since the number of pounds of nails cannot be harmful, we know that this solution is not possible. We can check by plugging in y = 3 (possible) into the first equation and seeing that x + 3 = 5, so x = 2.

Hence, Toni bought 2 lb of 3-inch nails and 3 lb of 2-inch nails.

Step-by-step explanation:

Answer: The scale factor is approximately 1.67

Step-by-step explanation:

30 × 1.67 = 50.1

50.1 ≈ 50

Incase you needed to know; y = 30 and x = 9

The sum of the series between the 16th and 25th term is 332.89

Given that

A(n) = 5(1.1)^n-1

To find the sum of the series A(n) = 5(1.1)^n-1 between the 16th and 25th term,

We first need to find the sum of the series up to the 15th term and up to the 25th term

In A(n) = 5(1.1)^n-1, we have

First term, a = 5

Common ratio, r = 1.1

So, the sum is

Sum = a(r^n - 1) / (r - 1)

S(15) = 5 * (1.1^15 - 1)/(1.1 - 1) = 158.86

S(25) = 5 * (1.1^25 - 1)/(1.1 - 1) = 491.75

Calculate the difference

Required sum = 491.75 - 158.86

Required sum = 332.89

Hence, the sum is 332.89

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The author would have sold  365396 books over the first 20 months.

The author sold 22000 books in the first month, and the sales declined by 7% each month.

This means that the number of books sold in each subsequent month is 93% of the number sold in the previous month (since 100% - 7% = 93%). Therefore, the number of books sold in the second month is:

0.93×22000

= 20460

The number of books sold in the third month is:

0.93 × 20460 = 19007

To find the total number of books sold over the first 20 months, we can use the formula for the sum of a geometric series:

S = a(1 - rⁿ) / (1 - r)

Substituting the values, we get:

S = 22000(1 - 0.93²⁰) / (1 - 0.93)

S = 22000(0.766)/0.07

S=240743

Therefore, the author would have sold 365396 books over the first 20 months.

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Answer:

trailing zeros can be ommited and have use in the real value, unless you are separating digits in a number

Step-by-step explanation:

trailing zeros can be ommited and have use in the real value, unless you are separating digits in a number

Answer:2500, 125000

Step-by-step explanation:

Multiply by 5

Answer:

there are 1 1/2 cups in 12 ounces

Step-by-step explanation:

The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

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

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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Answer:

136

Step-by-step explanation:

9*4=36+100=136

We start by rearranging the given differential equation into the standard form of a separable differential equation:

\(\frac{dh}{dt} = (\frac{-R}{v}) (\frac{h}{R+h})\)

=> \((\frac{v}{R+h)} \frac{dh}{h} = \frac{-R}{v} dt\)

Integrating both sides with respect to their respective variables, we get:

\(ln|h+R| - ln|R| = (\frac{-R}{v}) t + C\)

where C is the constant of integration. Simplifying, we have:

\(ln|h+R| = (\frac{-R}{v})t + ln|CR|\)

where CR is a positive constant obtained by combining R and the constant of integration.

Taking the exponential of both sides, we get:

\(|h+R| = e^{(\frac{-R}{v}) t} + ln|CR|)\)

=> \(|h+R| = e^{(\frac{-R}{v}) t} CR\)

We take cases for h+R being positive and negative:

Case 1: h+R > 0

Then we have:  \(|h+R| = e^{(\frac{-R}{v}) t} CR\)

\(h = (e^{(\frac{-R}{v}) t} CR) - R\)

Case 2: h+R < 0

Then we have:

\(|h+R| = e^{(\frac{-R}{v}) t} CR\)

=>\(h =- ((e^{(\frac{-R}{v}) t} CR)+R\)

Therefore, the general solution to the given differential equation is:

\(h(t)=e^{(\frac{-R}{v}) t} CR)-R\) if h+R > 0,

\(- (e^{\frac{-R}{v} }t ) CR)+R\)if h+R < 0}

where CR is a positive constant determined by the initial conditions.

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