A, B & C lie on a straight line.
D, B & E lie on a different straight line.
∠
CBE = 40°.
Work out the angle marked
x

The solution of the system using elimination method is x = 3 and y = 3

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

To solve this problem we must establish the equations according to the given data and solve the operations:

4x + 2y = 18       (1)

2x + 3y = 15      (2)

We have two equations with two unknowns, using the elimination method we have to multiply the (2) by -2 and we get:

-2*(2x + 3y) = 15

-4x - 6y = -30    

Now we solve the system:

4x  + 2y   = 18       (1)

-4x - 6y   = -30      (2)

0x   -4y   = -12

Clearing the variable:

-4y = -12

Multiply by (-1) we have:

4y = 12

y = 12/4

y = 3

Replacing the value of y in equation (1) we get the value of x:

4x + 2y = 18       (1)

4x +2*3 = 18

4x + 6 = 18

4x = 18-6

4x = 12

x = 12/4

x = 3

Both x and y are equal to 3 = (3 , 3)

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Correctly written question:

What is the solution of the system? Use the elimination method.

4x + 2y = 18

2x + 3y = 15

Answer:

A

Step-by-step explanation:

cause 4.am and 2.am so A

Answer:

(2,-1)

Step-by-step explanation:

Rewrite in vertex form

y = -1/4(x-2)^2-1

Answer:

Veinte para las dos

Step-by-step explanation:

twenty till 2

hope it helps!

Answer:

false

Step-by-step explanation:

The left side equals 0.01

The right side equals 0.4

The two sides are not equal. This is a false equation.

Answer:0.01=0.0001

Step-by-step explanation:

the remainder is - 1

when (x ³ - 7x + 5) is divided by (x + 3) the remindeer is f( -3 )

x + 3 = 0 => x = - 3

f(-3) = (-3)³ - 7(-3) + 5

= - 27 + 21 + 5

= - 1

1) General solution for second order differential equation, y" – 2y' + y = 0, is y = (c₁x + c₂)eˣ .

2) General solution for differential equation, 9y" + 6y' + y = 0, is y =(c₁x + c₂)e⁻³ˣ.

3) General solution for differential equation, 4y"- 4y'- 3y = 0, is y = c₁ e⁶ˣ+ c₂e⁻⁴ˣ.

4) General solution for differential equation, 4y" + 12y' +9y = 0, is y = (c₁x + c₂)e⁻⁶ˣ.

5) General solution for differential equation, y" – 2y' + 10y = 0, is y = eˣ (c₁cos(6x) + c₂sin(6x)).

6) General solution for differential equation, y" – 6y' +9y = 0 is y = (c₁x + c₂)e³ˣ.

7) General solution for differential equation, 4y" + 17y' + 4y = 0, is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) General solution for differential equation, 16y" + 24y' +9y = 0, is y = (c₁x + c₂)e⁻¹²ˣ.

9) General solution for differential equation, 25y" – 20y' + 4y = 0, is y = (c₁x + c₂)e¹⁰ˣ.

10) General solution for differential equation, 2y" + 2y' + y = 0, is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

General solution is also called complete solution and complete solution = complemantory function + particular Solution

Here right hand side is zero so particular solution is equals to zero. Therefore, evaluating the complementary function will be sufficient to determine the general solution to the differential equation.

1) y"-2y' + y = 0, --(1)

put D = d/dx, so (D² - 2D + 1)y =0

Auxiliary equation for (1) can be written as, m² - 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula,

\(m =\frac{-(- 2) ± \sqrt { 4 - 4}}{2}\)

=> m = 1 , 1

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)eˣ .

2) 9y" + 6y' + y = 0 or (9D² + 6D + 1)y =0 Auxiliary equation can be written as, 9m² + 6m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (6) ± \sqrt {36 - 4×4}}{2}\)

=> m = - 6/2

=> m = -3 , -3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻³ˣ.

3) 4y"- 4y'- 3y = 0

put D = d/dx, so (4D² - 4D - 3)y = 0

Auxiliary equation can be written as, 4m² - 4m - 3 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(-4) ± \sqrt {16 - 4×4×(-3)}}{2}\)

=> m = (4 ± 8)/2

=> m = -4 , 6

The roots of equation are real and equal. So, general solution is y = c₁ e⁶ˣ + c₂e⁻⁴ˣ.

4) 4y" + 12y' +9y = 0 or (4D² + 12D + 9)y= 0

Auxiliary equation can be written as, 4m² + 12m + 9= 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(12) ± \sqrt{144 - 4×4×9}}{2}\)

=> m = -12/2

=> m = -6 , -6

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻⁶ˣ.

5) y" – 2y' + 10y = 0 or (D² - 2D + 10)y = 0 Auxiliary equation can be written as, m² - 2m + 10 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-2) ± \sqrt {4 - 4×1×10}}{2}\)

=> m = (2 ± 6i)/2 ( since, √-1 = i)

=> m = 1 + 6i , 1-6i

The roots of equation are imaginary and unequal. So, general solution is y =eˣ (c₁cos(6x) + c₂sin(6x)).

6) y" – 6y' +9y = 0 or (D²- 6D + 9)y =0

Auxiliary equation can be written as, m² - 6m + 9 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-6) ± \sqrt {36 - 4×1×9}}{2}\)

=> m = 6/2 = 3,3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e³ˣ.

7) 4y" + 17y' + 4y = 0 or (4D²+ 17D + 4)y=0

Auxiliary equation can be written as, 4m² + 17m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{- (-17) ± \sqrt {16 - 4×4×17}}{2}\)

=> m = ( -17 ± 15)/2

=> m = (-17 + 15)/2, (- 17 - 15)/2= -1, -16

The roots of equation are real and unequal. So, general solution is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) 16y"+24y'+9y =0 or (16D²+ 24D + 9)y= 0

Auxiliary equation can be written as, 16m² + 24m + 9 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (24) ± \sqrt {576 - 4×9×16}}{2}\)

=> m = (-24 ± 0)/2

=> m = -12,-12

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻¹²ˣ.

9) 25y"- 20y' +4y =0 or (25D²-20D + 4)y = 0

Auxiliary equation can be written as, 25m²- 20m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (-20) ± \sqrt {400 - 4×4×25}}{2}\)

=> m = 20/2

=> m = 10 , 10

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e¹⁰ˣ.

10) 2y" + 2y' + y = 0 or (2D²+ 2D + 1)y =0

Auxiliary equation can be written as, 2m² + 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (2) ± \sqrt {4 - 4×1×2}}{2}\)

=> m = (- 2 ± 4i)/2 ( since, √-1 = i)

=> m = -1 + 2i , -1 - 2i

The roots of equation are imaginary and unequal. So, general solution is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)). Hence, required solution of differential equation is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

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The diagonal of a parallelogram bisects, so BE and DE are congruent, and AE is congruent with itself.

Assume that all four of it's angles at point E are 90°.

and Therefore, it is a congruence.

Triangles ABE and ADE are congruent through a side.

Therefore AB and AD are congruent.

Since opposite sides of a parallelogram are congruent, AD and BC are congruent and AB and CD are congruent.

Therefore all four sides are congruent. Therefore ABCD is a rhombus.

A parallelogram is a two-dimensional flat shape which is formed from two pairs of ribs and each of them is the same length and has two angles that are the same size in front of it.

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Answer:mutplion

Step-by-step explanation:

Answer:

$1,976.25

Step-by-step explanation:

Since one square foot cost $ 7.50 we simply multiply that by 263.5.

263.5 × 7.50= $1,976.25

We only need to use 7 bits to represent all the decimal integers from 0 to 100.

A computer uses bits as the fundamental unit of data. Bits are represented as a binary digit of either 0 or 1, and are the basic building blocks of digital communication and data processing.

The binary number system has only two digits, 0 and 1, making it easy to represent all kinds of data, including text, images, videos, and audio files. There are many benefits of using binary numbers to represent data, including their simplicity, speed, and reliability.

Each decimal integer from 0 to 100 can be represented in binary form. The minimum number of bits required to represent a decimal number depends on the maximum number of bits required to represent it in binary form.

The binary number system is a base-2 system, which means that there are only two possible digits, 0 and 1, that can be used to represent any number.

Therefore, to represent decimal integers from 0 to 100, a minimum of 7 bits per word are required, since 100 in binary form is 1100100, which requires 7 bits. However, since 2^7 = 128, which is greater than 100.

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Answer:

1043 correct me if im wrong

Answer:

54 degrees

Step-by-step explanation:

This is trigonometry. So we are given the adjacent leg and hypotenuse. So we can use cosine(cah from soh cah toa)

We will have to use the inverse of the trig ratios.

Remember!

cos^-1 is not 1/cos(that is sec)

cos^-1(27/46)

acos(27/46)

54.0586701 and so on

Round to nearest degree 54

Answer:

8^6

Step-by-step explanation:

Answer:

262144 (8^6)

Step-by-step explanation:

8^(12-6) = 8^6 = 262144

Answer:

A) only figure 1 and figure 2

Step-by-step explanation:

Answer: Choice A) only figure 1 and figure 2

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

Explanation:

Let's assume that figure 2 is similar to figure 3.

If this is the case, then the horizontal portions would divide to 30/15 = 2, showing that figure 3 has sides that are twice as long compared to figure 2. But then notice that the vertical sides divide to 36/24 = 1.5, which doesn't match with the previous result of 2.

Figures 2 and 3 cannot be similar for that reason.

Also, figures 1 and 3 are not similar either. Note the horizontal portions divide to 30/10 = 3 while the vertical portions divide to 36/16 = 2.25; the results 3 and 2.25 don't match.

We eliminate answers B, C and D. The only thing left is choice A.

-------------------

To verify choice A is true, we divide each corresponding piece like so

Each division leads to the same result of 1.5, meaning that figure 2's side lengths are 1.5 times longer than the corresponding side lengths of figure 1. So this confirms that figure 1 is similar to figure 2.

\( \frac{11}{16} = 0.6875\)

\(0.7\)

The formula used is \($N(t) = N_0 e^{rt}$\). If a new social network has 1000 users currently and at growth rate of 10% per month, it can be predicted that there will be approximately 2452 users in seven and a half months assuming similar exponential growth.

In the formula used in the spreadsheet model for measuring exponential growth i.e. \($N(t) = N_0 e^{rt}$\)

N(t) is the number of cases at time t

N₀ is the initial number of cases

e is the mathematical constant approximately equal to 2.71828

r is the growth rate (expressed as a decimal)

To adapt this formula to predict the number of users of a new social network, we can replace the variables with the appropriate values. For example, if the new social network has 1000 users currently and is growing at a rate of 10% per month, we can write:

N(t) = 1000 x \(e^{rt}$\)

To find the predicted number of users in seven and a half months, we can substitute t = 7.5 into the equation and solve for N(7.5):

N(7.5) = 1000 x \(e^{rt}$\)

N(7.5) ≈ 2452.22

Therefore, we would expect to have approximately 2452 users on the new social network in seven and a half months if it continues to experience similar exponential growth.

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The complete question is :

What is the formula used in the spreadsheet model discussed in this module for measuring exponential growth of an epidemic, and how can it be adapted to predict the number of users of a new social network at a future date assuming similar exponential growth? In particular, if the new social network has 1000 users currently and is growing at a rate of 10% per month, how many users would we expect to have in seven and a half months?

Given expression is:

Take 3 common from it:

So the factor are:

Salik and Maya are discussing a project that examines the relationship between the number of siblings someone has and their household income. Maya predicts that those with more siblings will have a higher household income. Salik questions whether the number of siblings is a categorical variable since it is a whole number. Our response can be : "In order to conduct this project, we need to choose two quantitative variables, which are variables that can be measured and expressed as numbers. The number of siblings is not a categorical variable because it is a continuous variable that can take on any whole number value."

The number of siblings is a quantitative variable because it can be expressed as a whole number. Household income is also a quantitative variable because it can be measured and expressed as a numerical value. Categorical variables are variables that can be divided into distinct categories or groups, such as gender, race, or occupation. The number of siblings is not a categorical variable because it is a continuous variable that can take on any whole number value.

To examine the relationship between the number of siblings and household income, Maya and Salik could use statistics to analyze their data. They could calculate descriptive statistics such as the mean and standard deviation for each variable, as well as the correlation coefficient to determine the strength and direction of the relationship between the two variables. They could also use probability theory to make predictions about the likelihood of certain outcomes, such as the probability that someone with more siblings will have a higher household income.

The complete question is:

Our classmates, Maya and Salik, are talking about the variables they want to study and how they plan to collect their samples. Here is part of their conversation. Respond in the places that say “your response.”

Double-check that both of their variables are quantitative.

Maya: I want to look at the relationship between the number of siblings someone has and the household income. I predict that those with more siblings have a higher household income.

Salik: We need two quantitative variables for this project. Wouldn’t number of siblings be categorical since it is whole numbers?

Your response:.........

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Answer:

43 dollar bills and 12 ten dollar bills

Step-by-step explanation:

let x = number of $1

y = number of $10

x + 10y = 163

x+y = 55

x = 55 - y

x + 10y = 163

(55-y) + 10y =163

55 - y + 10y = 163

9y = 163 - 55

9y = 108

y = 12

x = 55 - 12

x = 43

When deciding which area has better air quality between the two suburbs, it is more appropriate to use the median rather than the mean as a measure. This is because the populations of air quality in the suburbs are skewed.

Skewed distributions have extreme values that can significantly affect the mean. In this case, the suburb with hybrid cars and solar panels may have a few exceptionally clean air quality readings, while the other suburb with convenient bus routes and availability of Hummer dealerships may have a few extremely polluted air quality readings. These extreme values can pull the mean in one direction or another, potentially misrepresenting the overall air quality. The median, on the other hand, is less affected by extreme values and provides a more robust measure of the central tendency in skewed distributions. By comparing the medians of the two suburbs, the Lee family can make a more reliable assessment of which area has better air quality based on the majority of the data rather than being heavily influenced by outliers.

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Answer:

263

280

Step-by-step explanation:

280- 17= 263

263 tickets were the ones which were sold to other people apart from Daniel

So probability that he does not win is 263

280

A⁣⁣⁣⁣nswer i⁣⁣⁣s i⁣⁣⁣n a p⁣⁣⁣hoto. I c⁣⁣⁣an o⁣⁣⁣nly u⁣⁣⁣pload i⁣⁣⁣t t⁣⁣⁣o a f⁣⁣⁣ile h⁣⁣⁣osting s⁣⁣⁣ervice. l⁣⁣⁣ink b⁣⁣⁣elow!

bit.\(^{}\)ly/3a8Nt8n

Answer:

me

Step-by-step explanation:

becssu imthe best guy

Answer:

7.4

Step-by-step explanation:

The Department of Energy was also eager to sign on, in part because it wanted to learn about how radiation causes genetic mutations.

An modification in the nucleic acid sequence of an organism's, virus's, or extrachromosomal DNA is referred to as a mutation. DNA or RNA can be found in the viral genome.

Any alteration to a cell's DNA sequence. Mistakes in cell division can result in mutations, as can exposure to environmental DNA-damaging substances.

Ionizing radiation may harm genetic material (mutations) in gonads or germ cells, which can result in disorders with a genetic component (hereditary defects). Malformations, metabolic issues, immune system deficits, etc. might occur from them.

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Answer:

It is similar to a mountain in that it is dramatically higher than what is immediately around it. But mountains usually have a distinct apex or peak that is very small relative to the base and not typically level. Plateaus and mesas have tops only a little smaller than the base, and relatively flat. If the aspect ratio is less than 1, plateau. If greater than 1, mesa.

Step-by-step explanation:

The library is 8 kilometres away from Bree's residence.

1. The equation represents the total travel time of 2 hours.

2. Bree's speed on her way to the library is 6 mph, so the time taken for this part is x/6 hours.

3. Bree's speed on her way home is 12 mph, so the time taken for this part is x/12 hours.

4. Adding the time taken for both parts, we get the equation: x/6 + x/12 = 2.

5. This equation can be solved to find the value of x, which represents the distance from Bree's house to the library.

6. Simplifying the equation further, we have (2x + x)/12 = 2.

7. Combining like terms, we get 3x/12 = 2.

8. Multiplying both sides by 12, we have 3x = 24.

9. Dividing both sides by 3, we find that x = 8.

10. Therefore, the distance from Bree's house to the library is 8 miles.

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Answer:

his profit percentage is 84

Joseph's percentage gain (profit) is 18.9 %.

Given the following data:

To find the percentage gain (profit);

First of all, we would determine the cost price.

\(Cost \; price = Cost\; of \;software + Cost \;of\; laptop\\\\Cost \; price = 2600 + 26000\)

Cost price = Rs. 28600

\(Profit = Selling \; price - Cost \; price\\\\Profit = 34000 - 28600\)

Profit = Rs 5400

Next, we would solve for the percentage gain (profit) by using the mathematical expression;

\(Percent \;profit = \frac{Profit}{Cost\; profit}\) × \(100\)

\(Percent \;profit = \frac{5400}{28600}\) × \(100\)

\(Percent \;profit = 0.189\) × \(100\)

Percent profit = 18.9 %

Therefore, Joseph's percentage gain (profit) is 18.9 %.

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Answer: 88 square inches

Step-by-step explanation:

The condition that p(x)/q(x) is an integer for any number of inputs of integers x is satisfied by the integer polynomials p and q. It's not necessary for q(x) to split p(x).

In mathematics, a polynomial with integer values (also called a numerical polynomial) has an integer value for each integer n.

Contrary to popular belief, every polynomial with integer coefficients has integer values.

For instance, when t is an integer, the polynomial takes on integer values.

So, polynomials are the sums of terms of the form kˣⁿ, where k is any number and n is a positive integer.

A description of polynomials, such as the polynomial 3x+2x-5.

The concepts of degree, standard form, monomial, binomial, and trinomial are all covered in this section.

Therefore, the condition that p(x)/q(x) is an integer for any number of inputs of integers x is satisfied by the integer polynomials p and q. It's not necessary for q(x) to split p(x).

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