What will be congruence criterion

Considering the expression of a line,  the equation of the line passing through the points (-3,11) and (1,-1) is y=-3x +2.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope and the value of one of the points, the value of the ordinate to the origin can be obtained.

In this case, being (x₁, y₁)= (-3, 11) and (x₂, y₂)= (1, -1), the slope can be calculated as:

m= (-1 - 11)÷ (1 - (-3))

m= (-1 - 11)÷ (1 + 3)

m= (-12)÷ 4

m= -3

Considering point 2 and the slope, you obtain:

-1= (-3)×1 + b

-1= -3 + b

-1 +3= b

2= b

Finally, the equation of the line is y=-3x +2.

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In this situation, y varies directly with x since the constant of variation, k, is 1.6 and can be represented by the equation, y = 1.6x.

The constant of variation refers to the ratio or unit rate (slope) between two variables in a direct variation.

In an inverse variation, the constant of variation is the product of the two variables of interest.

In this situation, the constant of variation is the quotient of the division operation between y and x.

x        y     Ratio

4      6.4    1.6 (6.4/4)

7.     11.2    1.6 (11.2/7)

10    16      1.6 (16/10)

13.  20.8   1.6 (20.8)

Thus, as y increases, x directly increases at a constant rate of 1.6.

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The percentages are given as follows:

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 20300, \sigma = 60[/tex]

The proportion of 20,240 of fewer is the p-value of Z when X = 20240, hence:

Z = (20240 - 20300)/60

Z = -1

Z = -1 has a p-value of 0.1587.

The proportion of 20,420 of fewer is the p-value of Z when X = 20420, hence:

Z = (20420 - 20300)/60

Z = 2

Z = 2 has a p-value of 0.9772.

The proportion of 20480 or more is one subtracted by the p-value of Z when X = 20480, hence:

Z = (20480 - 20300)/60

Z = 3

Z = 3 has a p-value of 0.9987.

1 - 0.9987 = 0.0013.

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The solution to the inequality 0 ≤ u² - 2u + 5 is all real numbers.

The solution of the inequality is calculated by applying the following method as shown below.

−u² ≤ −2u + 5

0 ≤ u² - 2u + 5

Now, to find the zeros of this quadratic equation, we can use the quadratic formula:

u = (-b ± √(b² - 4ac)) / 2a

where;

a = 1,

b = -2, and

c = 5.

u = (2 ± √(2² - (4 x 1 x 5)) / (2 x 1 )

u = (2 ± √(-16)) / 2

Since the square root of a negative number is not defined in real numbers, this means that the quadratic equation has no real zeros.

But we can still find the solution to the inequality by using the fact that a parabolic function y = ax² + bx + c is greater than or equal to 0 when it has x-intercepts that are both real and positive.

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Answer:

Question 1:

Diameter: 10

radius: 5

circumference: 15.70796

Area: 78.53981

Question 2:

98 Gallons of paint

Step-by-step explanation:

Question 1:

Diameter: 10

radius: 5

circumference: 2π x 5

                        = 15.70796

Area: π x [tex]5^{2}[/tex]

       = 78.53981

Question 2:

To find the radius of the sphere: r=(3V4π)⅓

                                                         =(3·66844·π)⅓

                                                         ≈11.68555

To find the surface area of the sphere: A=4πr2

                                                                      =4·π·11.692

                                                                      ≈1715.96403                      

Since surface area is 1715.96403 and each gallon of paint can cover 350 square feet the number of gallons of paint needed to paint the water tower is:

                          1715.96403÷35x2

                         =98 gallons of paint is needed to paint the entire water tower twice

Answer: x = 666

Step-by-step explanation:

solve for the area while doing pi squared and then solve it with the hypotenuse of the area

Graph H is a simple undirected graph, meaning that it has no self-loops or multiple edges between the same pair of vertices. The vertex set is {v1, v2, v3, v4, v5}. The edge set is {e1, e2, e3, e4}.

To draw the graph, we start by placing the vertices on a plane and then connecting them with edges according to the edge-endpoint function.

For example:

Note that v4 and v5 are not included in the edge-endpoint function and are not part of the graph.

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Complete Question:

Graph H has a vertex set {v1, v2, v3, v4, v5}, edge set {e1, e2, e3, e4} and edge-endpoint function: Edge Endpoints e1 {v1} e2 {v2, v3} e3 {v2, v3} e4 {v1, v3} Draw the graph.

Answer:

eefawdfa

Step-by-step explanation:

to do cool u do cool 69696969

Answer:

yes, it is a funtion

Step-by-step explanation:

we can rewrite the equation as,

y = 14/5 - 7x/5

there us only one value of y for every real no of x

The relation 7x = 14 - 5y is a function.

To determine whether the relation 7x = 14 - 5y represents a function, we need to check if each value of x corresponds to a unique value of y.

First, let's isolate y in terms of x:

7x = 14 - 5y

Subtract 14 from both sides:

7x - 14 = -5y

Divide by -5:

(7x - 14) / -5 = y

Simplifying further:

y = (-7x + 14) / 5

Since we have found a formula for y in terms of x, this relation represents a function.

For each value of x, there is a unique corresponding value of y based on the equation y = (-7x + 14) / 5.

Therefore, the relation 7x = 14 - 5y is a function.

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Answer:

Step-by-step explanation:

Perimeter:

2(9x) + 2(2x + 7)

18x + 4x + 14 = 22x + 14

Area:

9x(2x + 7)

18x^2 + 63x

9x(2x + 7)

Answer:

I believe it is about 3

Step-by-step explanation:

Go to y=2 then move across until you hit the line.

From 2000 to 2015, total spending on personal consumption increased by 77.5%, while health care spending increased by 129.9%.

a. The approximate annual per capita spending on personal consumption in 2015 was $38,218. This figure was calculated by dividing the estimated total personal consumption expenditure of $12.3 trillion by the population of 321 million.

b. The approximate daily per capita spending on personal consumption in 2015 was $104.89. This figure was calculated by dividing the approximate annual per capita spending of $38,218 by 365 days.

c. Services accounted for approximately 67.2% of personal consumption spending in 2015. This figure was calculated by dividing the estimated total spending on services of $8.3 trillion by the total personal consumption expenditure of $12.3 trillion. This figure is consistent with my own spending, as the majority of my expenditure is devoted to services such as transportation, food delivery, and entertainment.

d. Health care accounted for approximately 17.1% of all personal consumption spending in 2015. This figure was calculated by dividing the estimated total spending on health care of $2.1 trillion by the total personal consumption expenditure of $12.3 trillion.

e. The percentage increase in total spending between 2000 and 2015 was 77.5%, while the percentage increase in health care spending between 2000 and 2015 was 129.9%. This was calculated by first subtracting the total spending on personal consumption in 2000 of $6.8 trillion from the total spending on personal consumption in 2015 of $12.3 trillion, and then dividing the result by the total spending in 2000. This was done for both total spending and health care spending, and the results were then multiplied by 100 to get the percentage increase.

From 2000 to 2015, total spending on personal consumption increased by 77.5%, while health care spending increased by 129.9%.

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first off let's find the slope of M

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{(-2)}}} \implies \cfrac{1 +8}{1 +2} \implies \cfrac{ 9 }{ 3 } \implies \text{\LARGE 3}[/tex]

now, any line that intersects M will have a different slope than M, and since they're both lines and going to infinity, they will intersect at some point, so let's check those points for their slope, who is different than M's

[tex]\boxed{A}\qquad (\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{ 3 }{ 1 } \implies 3 ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{B}\qquad (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{14}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{14 +1}{3 +2} \implies \cfrac{ 15 }{ 5 } \implies 3 ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{C}\qquad (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-20}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-20}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{2}}} \implies \cfrac{ -21 }{ -7 } \implies 3 ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{D}\qquad (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-3)}}} \implies \cfrac{6 +2}{2 +3} \implies \cfrac{ 8 }{ 5 } ~~ \textit{\LARGE \checkmark}[/tex]

For the given transactions, the general journal, T accounts, and trial balance is attached.

In the given case, it is required to record all transactions using the general journal, post them into corresponding T accounts. After posting all transactions, ending balances are calculated. The ending balances are used to create a Trial Balance.

The general journal is a book of original entries where the raw business transactions is recorded according to the date events occur. It is the first place where data is recorded . The general journal for the provided data is attached (figure 1).

Each transaction from the journal to corresponding T-accounts and their ending balances are calculated by subtracting credits from debits for accounts with debit balance and subtracting debits from credits for account with credit balance. A T-account is an informal term which is used for a set of financial records that use double-entry bookkeeping.  It is a graphical representation of a general ledger where business’ transactions are recorded. It consists of the an account title at the top, a debit side on the left, and a credit side on the right. It is called a T-account because the bookkeeping entries are laid out in a way that resembles a T-shape. The T-account for the given data is attached (figure 2 and 3).

Trial balance is prepared by entering corresponding ending balances from T accounts and calculating the sums of debit and credit. A trial balance refers to a bookkeeping worksheet where the balances of all ledgers are compiled into debit and credit account column totals that are equal. The general purpose is to ensure that the entries in a company’s bookkeeping system are mathematically correct. The trial balance for the given data is attached (figure 4).

Note: The question is incomplete. The complete question probably is: Boilermaker House Painting Company incurs the following transactions for September. Record each transaction. Boilermaker uses the following accounts: Cash, Accounts Receivable, Supplies, Equipment, Accounts Payable, Deferred Revenue, Common Stock, Retained Earnings, Service Revenue, Salaries Expense, Advertising Expense, and Rent Expense. 2. Post each transaction to T-accounts and compute the ending balance of each account. 3. After calculating the ending balance of each account, prepare a trial balance.

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The function f(t) can be represented as f(t) = a + bt, where a and b are constants that depend on the initial position and velocity of the particles.

In this function, a represents the initial distance from the wall when t = 0 and b represents the rate of change of the distance from the wall over time. The value of a and b can be determined from the initial conditions and the velocity of the particles.

The function f(t) is a linear function that models the combined distance of the particles from the wall as a function of time. As t increases, the value of f(t) increases linearly with a slope of b, representing the increase in distance from the wall over time.

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Note that in the problem above, CL is 9m. This is resolved using the theorem of the Angle Bisector.

The angle bisector theorem in geometry is concerned with the relative lengths of the two segments of a triangle's side that are separated by a line that bisects the opposing angle. It compares their lengths to the lengths of the other two sides of the triangle.

In geometry, the angle bisector is the ray, line, or segment that splits a given angle into two equal places.

Thus, given that, in ∆ABC, m∠C= 90° AL is an angle bisector m∠ABC = 30°, LB = 18 m,

CL is derived using the SOH principle; that is: Sine of the Angle = Opposite /Hypothenus

Sin 30° = CL/BL
⇒ 1/2 = CL/18

⇒ CL=9 m

Thus, the measure of CL is 9 m. See the attached image.

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Answer:

(-7, 8)

Step-by-step explanation:

Hope it helps! =D

Answer:

y≤-3x-6

Explaination:

First you distribute the -3 to the x and -6.

So you would then have y-6≤-3x-12.

Then you would add 6 to each side.

After doing this you will have y≤-3x-12+6.

Then you combine like terms which are -12 and 6 to get -6. Then you are left with your final answer of y≤-3x-6.

I hope this helped :) (I believe I did it correctly based off of my knowlege)

The procedure used to show the converse of the Pythagorean Theorem is given as follows:

D. Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The five foot side will fit to form a right triangle.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

Hence:

h² = 3² + 4²

h² = 25

h = 5.

The hypotenuse has the larger side length, hence the sides that are connected by the right triangle must be the two smaller sides, the three foot side and the four foot side, hence option D is correct.

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If the doctor tells Mr. Hyper Chonder that he is fit for travel, he will travel and expect 28 utils, and if the doctor tells him that he is unfit for travel, he will not travel and expect 24 utils.

Mr. Hyper Chonder expects to receive a "Fit for Travel" evaluation with a probability of P(Fit) = 0.25 and an "Unfit for Travel" evaluation with a probability of P(Unfit) = 0.75. He believes that if the doctor finds that he will stay healthy, there is a P(Fit Healthy) = 0.8 chance of being evaluated as fit to travel and a P(Unfit Healthy) = 0.2 chance of being evaluated as unfit to travel. If the doctor finds that he will become sick, there is a P(Fit | Sick) = 0.4 chance of being evaluated as fit to travel and a P(Unfit | Sick) = 0.6 chance of being evaluated as unfit to travel.

If the doctor tells Mr. Hyper Chonder that he is fit for travel, he assigns a probability of P(Healthy | Fit) = 0.8 to staying healthy. If the doctor tells him that he is unfit for travel, he assigns a probability of P(Healthy | Unfit) = 0.2 to staying healthy and a probability of P(Sick | Unfit) = 0.8 to getting sick.

If the doctor tells Mr. Hyper Chonder that he is fit for travel, he will travel and expect a utility of 28 utils. If the doctor tells him that he is unfit for travel, he will not travel and expect a utility of 24 utils.

If the doctor tells Mr. Hyper Chonder that he is fit for travel, he will travel and expect 28 utils, and if the doctor tells him that he is unfit for travel, he will not travel and expect 24 utils.

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The vertices of triangle DEF after dilation are D'(4, -M), E'(-2, M) and F'(-2, -M)

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given a triangle DEF which is being dilated by a dilation factor of (2,M) we need to find the vertices of the image,

The vertices before dilation are D(2, -1), E(-1, 1) and F(-1, -1)

Since, the dilation factor is (2,M), so the new vertices are,

D'(2×2, -1×M)

D'(4, -M)

E'(-1×2, 1×M)

E'(-2, M)

F'(-1×2, -1×M)

F'(-2, -M)

Hence, the vertices of triangle DEF after dilation are D'(4, -M), E'(-2, M) and F'(-2, -M)

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D is zero

Answer:12d-18

Step-by-step explanation:

The solution to the given fraction 2 3/8 x 5 3/4 is 13 21/32

A fraction is a number which has a numerator and a denominator. A numerator is the top or upper value while a denominator is the bottom or lower value.

2 3/8 x 5 3/4

= 19/8 × 23/4

Multiply numerator and denominator respectively

= (19 × 23) / (8 × 4)

= 437 / 32

= 13 21/32

Therefore, 13 21/32 is the solution to the fraction.

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A statement which best describes a graph of paired points that form a proportional relationship include the following: F. a straight line can be drawn through all the points, and the line passes through the point, begin ordered pair 0 comma 0 end ordered pair.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Generally speaking, the graph of any proportional relationship such as the linear equation is characterized by a straight line that passes through all the points and the origin, which is denoted by the ordered pair (0, 0).

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This triangle is similar by the rule of (d)SAS.

When applying a scale factor, similar shapes are enlarged versions of one another. All of the corresponding angles and lengths in related shapes are equal and in the same ratio.

We divide the length of the enlarged shape by the length of the original shape to calculate the length scale factor.

In this given diagram, there are two triangle ΔRST and ΔRUV

where, RS/SU = RT/RV

and ∠SRT = ∠URV

So ΔRST ~ ΔRUV by the rule of SAS

So that option (d) is correct answer.

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B) About 90% of the confidence intervals will contain μ

The 90% confidence interval is a range of values that is constructed from a sample of data that has a 90% probability of containing the true population mean, μ. To calculate the 90% confidence interval from a sample, we use the formula:

[tex]CI = X ± z* (σ/√n)[/tex]

Where X is the sample mean, z is the z-score corresponding to a 90% confidence level, σ is the population standard deviation, and n is the sample size.

In this case, 110 students each selected a sample of 35 quiz scores from a population of 5000. So the sample size is n = 35. Assuming the population standard deviation is known, then we can use the formula to calculate the 90% confidence interval for each student. We expect that around 90% of the confidence intervals will contain μ, the true population mean.

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Answer:Multiply 3 times twelve and add one. You will get 37 inches tall. He needs to be 42 inches tall. subtract 42 - 37 and you will get 5. William needs to be five inches taller.

Step-by-step explanation:

An addition inequality to find the how much taller William to ride the coaster is, Height of William + x ≥ 42.

Inequality can be defined relation that compares two numbers or other mathematical expressions in an unequal way.

We are Given, Riders should be at least 42 inches tall to ride the coaster, and 'x' be the variable representing how much taller William should be.

Therefore,

The inequality which may be used to calculate how much taller William has to be in order to ride the coaster.

Height of William + x ≥ 42

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Total cost of Airline per month = 3,900,000$. Total revenue of airline per month = $ 90,000. The break even point= 55.56. Rise in flight to make end meet = 222.24%

The growth rate formula is the ratio of the increased value to the original value multiplied by 100, expressed as a percentage. As the value of something increases, the percentage of the value increases. 

A. To calculate your total cost per month, you need to find the sum of your fixed and variable costs. The fixed cost is $100,000 per day and the variable cost is $2,000 per flight per day. So the formula for total cost per month is:

$100,000 * 30 + $2,000 * 15 * 30 = $3,000,000 + $900,000 = $3,900,000

B. To calculate your total revenue per month, multiply your average revenue per flight ($200) by the average number of flights per day (15), then multiply by the number of days in a month (30) is needed. So the formula for total sales per month is:

$200 * 15 * 30 = $90,000

C. To calculate your break-even point, you must determine the number of flights required per day so that your total revenue equals your total cost. We can formulate an equation for this:

$200 * x = $100,000 + $2,000 * x

200x = 100,000 + 2,000x

-1,800x = -100,000

x = 55.56 (rounded to two decimal places)

Therefore, the breakeven point is 55.56 flights per day.

D. To find the percentage of Rise's total flight capacity that needs to be in the air each day to break even, divide the number of flights required to reach breakeven into the maximum number of flights you can fly in a day. You need to divide by the number of times (25). . This can be expressed as:

55.56/25 = 2.2224

2.2224 * 100 = 222.24D

44 Therefore, about 222.24% of Rise's total flight capacity needs to be in the air that day to make ends meet.

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The solution of the given equation is (-11, 4). the graph is attached below.

Simultaneous equations, a system of equations are Two or more equations in algebra that must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation x + 3y = 1 and  -3 - 3y = -15

Before solving it with a graph we need to simplify the equation:

From equation 1

=> -3 - 3y = -15

=> -3y = -12

=> y = 4

From substitution in equation 1

x = -11

therefore, The solution of the given equation is (-11, 4).

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