Witch is an equivalent expression to n3 and n6

In order to prove that △VWZ ~ △YXZ by SAS theorem we must have ∠VZW ≅ ∠YZX. Thus, option c is the most appropriate choice.

To prove that △VWZ ~ △YXZ by SAS theorem, we must prove that two sides of each triangle such that the angle between these sides is congruent are also congruent.

now △VWZ ~ △YXZ is to be proved, it implies that -

∠V ↔︎ ∠Y

∠W ↔︎ ∠X

∠Z ↔︎ ∠Z

thus  ∠VZW ≅ ∠YZX should be true.

hence, option c is correct and that automatically strikes out option d.

now the sides involving Z should also be congruent to prove that

△VWZ ~ △YXZ

thus, side WZ ≅ side XZ and side VZ ≅ side YZ

since we don't have such an option- options a and b are not the correct choices for this question.

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The complete question is -

In the diagram, VZ/YZ=WZ/XZ

To prove that VWZ~YXZ by the SAS similarity theorem, Which other sides or angles should be used?

a. WV and XY

b. WV and YZ

c. ∠VZW ≅ ∠YZX

d. ∠VWZ ≅ ∠YXZ

Answer:$15.25

Step-by-step explanation:just multiply $1.25x9 then add 4

The mean height for both groups put together is 161.75 cm

To find the mean height for both groups put together, we need to calculate the overall mean of all the heights. We can do this by finding the total height of all the men and women and then dividing the total number of people in the sample.

For the men, the mean height was 178 cm. There were 18 men in the sample, so the total height of all the men would be 178 cm x 18 = 3,204 cm.

For the women, the mean height was 152 cm. There were 30 women in the sample, so the total height of all the women would be 152 cm x 30 = 4,560 cm.

To find the total height of all the people in the sample, we can add the total height of the men and the total height of the women: 3,204 cm + 4,560 cm = 7,764 cm.

To find the mean height for both groups put together, we need to divide the total height by the total number of people in the sample. In this case, there were 18 men + 30 women = 48 people in the sample. So, the mean height for both groups put together would be 7,764 cm ÷ 48 = 161.75 cm.

Therefore, the mean height for both groups together is 161.75 cm.

It's important to note that this calculation assumes that the samples are representative of the larger population and that the samples were selected randomly. Additionally, the sample size is relatively small, so the results may not be entirely accurate or representative. However, the calculation gives us a rough estimate of the mean height for both groups put together.

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Government can help reduce greenhouse gas emissions by addressing market failures. These taxes internalize the external costs associated with emissions, providing economic incentives for polluters.

When greenhouse gas emissions occur, they often impose external costs on society in the form of environmental damage and climate change. However, in a free market, these costs are not taken into account by polluters, resulting in an overproduction of emissions, which is a market failure.

To address this market failure, government intervention in the form of permissible taxes can be implemented. These taxes are designed to reflect the external costs associated with emissions. By levying taxes on polluters based on the quantity of emissions they produce, the government internalizes the external costs and creates economic incentives for polluters to reduce their emissions.

The economic diagram illustrating this intervention would show the supply and demand curves for the good or service that generates emissions. Initially, the supply curve would not account for the external costs, resulting in a market equilibrium that leads to excessive emissions.

With the introduction of permissible taxes, the supply curve would shift upward, reflecting the additional costs imposed by emissions. This shift would increase the price of the good or service, reducing the quantity demanded and incentivizing producers to find cleaner and more efficient production methods.

The new equilibrium would result in a lower level of emissions and a more efficient allocation of resources. Overall, permissible taxes help internalize the external costs of emissions, encouraging polluters to reduce their emissions and mitigating the negative environmental impacts.

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Answer: 5.1

Step-by-step explanation: 5 . 1 easy

The base-ten positional numeral system, sometimes known as the decimal numeral system, is typically used to represent both integer and non-integer numbers and 5 over 1 can be written as 5/1 = 5.

The usual system for designating both integer and non-integer numbers is the decimal numeral system, commonly known as the base-ten positional numeral system.

It is the expansion of the Hindu-Arabic numeral system to non-integer values.

Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal numeral refers broadly to the notation of a number in the decimal numeral system (also frequently merely called a decimal or, less accurately, a decimal number).

So, we have:

5 over 1 which can be written as,

= 5/1

= 5

Therefore, the base-ten positional numeral system, sometimes known as the decimal numeral system, is typically used to represent both integer and non-integer numbers and 5 over 1 can be written as 5/1 = 5.

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Answer:

4/7

Step-by-step explanation:

Distance remaining at the end of Saturday's trip = 1 - 2/7

= 7/7 - 2/7 = 5/7

Fraction travelled on Sunday = 5/7 x 4/5 = 4/7

Answer:

The slope is the same as -5 so its B

Step-by-step explanation:

The only difference is the y intercept but the slope has to be the same for it to  increase the same rate as its parallel line. Though it's parallel it cannot start from 3 (in-5x+3) but it can start from 4, 5, or 6, or any number

Answer:

-x+3=-2.

we switch the places to change the signs and put x as positive.

so it will be written as 3+2=x.

then we simply solve it and :

5=x

Answer:

x=5

Step-by-step explanation:

1) -x=-3 -2

2) -x=-5

5) x=5 (the minus goes away as it is in both sides)

The requried solution of the given equation is x =2 and y = 3.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,

Given equation,

-x + 6y = 16  - - - - - - (1)
8x -6y = -2   - - - - - - -(2)

Adding equation 1 and 2,
8x - x + 6y - 6y = 16 -2
7x = 14
x = 2

Now,
-2 + 6y = 16
y = 3

Thus, the requried solution of the given equation is x =2 and y = 3.

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The principal sum refers to the amount payable in one sum in the case of accidental death and, in some cases, accidental dismemberment.

The amount paid in the case of accident or medical insurance in the event that the insured person dies, loses a limb, or loses sight is known to be as principal sum. It means that the principal sum amount is the maximum amount paid to the insured person for all injuries resulting from the accident.

Thus, the principal sum is the amount insured to be paid by the company to the beneficiary in the case of the insured individual's accidental death as well as in the loss of limb or sight.

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The best recommendation for the polling firm to follow in the future would be to sample people who have cell phones, in addition to those with landlines.

This approach would help in increasing the diversity of the sample, as relying solely on landline telephones may lead to underrepresentation of certain demographics, such as younger voters who are more likely to use cell phones instead of landlines.

By including both landline and cell phone users, the firm would be able to gather a more accurate and representative sample of the population, which would result in better predictions for the election outcomes.

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Answer:

m=4 and c=-1

Step-by-step explanation:

I'm assuming that m is the slope and c is the y-intercept. (If this is not the case, please tell me and I'll fix my answer).

The equation is already in the form y=mx+c so you just take the numbers from the problem y=4x-1.

Answer:

m = 4    c=-1

Step-by-step explanation:

The slope form is y = mx + b.

M is the slope which is 4.

B is the y=intercept which is -1.

Answer:

60 :)

Step-by-step explanation:

The middle two numbers are 59 and 61 so you add them together and divide by 2.

Answer:

the answer is 50, trust me!

Step-by-step explanation:

The measure of AU is 50.

An arc is a part of a curve that is a continuous portion of the circumference of a circle or an ellipse. It is defined by two endpoints and the arc itself, which is the curved section between the endpoints.

Given:

arc QU = 88 and <QUA = 111

So, QDA = 2 <QUA

        = 2 X 111

        = 222

Now, QUA = 360- 222 = 138

and, arc AU = QUA - arc QU

           = 138- 58

           = 50

Hence, the measure of AU is 50.

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

yes

Step-by-step explanation:

you plug in (2,8) so 8 = y and 2=x.

so 8=4(2) 8=8 which is correct

then 8= 2+6 8=8 which is correct

Answer:

C because its the only one that fits the question its asking. 12-6 8-4 4-2

Step-by-step explanation:

9514 1404 393

Answer:

  ∠A = 66.2°

Step-by-step explanation:

The sum of exterior angles of any polygon is 360°, so you have ...

  (3x +10)° +(5x)° +(2x +4)° = 360°

  10x +14 = 360 . . . . . . . . . . . . . . .collect terms, divide by °

  x + 1.4 = 36 . . . . . . . . . divide by 10

  x = 34.6

The interior angle at A is the supplement of the exterior angle there:

  ∠A = 180° -(3x +10)° = 180° -(3(34.6) +10)°

  ∠A = 66.2°

Answer:

1. Given

2. Distributive Prop

3. Addition Prop

4. Division Prop

Step-by-step explanation:

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:52x18=936$

Step-by-step explanation:

have a total of 52 weeks in a year, save $18 each week, multiply $18 by the number of weeks in a year and then you get the answer

The results will not represent the true ability of the students at school because the sample size of students is not representative. Also, the administrators are allowed to choose who gets to take the exam, which may lead to bias in the selection of students. There are several forms of bias that can occur when a sample is not representative, including sampling bias, response bias, and measurement bias.

In this scenario, sampling bias is the most likely form of bias that could occur. This is because the administrators are allowed to choose who gets to take the exam, which means they have control over the sample size and the selection of students. This means that the sample of students may not be representative of the entire student population, and the results may be biased towards the abilities of the students who were selected to take the exam. Therefore, it is important to have a sample of students that is representative of the entire student population to ensure that the results are accurate and unbiased. This can be achieved by selecting students randomly from the entire student population, rather than allowing administrators to choose who gets to take the exam.

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Answer:

\(x + 0.05x = 15\), solution is $14.29

Step-by-step explanation:

We can create an equation for this scenario to try and solve it.

Assuming the cost of the CD is x, it’s sale tax will be 0.05x (as that is 5% of x, 0.05.)

We can write the equation in two ways:

\(x + 0.05x = 15\) or \(1.05x = 15\).

Assuming we take the second one (easier to work with), we can divide both sides by 1.05. The equation simplifies to x = 14.289... which rounds to x = 14.29.

Therefore, the equation is \(x + 0.05x = 15\) and the solution is $14.29.

Hope this helped!

Answer:

x + 0.05x = 15; x = $14.29

Step-by-step explanation:

Answer:

D) 2

The average rate of change of f(x)

A(x) =2

Step-by-step explanation:

Step(i):-

Given that the function f(x) = x² - 3x -10

Given x =a = -5   and y = b = 10

The average rate of change of f(x)

\(A(x) = \frac{f(b)-f(a)}{b-a}\)

Step(ii):-

f(x) = x² - 3x -10

f(-5) = (-5)² - 3(-5) -10 = 25+15-10=30

f(10) = (10)² -3(10)-10 = 100 -30 -10 =60

The average rate of change of f(x)

\(A(x) = \frac{f(b)-f(a)}{b-a}\)

\(A(x) = \frac{60-30}{10-(-5)}= \frac{30}{15} = 2\)

A(x) =2

Answer:

D.

tangent = opp over adj

Step-by-step explanation:

The height to which the hollow sphere rolls up the incline is the same as the height to which the hollow cylinder rolls up, which is 1.0 m in this case.

To determine the height to which the hollow sphere rolls up the incline, we can use the principle of conservation of energy. The initial kinetic energy of both the hollow cylinder and hollow sphere is the same since they have the same mass and initial velocity. This kinetic energy is converted into potential energy as they roll up the incline. The potential energy gained by an object of mass m and height h is given by the formula:

PE = mgh

Since both the hollow cylinder and hollow sphere have the same mass, we can compare their potential energies. Let's assume the potential energy gained by the hollow cylinder is PE_cylinder and the potential energy gained by the hollow sphere is PE_sphere.

PE_cylinder = mgh_cylinder  ... (1)

PE_sphere = mgh_sphere  ... (2)

Since the initial velocity and mass are the same for both objects, we can equate their potential energies:

PE_cylinder = PE_sphere

mgh_cylinder = mgh_sphere

h_cylinder = h_sphere

Therefore, the height to which the hollow sphere rolls up the incline is the same as the height to which the hollow cylinder rolls up, which is 1.0 m in this case.

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Answer:

17.5 - A

8.1 B

C 10

D 12

Step-by-step explanation:

the thingy you use to plug numbers in for circumference is 2πr

and to find radius from circumference you can just divide by 2 and then divide by π

Answer:

I'll do all four, just for fun (I'll use 22/7 for pi on A and B, 3.14 on C & D)

A: 17.6

B: 81.8

C: 18

D: 24

Step-by-step explanation:

A.

\(\frac{56}{10}*\frac{22}{7}\\\frac{28}{5}*\frac{22}{7} \\\frac{616}{35}=\frac{88}{5}=17.6\)

B.

\(\frac{26*22}{7}=\frac{972}{7}=40\frac{6}{7} approx. = 40.9 * 2 = approx 81.8\)

C.

\(\frac{5650}{314}=\frac{2825}{157}=17\frac{156}{157} approx. = 18\)

D.

\(\frac{7540}{314}=\frac{3770}{157}=24\frac{2}{157} approx. = 24\)

All of the factors listed in options a, b, c, and d are important in determining whether an individual is required to file an income tax return, except for option e, which states that none of the choices are correct.

When determining whether an individual is required to file an income tax return, several factors come into play. The first factor, option a, is the taxpayer's gross income. The Internal Revenue Service (IRS) sets specific income thresholds, and if an individual's gross income exceeds those thresholds, they are generally required to file a tax return.

The second factor, option b, is the taxpayer's filing status. Different filing statuses, such as single, married filing jointly, or head of household, have different income thresholds for filing requirements. Therefore, a taxpayer's filing status is an important consideration in determining whether they need to file a tax return.

The third factor, option c, is the taxpayer's total itemized deductions. Itemized deductions can reduce a taxpayer's taxable income, and if these deductions are substantial, it may affect the requirement to file a tax return.

The fourth factor, option d, is the availability of the additional standard deduction for taxpayers

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Equation of the tangent line at x = 3 is y = (3/2√10)x – (9/2√10) + 4.

We first need to find the derivative of y(x):

y(x) = √(6x – 2)
y'(x) = (1/2)(6x – 2)⁻¹/²(6)

At x = 3, the slope of the tangent line is:

y'(3) = (1/2)(6(3) – 2)⁻¹/²(6) = 3/2√10

To find the equation of the tangent line at x = 3, we can use the point-slope form of a line:

y – y1 = m(x – x1)

Where m is the slope we just found, and (x1, y1) is the point (3, y(3)). Puting in the values, we get:

y – y(3) = (3/2√10)(x – 3)

Simplifying, we get the equation of the tangent line at x = 3:

y = (3/2√10)(x – 3) + √16 = (3/2√10)x – (9/2√10) + 4

So the equation of the tangent line at x = 3 is y = (3/2√10)x – (9/2√10) + 4.

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