Subtracting the same number from each side of an equation always gives an equivalent equation. true false (b) multiplying each side of an equation by the same non-zero number always gives an equivalent equation. true false (c) squaring each side of an equation always gives an equivalent equation. true false

Answer:

The answer is 18x^2 - 33x + 12.

Step-by-step explanation:

Use the FOIL method: first, outer, inner, and last.

(6x - 3)(3x - 4)

6x • 3x = 18x^2

6x • (-4) = -24x

(-3) • 3x = -9x

(-3)(-4) = 12

= 18x^2 - 24x - 9x + 12

= 18x^2 - 33x + 12

Answer:

-2x^2 -5x -3

Step-by-step explanation:

(3x^2 – 3x + 6) – (5x^2 + 2x + 9)

Distribute the minus sign

(3x^2 – 3x + 6) – 5x^2 - 2x - 9

Combine like terms

3x^2   – 5x^2 - 2x– 3x - 9+ 6

-2x^2 -5x -3

Answer:

Step-by-step explanation:

To solve this problem you have to complete the square. To do that, set the quadratic equal to 0, then move the constant over to the other side. That's 2 steps in one, but they're simple ones:

\(-5t^2+10t=-65\)

The first picky rule that completing the square has to follow is that the coefficient on the squared term has to be a 1. Ours is a -5, so we factor it out:

\(-5(t^2-2t)=-65\) . Now it gets even pickier. To create a perfect square binomial on the left, we take half the linear term, square it, and add it in to both sides. Our linear term is a -2. Half of -2 is -1, and -1 squared is 1, so we add 1 into the set of parenthesis. BUT the -5 out front is a multiplier and refuses to be ignored. To offset the addition of the 1 inside the parenthesis, we have to multiply it by the -5 out front to get -5:

\(-5(t^2-2t+1)=-65-5\)

The perfect square binomial on the left side and simplifying the right:

\(-5(t-1)^2=-70\) . Now we'll move the 70 over and set the quadratic back equal to y:

\(-5(t-1)^2+70=y\)

That's the quadratic in vertex form. The vertex here is (1, 70) which serves to answer 2 questions for us: the max height of the ball along with the time it was at that max height. For us, the ball reached a max height of 70 m after 1 second in its travels.

You could also do it the "calculus way" which is to find the derivative of the position function, which is

-10t + 10 = 0 and solve for t:

-10t = -10 so

t = 1. That's the time that the ball is at its highest point, and to find the highest point, sub that value in for t in the position function:

\(h(t)=-5(1)+10(1)+65\) which comes to 70 m. I'm not sure what class you're taking so I did both! Calculus is way easier.

The initial value problems can be solved using the method of Laplace transforms. For problem 1, the solution is y(t) =\(e^t(cos(2t) + 3sin(2t))\). For problem 3, the solution is y(t) = \(e^(-3t)\)(2cost - sint). For problem 7, the solution is y(t) = 2e^(2t) + 3e^(5t) + (2/3)cost - (1/3)sint.

For problem 1, taking the Laplace transform of y" - 2y' + 5y = 0 gives us s^2Y(s) - 2sY(s) + 5Y(s) = Y''(s) - 2sY(s) + 5Y(s) = 0. Applying the initial conditions, we get Y(s) = \((s + 1)/(s^2 - 2s + 5)\). Simplifying and finding the inverse Laplace transform, we obtain y(t) = \(e^t\)(cos(2t) + 3sin(2t)).

For problem 3, taking the Laplace transform of y" + 6y' + 9y = 0 gives us s^2Y(s) + 6sY(s) + 9Y(s) = Y''(s) + 6sY(s) + 9Y(s) = 0. Applying the initial conditions, we get Y(s) = \((s + 3)/(s^2 + 6s + 9)\). Simplifying and finding the inverse Laplace transform, we obtain y(t) = e^(-3t)(2cost - sint).

For problem 7, taking the Laplace transform of y" - 7y' + 10y = 9cost + 7sint gives us \(s^2Y(s)\) - 7sY(s) + 10Y(s) = \((9s)/(s^2 + 1)\) + \((7)/(s^2 + 1).\)Applying the initial conditions, we get Y(s) = \((9s + 7)/(s^2 - 7s + 10).\) Simplifying and finding the inverse Laplace transform, we obtain y(t) = \(2e^(2t) + 3e^(5t) + (2/3)\)cost - (1/3)sint.

These solutions are obtained by applying the method of Laplace transforms to the given initial value problems, providing the solutions in the time domain.

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The utility functions in options a, b, c, and f are not risk-averse on the interval [a,b], while the utility functions in options d and e are risk-averse on the interval [a,b].

In economics and finance, risk aversion refers to a preference for less risky options over riskier ones. Utility functions are mathematical representations of an individual's preferences, and they help determine whether someone is risk-averse, risk-neutral, or risk-seeking. A risk-averse individual would have a concave utility function, indicating a decreasing marginal utility of wealth.

For options a, b, c, and f, the utility functions are and f(x) = -ln(x), g(x) = \(-e^(^-^x^)\), h(x) = \(-4x^2\) - 10x, respectively. These utility functions do not exhibit concavity, which means they are not risk-averse. Instead, they either show risk-seeking behavior (options a and b) or risk-neutrality (options c and f).

On the other hand, options d and e have utility functions f(x) = ln(x), g(x) = 1/(e^(2x)), h(x) = \(-x^2\) + 10,000x and f(x) = ln(-2x), g(x) = -1/(\(e^(^2^x^)\)), h(x) = \(x^2\) - 100,000x, respectively. These utility functions display concavity, indicating a decreasing marginal utility of wealth. Thus, options d and e can be considered risk-averse on the interval [a,b].

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The beta of the portfolio, considering $1 with a beta of 3% and $2 with a beta of 7% and a weight of 0.1 (w1), is 6.6%.


The beta of a portfolio measures its sensitivity to overall market movements. To calculate the beta of a portfolio, we need the individual asset weights and betas of each asset. Given that $1 has a beta of 3% and $2 has a beta of 7%, with a weight of 0.1 (w1), we can determine the beta of the portfolio.

To calculate the beta of the portfolio, we use the following formula:

β(portfolio) = (w1 * β1) + (w2 * β2) + ...

In this case, the portfolio contains two assets, so the formula becomes:

β(portfolio) = (w1 * β1) + (w2 * β2)

Substituting the given values:

β(portfolio) = (0.1 * 3%) + (0.9 * 7%)

β(portfolio) = 0.3% + 6.3%

β(portfolio) = 6.6%

Therefore, the beta of the portfolio is 6.6%.

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SOLUTION:

Case: Ratios

A ratio says how much of one thing there is compared to another thing.

Given:

30 women and 28 men in a school marching brand

Required: Get the ratio of women to men

Method:

Step 1: Expressing as ratio:

30 women: 28 men

Step 2:

30:28

Divide both by 2

15:14

Final answer:

Simplest ratio is 15:14 OR 15/14

Answer:

When t= 0

f(t)= 40 degrees

The value of −32(2.718)^−0.06t approach 0 as t increases

If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72

Step-by-step explanation:

The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator.

f(t)=72−32(2.718)^−0.06t

When t= 0

f(t)=72−32(2.718)^−0.06(0)

f(t)=72−32(2.718)^(0)

f(t)=72−32(1)

f(t)=72−32

f(t)= 40 degrees

As t increases −32(2.718)^−0.06t

Let t= 1

=−32(2.718)^−0.06(1)

= −32(2.718)^−0.06

= -30.14

Let t = 2

=−32(2.718)^−0.06(2)

=−32(2.718)^−0.12

=−32(0.8869)

= -28.38

The value of −32(2.718)^−0.06t approach 0 as t increases

If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72

When t = 0, the temperature of the juice is 40°.

                    As time increases, \(-32(2.718)^{-0.06\times 0}\) gets closer and closer to 0.

                    So, f(t) gets close to 72°

    Function representing the temperature of of the juice at any time 't' is,

\(f(t)=72-32(2.718)^{-0.06t}\)

1). If t = 0,

  \(f(0)=72-32(2.718)^{-0.06\times 0}\)

          \(=72-32(1)\)

          \(=40\) degrees

2). If \(t\rightarrow \infty\),

    \(-\frac{1}{32(2.718)^{0.06t}} \rightarrow 0\)  

[As denominator of the fraction becomes larger and larger with the increase in the value of t, value of fraction gets smaller and smaller]

3). if \(t\rightarrow \infty\), \(f(t)\rightarrow 72\)

  Therefore, when t = 0, the temperature of the juice is 40°.

                    As time increases, \(-32(2.718)^{-0.06\times 0}\) gets closer and closer to 0.

                    So, f(t) gets close to 72°.

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The correct algebraic expression that describes the circuit displayed is option A. (a + b)c' + ab.

To determine the correct expression, we can use the distributive property and the fact that the complement of a product is equal to the sum of the complements. In other words, (ab)' = a' + b'.

Using the distributive property, we can simplify the expression in option A:
(a + b)c' + ab = ac' + bc' + ab

Now, using the fact that the complement of a product is equal to the sum of the complements, we can simplify further:
ac' + bc' + ab = (a + b)c' + ab

This expression matches the original expression in option A, so option A is the correct answer.

Therefore, the correct algebraic expression that describes the circuit displayed is (a + b)c' + ab.

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The correct option is b. Yes, it always follows the polarity of the battery. In a complicated circuit, the current flow is determined by the voltage difference across the circuit.

Since the battery provides the voltage difference, the current always flows in the direction of the battery's polarity. However, there may be other components in the circuit, such as resistors or capacitors, that can affect the flow of current and cause it to change direction temporarily.

Nonetheless, the overall direction of the current in the circuit will always follow the polarity of the battery.

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Answer:

y = x(4+z)+6

y-6 = x(4+z)

x=(y-6)/(4+z)

Step-by-step explanation:

A sample that does not represent the entire group of interest is called a biased sample.

A biased sample is a sample that doesn't reflect the real-world population it is supposed to represent. It happens when the sample is chosen in such a way that some members of the population are less likely to be included than others.

Therefore, a biased sample may not be an accurate representation of the entire population.

For example, if a researcher wants to know how many people in a given area have access to the internet and chooses a sample of people from a high-income neighborhood, the results may be biased because people from low-income areas may have lower rates of internet access.

A biased sample can lead to inaccurate conclusions, and therefore, it's important to ensure that the sample is representative of the population. A random sample, on the other hand, ensures that all members of the population have an equal chance of being included in the sample.

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In the given scenario ladder is 6.52 feet long.

Given that,

The angle between ground and ladder = 62 degree

The distance of ladder from ground and ladder = 3 feet

We have to find the length of  ladder.

Since we know that,

The trigonometric ratio

cosθ = adjacent/ Hypotenuse

Here we have,

Adjacent =  3 feet

Hypotenuse = length of ladder

Thus to find the length of ladder we have to find the value of hypotenuse.

Therefore,

⇒ cos62 = 3/ Hypotenuse

⇒    0.46 = 3/ Hypotenuse

⇒ Hypotenuse =  3/0.46

                          = 6.52

Thus,

length of ladder  = 6.52 feet.

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Answer:

x = 7

Step-by-step explanation:

2 (-4x + 2) + 5x - 2 = -19       Distribute 2 to -4x and 2

-8x + 4 + 5x - 2 = -19            Combine like terms

-3x + 2 = -19                          Subtract 2 from both sides

-3x = -21                                To get x by itself, divide -3 on both sides

x = 7

In Luther v. Borden, 1849, it is true that the Supreme Court abdicated its role in clarifying whether the people had the right to abolish their state governments. The great statesman Daniel Webster argued that people do indeed possess the right to overthrow their government.

Luther v. Borden, 1849 was a United States Supreme Court case that decided whether the court should intervene in a political question, specifically the Rhode Island Dorr Rebellion of 1841 to 1842. In this case, the court declined to do so and ruled that the authority to decide whether a rebellion against a state government exists or not, rests solely with the United States government. The Court refused to support either side in the rebellion and thus upheld the lower court's decision.

The decision is well-known for declaring that the federal government must guarantee a "republican form of government" in the states. In this context, Webster argued that people possess the right to overthrow their government as they possess the ultimate sovereignty. True.

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Togetherly Paige and Malia can complete the job in 2.4 hours,

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
Let the amount of work be x,
Paige complete x work in 6 hours
So the unit rate of doing work of page = x / 6
Similarly,
The unit rate of doing x work of Malia = x / 4

Sum of the unit rate = x / 6 + x /4 = 5x/12
Now,
Time = work/unit rate
Time = x / [5x/12]
Time = 12/5
Time = 2.4 hours

Here, togetherly Paige and Malia can complete the job in 2.4 hours,

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we are 90% confident that the true mean price of hard back statics is between $93.15 and $95.85.

What is statistics and its types?

Since the 90% confidence interuale tells that when you are going to construct a confidence interuale of size 30 100firmes , out of this 100, 90 times the truew means will lie in the confidence interuale.

So option 1) & 2) are incorrect.

Similarly option 4 will no be correct .

So option c is correct.

i.e. we are 90% confident that the true mean price of hard back statics is between $93.15 and $95.85.

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Two samples can have the same mean but different standard deviations if one sample has more variability than the other. For example, one sample may have data points that are tightly clustered around the mean, while the other sample may have data points that are more spread out.

This can result in the same mean value for both samples, but different levels of variability.

Here's an example bar graph to illustrate this concept:

     Sample 1                Sample 2

 ╭────────────────╮   ╭────────────────╮

 │      Mean      │   │      Mean      │

 ├────────────────┤   ├────────────────┤

 │                │   │    ╭─╮         │

 │                │   │    │ │         │

 │                │   │    │ │         │

 │                │   │    ╰─╯         │

 │     o o o      │   │  o o o o o o  │

 │                │   │                │

 │                │   │                │

 │                │   │                │

 ╰────────────────╯   ╰────────────────╯

     Std. Dev.            Std. Dev.

In this example, both Sample 1 and Sample 2 have a mean value of 5. However, Sample 1 has lower variability with a standard deviation of 1, while Sample 2 has higher variability with a standard deviation of 3. The error bars on the graph represent the standard deviation for each sample.

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The value stored in the variable x after the execution of the following code snippet will be b) 2.

The right-click context menu option or a combination of hotkeys can be used to add code snippets, which are compact chunks of reusable code, to a code file. Although try-finally and if-else blocks, for example, are frequently used code blocks found in code snippets, you can also use them to add whole classes or methods.

Learn more about using the templates tool to create reusable emails. Applications and web pages use snippets. Snippets are made to be reusable and to add functionality, like connecting various parts of a program.

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The equation that can be used to solve for c in the given right triangle is the sine function: c = (3 meters) / sin(50°).

In the given right triangle ABC, we are given that angle ACB is a right angle (90°) and angle CBA is 50°. We also know the length of side AC, which is 3 meters. The length of side CB is denoted by "a," and the length of the hypotenuse AB is denoted by "c." To solve for c, we can use the trigonometric function sine (sin). In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can use the sine of angle CBA (50°) to find the ratio between side CB (a) and the hypotenuse AB (c).

The equation c = (3 meters) / sin(50°) represents this relationship. By dividing the length of side AC (3 meters) by the sine of angle CBA (50°), we can find the length of the hypotenuse AB (c) in meters. Using the given equation, we can calculate the value of c by evaluating the sine of 50° (approximately 0.766) and dividing 3 meters by this value. The resulting value will give us the length of the hypotenuse AB, completing the solution for the right triangle.

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Answer:

it should be 10x+3y=30 if im not mistaken

Step-by-step explanation:

you just add straight down with corresponding variables

To find the difference between the numbers, we need to substract 7.43 from 35.6.

First we align out values with the decimal point:

We add a zero to 35.6 to have the same number of decimals as 7.43

Now we start the substraction by borrowing one from the 4:

We have that 10-3 is 7, we continue with 6-5 (the number 5 is because of 4 and 1 we added is 5)

In this step, we also lower the decimal point.

we finish the substraction by also borrowing one for the 5 to become a 15, and we give it back just bellow the 3:

This is because 15-7 is equal to 8, and 3-1 is equal to 2

Answer:

(-4.58, -2)

Step-by-step explanation:

\(\theta $ is in between \pi$ and $\frac{3\pi}{2}$ radians \\Therefore, \theta$ is in Quadrant III\\If \csc \theta = -\dfrac{5}{2}$ and cosec \theta = \dfrac{Hypotenuse}{Opposite} \\ $Therefore:\\Hypotenuse = 5\\Opposite $=-2\)

Using Pythagoras Theorem

\(5^2=(-2)^2+ x^2\\25=4+x^2\\x^2=21\\x=\sqrt{21} \approx 4.58\)

Since the angle is in the third Quadrant, Adjacent = -4.58.

Therefore, the coordinates of P(x,y) is (-4.58, -2)

Answer: a

Step-by-step explanation: edge 2021

The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

A hypothesis is a put forth explanation for a phenomenon (plural: hypotheses).

A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.

Despite the frequent confusion between the terms "hypothesis" and "theory," a scientific hypothesis differs from a scientific theory.

A working hypothesis is a theory that has been tentatively accepted and is proposed for future study[1], starting with an informed guess or thinking.

Hence, The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

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Answer:

24 cookies got eaten 12 weren't eaten

Step-by-step explanation:

36 divided by 3 = 12

12 x 2 = 24 ( since they ate 2/3)

36-24=12 (12 weren't eaten)

Answer:

take deep slow breaths

Step-by-step explanation:

the slope is 5/1, the y-intercept is 0

y = 5x

I can't see the title for the x axis,

so it would be from the information i can see:

This goes up as this amount of water is used

Answer:

rational

Step-by-step explanation:

Answer:

The fraction 3/10 is a rational number. All fractions are rational numbers.