Quadrilateral ABCD has vertices A = (2, 5), B = (2, 2), C = (4, 3) and D = (4, 6). Quadrilateral A'B'C'D' is formed when Quadrilateral ABCD is dilated by a scale factor of 2. Which statement is true? Select all that apply

Choose all that apply:

A) None of the answers apply

B) The angles of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same.

C) The side lengths of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same.

Answer:

It's 4

Step-by-step explanation:

4x-5=11

4x=11+5

4x=16

Divide by 4

X=4

Use the given value of x to find the value of y by replacing it in the first equation.

The solution is x=-10 and y=-7. It means, the right answer is the first one (-10,-7).

The rational root of the function is x = -1/2, and the complex roots are x = 21/4 and x = 1.

To find the rational root of the function f(x) = 4x³ - 17x² - 39x - 18, we can apply the Rational Root Theorem. According to the theorem, any rational root of the function must be of the form p/q, where p is a factor of the constant term (in this case, -18) and q is a factor of the leading coefficient (in this case, 4).

Let's list the factors of -18: ±1, ±2, ±3, ±6, ±9, ±18.

And now the factors of 4: ±1, ±2, ±4.

Possible rational roots are formed by dividing a factor of the constant term by a factor of the leading coefficient. So the possible rational roots are:

±1/1, ±1/2, ±1/4, ±2/1, ±2/2, ±2/4, ±3/1, ±3/2, ±3/4, ±6/1, ±6/2, ±6/4, ±9/1, ±9/2, ±9/4, ±18/1, ±18/2, ±18/4.

Now, test each of these possible roots by substituting them into the function f(x) and see if any of them result in f(x) = 0.

By evaluating the function for each of these possible roots, the rational root is x = -1/2.

Now let's proceed to find the complex roots of the function. To do this, use polynomial division or synthetic division to divide f(x) by (x - (-1/2)).

Performing the synthetic division, we have:

4 | 4 -17 -39 -18

| -8 60 -105

| ___________________

| 4 -25 21 -123

The result of the synthetic division is 4x² - 25x + 21 with a remainder of -123. Now we have a quadratic equation. To solve it, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our quadratic equation 4x² - 25x + 21, the coefficients are:

a = 4

b = -25

c = 21

Applying the quadratic formula, we get:

x = (-(-25) ± √((-25)² - 4 x 4 x 21)) / (2 x 4)

= (25 ± √(625 - 336)) / 8

= (25 ± √289) / 8

= (25 ± 17) / 8

So the two complex roots are:

x = (25 + 17) / 8 = 42 / 8 = 21 / 4

x = (25 - 17) / 8 = 8 / 8 = 1

Therefore, the rational root of the function is x = -1/2, and the complex roots are x = 21/4 and x = 1.

learn more about rational root of the function: https://brainly.com/question/29546977

#SPJ1

Answer: 5798

Step-by-step explanation:

Probability of \(1\) success as per given condition is equals to \(0.384475\) ≈ \(0.4\).

" Probability is defined as the ratio of number of favourable outcomes to the total number of outcomes.Probability is always less than or equals to one."

Formula used

For binomial experiment

Probability =  \(^n C_r p^{r} q^{n-r}\)

\(p =\)success rate

\(q=\) failure rate

\(p+q=1\)

\(n=\)Number of trials

\(r=\) number of success

According to the question,

Total number of trials \('n' =4\)

Number of success \('r' =1\)

\(p = 0.35\\\\q = 1-0.35\\ \\\implies q = 0.65\)

Substitute the value to get the required probability,

Probability \(= ^4C_1 (0.35)^{1}(0.65)^{4-1}\)

                   \(=\frac{4!}{(4-1)!1!} \times\frac{35}{100}\times(\frac{65}{100})^{3} \\\\= 4 \times \frac{35}{100}\times \frac{274625}{1000000} \\\\= 0.384475\)

                   ≈ \(0.4\)

Hence, probability of \(1\) success as per given condition is equals to \(0.384475\) ≈ \(0.4\).

Learn more about probability here

brainly.com/question/11234923

#SPJ2

When the wheel weighs 19.5 pounds, this implies that each hub cover weighs approximately 11.08 pounds.

A mathematical equation is a statement that expresses the connection between two or more quantities using symbols like elements, numbers, and mathematical operations. It may also signify a requirement that must be met or an issue that must be resolved. There are numerous ways to express equations in writing, including the algebraic, geometric, logarithmic, and exponential formats. The expression y = mx + b, for instance, depicts a linear connection between variables x and y, with m denoting the line's slope and b its y-intercept. The sine function and the variable x are related in a trigonometric way by the solution sin(x) = 0.5, where sin(x) is the ratio of a right triangle's opposing side's length to its hypotenuse's length.

given

Let's suppose that each hubcap weighs x pounds.

Since there are 6 of the same hubcaps, their combined weight is 6.

The hubcaps and the tire together weigh 86 pounds, according to the issue. Thus, the following solution can be written:

6x + 19.5 = 86

We can begin by removing 19.5 from both sides to find x:

6x = 86 - 19.5

6x = 66.5

Finally, we can identify x by dividing both sides by 6:

x = 11.08

When the wheel weighs 19.5 pounds, this implies that each hub cover weighs approximately 11.08 pounds.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

Read more on inequality:

https://brainly.com/question/25275758

#SPJ1

Answer:

p represents the original per pound price

3p represents the cost of three pounds

3p + 3(0.75) = 5.88           multiply

3p + 2.25 = 5.88               subtract 2.55 from both sides

3p = 3.63                          divide both sidesby 3

p = 1.21

The original price was $1.21 per pound.

1.21 = 0.75

1.96

3(1.96)

5.88

During the winter season, a family sets up a hot chocolate stand near a local ice skating rink. They sell cups of hot chocolate for $1.50 each and typically sell 50 cups per day.

However, due to changes in weather conditions and customer preferences, the family decides to conduct a market experiment by varying the price of hot chocolate to assess the impact on sales volume. The experiment involves increasing the price to $2.00 per cup and monitoring the resulting sales.

By increasing the price of hot chocolate from $1.50 to $2.00 per cup, the family aims to observe how the change in price affects the demand for their product. The experiment helps them understand the price elasticity of demand, which measures the responsiveness of quantity demanded to changes in price. If the increase in price leads to a significant decrease in sales volume, it suggests that the demand for hot chocolate is elastic, meaning consumers are sensitive to price changes. Conversely, if sales remain relatively stable despite the price increase, it indicates that the demand is inelastic, indicating that consumers are less sensitive to price changes. The family can analyze the results of this experiment to make informed pricing decisions and optimize their profitability during the winter season.

To learn more about profitability: -

brainly.com/question/29662354

#SPJ11

Answer:

false

Step-by-step explanation:

in order for it to form a triangle, the two smaller sides must add up to be bigger than the bigger sides

5+7 > 10, 12 > 10 so it is a triangle

to see if it is a right triangle you must use c^2 = a^2+b^2

100 = 25 + 49

100 = 74

not a right triangle

Answer:

Step-by-step explanation:

answer for 1 & 2 & 3

Answer:

Yes

Step-by-step explanation:

I think so

The first-order system of equations:x1' = x2, x2' = 3x2 - 7x1 + \(t^2\)

To convert the nonhomogeneous differential equation y′′ + 3y′ + 7y = \(t^2\) to a first order system, we can define two new variables, x1 = y and x2 = y′.

Then, we can express the derivatives of x1 and x2 in terms of themselves and t:

x1' = y' = x2

x2' = y'' = t^2 - 3y' - 7y

Now, we have a system of two first-order differential equations:

x1' = x2

x2' = t^2 - 3x2 - 7x1

We can rewrite this system in matrix form:

[x1']   [0 1][x1]   [0]

[x2'] = [7 -3][x2] + \(t^2\)

where the matrix on the left-hand side is the coefficient matrix, the column vector on the right-hand side contains the forcing functions, and the column vector on the left-hand side contains the derivatives of x1 and x2.

Thus, the first order system for the nonhomogeneous differential equation y′′ + 3y′ + 7y = \(t^2\) is:

[x1'] = [0 1][x1]

[x2']   [7 -3][x2] + \(t^2\)
To convert the nonhomogeneous differential equation y'' - 3y' + 7y =\(t^2\) to a first-order system, let x1 = y and x2 = y'. Then, we have:

x1' = y' = x2
x2' = y'' = 3y' - 7y + \(t^2\)

Now, substitute the expressions for x1 and x2:

x1' = x2
x2' = 3x2 - 7x1 + \(t^2\)

This gives us a first-order system of equations:

x1' = x2
x2' = 3x2 - 7x1 +\(t^2\)

To learn more about equation visit;

brainly.com/question/29538993

#SPJ11

Answer:

Answers are below

Step-by-step explanation:

The terms include: 5z, 6, and y^2

The coefficients include: 5

The constants include: 6

P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Answer:

Pretty sure the one you pointed an arrow to is correct.

Step-by-step explanation:

It has a circle at the bottom and the top as well as a slip for the body!

The net of the food container is the first diagram in the options.

The net of a shape is the shape of the object when it is laid out flat. The food container has the shape of a cylinder. A cylinder is a three-dimensional object. It is a prism with a circular base.

The net of a cylinder is two circles and a rectangle.

To learn more about a cylinder, check: https://brainly.com/question/9624219

The Expected value for 4 tickets = $ 7.6

Given - A lottery offers one $900 prize, one $600 Prize, three $400 prizes, and four $100 prizes. One thousand tickets are sold at $5 each.

To find - Find the expectation if a person buys four tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.

Proof -

Given that,

A lottery offers

one $ 900 prize

one $ 600 prize

three $ 400 prizes

Four $ 100 prizes

And

One thousand tickets are sold at $ 5 each

Now,

If the person bought 1000 tickets then the prize he gets is

= 900 + 600 + 3×400 + 4×100

= 900 + 600 + 1200 + 400

= $3100

And

The cost of 1000 tickets = 5×1000 = $ 5000

Now,

Price 1 ticket =   $ 3.1

⇒Expectation of 1 ticket = 5 - $ 3.1  = $ 1.9      (Here $5 is price of 1 ticket)

⇒Expected value for 4 tickets = $ 4× -1.9 = $ 7.6

⇒Expected value for 4 tickets = $ 7.6

Learn more about Expected value:

https://brainly.com/question/18523098

#SPJ4

Answer:

About 706.5 or 707

Explanation:

3.14 • 5² (5² is also 25) = 78.5

78.5 • 9 = 706.5 or 707

Edit: Also posted a better picture for explanation. See the attachment.

Type of Attention Impact on Encoding Process

1. Sustained attention Facilitates thorough encoding of information.

2. Selective attention Enhances encoding of attended stimuli while filtering out irrelevant information.

3. Divided attention Impairs encoding by dividing attentional resources among multiple tasks.

4. Exogenous attention Captures attention involuntarily, potentially interrupting the encoding process.

5. Endogenous attention Voluntarily directed attention that can prioritize specific information for encoding.

1. Sustained attention: Sustained attention refers to the ability to maintain focus over an extended period. It has a positive impact on the encoding process as it allows for thorough and comprehensive encoding of information.

2. Selective attention: Selective attention involves focusing on specific stimuli while filtering out irrelevant information. It enhances the encoding process by directing attention to the relevant stimuli, promoting their effective encoding.

3. Divided attention: Divided attention refers to the attempt to allocate attention to multiple tasks simultaneously. Dividing attention among multiple tasks impairs the encoding process as attentional resources become fragmented, leading to less effective encoding of information.

4. Exogenous attention: Exogenous attention is captured involuntarily by external stimuli, potentially interrupting the encoding process. It can divert attention away from the intended encoding task, resulting in a negative impact on encoding.

5. Endogenous attention: Endogenous attention is voluntarily directed attention that allows individuals to prioritize specific information for encoding. It enhances the encoding process by selectively focusing on relevant stimuli and allocating cognitive resources accordingly.

Different types of attention have varying impacts on the encoding process. Sustained attention and selective attention positively influence encoding, while divided attention and exogenous attention have negative effects. Endogenous attention, on the other hand, can enhance encoding by prioritizing specific information.

To know more about encoding task, visit

https://brainly.com/question/8567493

#SPJ11

Answer:it’s 48 ounces

Step-by-step explanation:

Answer:

48 ounces

Step-by-step explanation:

16 ounces in a pound. 16 times 3 is 48 ounces.

Can I get a brainliest?

Answer: \(\angle 3\) and \(\angle 4\) are congruent because they are a pair of alternate exterior angles.

Statistical considerations for the use of composite health-related quality-of-life scores in randomised trials

This is a research paper whose author is Andrew J. Vickers.

Abstract:

Conclusions:

To learn more about statistics, visit :

https://brainly.com/question/23091366

#SPJ4

Answer:

the rate of change is 4/1

To determine the number of solutions that the following linear system of equations has: y = 3x -4 and y = -4x - 4, we need to solve for x and y, and then analyze the result obtained. So,  the linear system of equations y = 3x -4 and y = -4x - 4 has only one solution

Solution. Step 1: Substitute the value of y in the first equation with the expression of y in the second equation: y = 3x - 4y = -4x - 4We have: 3x - 4 = -4x - 4

Step 2: Combine like terms on each side of the equation: 3x + 4x = - 4 + 4x = -1x = -1/(-1) x =

3: Substitute the value of x into any of the original equations to find the value of y: y = 3x - 4y = 3(1) - 4y = -1

Since we have a unique solution for x and y (x = 1, y = -1), the linear system of equations y = 3x -4 and y = -4x - 4 has only one solution. Answer: one.

For more questions on: linear

https://brainly.com/question/28732353

#SPJ8

Trapezoidal Rule: \((b-a)^3 / 96n^2,\) Simpson's Rule: \((b-a)^5 / 2880n^4\\\).  Both approximations have error of 0.0208.

For the Trapezoidal Rule, the formula for estimating the error is |E| ≤ (b − a)3/12n2[max |f ''(x)|], a ≤ x ≤ b. In this case, the integral is from x=1 to x=3, so b-a = 2. Plugging in all the values, we get \(|E| ≤ 2^3/12(4)^2(2)\) or |E| ≤ 0.0208. For the Simpson's Rule, the formula for estimating the error is |E| ≤ (b − a)5/180n4[max |f (4)(x)|], a ≤ x ≤ b. Again, b-a = 2. Plugging in all the values, we get\(|E| ≤ 2^5/180(4)^4(2)\) or |E| ≤ 0.0208. Therefore, the error in approximating the integral with n = 4, using the Trapezoidal Rule and Simpson's Rule, is 0.0208.

Learn more about Trapezoidal Rule here

https://brainly.com/question/29115826

#SPJ4

An equivalent function of the given function in the form G(t) = \(ab^t\) is G(t) = 24000\((0.9025)^t\).

The given function for the value of a car that depreciates over time is G(t) = 24000\((0.95)^{2t\). To write an equivalent function of the form G(t) = \(ab^t\), we need to rewrite the function using exponent rules.

First, we can rewrite \((0.95)^{2t\) as \([(0.95)^{2}]^{t\), which simplifies to \((0.9025)^t\). Therefore, we have:

G(t) = 24000\((0.9025)^t\)

Next, we need to express 24000 as a product of two factors, a and b. We can choose a = 24000 and b = 0.9025, so we have:

G(t) = 24000\((0.9025)^t\) = 24000\((0.9025)^t\)

This function gives the value of the car at time t, where t is the number of years after the initial purchase, with a starting value of 24000 and a depreciation rate of 9.75% per year.

To learn more about function click on,

https://brainly.com/question/31405661

#SPJ1

Answer:effect size

Step-by-step explanation:

A measure of spread is a numerical value that describes the extent of variability within a distribution of scores.

Measures of spread provide insights into how scores or data points are dispersed or scattered around a central tendency. One commonly used measure of spread is the standard deviation.

It quantifies the average amount of deviation from the mean, indicating how much individual scores differ from the average. A larger standard deviation suggests greater variability and spread, while a smaller value indicates more closely clustered scores.

Other measures of spread include the range, which is the difference between the highest and lowest scores, and the interquartile range, which focuses on the middle 50% of scores.

These measures help researchers and analysts understand the degree of dispersion in a distribution, providing valuable information about the data's overall variability.

Learn more about Variability click here :brainly.com/question/22046046

#SPJ11

Answer:

-1

Step-by-step explanation:

-2.75+(-3.25)+5

\(-\frac{275}{100} +(-\frac{325}{100} )+5\)

\(\frac{5^{2}*11 }{2^{2}*5^{2} } +(-\frac{5x^{2} *13}{2^{2}*5^{2} } )+5\)

-1

hope this helps.

The measure of an angle that is coterminal with a 135° angle is 495°.

Coterminal angles are angles that share the same initial and terminal sides, meaning that they differ by a multiple of 360°.

Therefore, to find an angle that is coterminal with 135°, we need to add or subtract multiples of 360° until we get an angle within the given range.

Here, we have the following options:135° + 360° = 495° (this is the smallest positive angle that is coterminal with 135°)135° - 360° = -225° (this is a negative angle that is coterminal with 135°)Since we are given a list of positive angles as answer choices, the correct answer is 495°.

Learn more about "coterminal angle": https://brainly.com/question/3286526

#SPJ11

The standard deviation of the sample of shopping times is approximately 9.18 minutes.

To calculate the standard deviation, we follow these steps:

1. Calculate the mean (average) of the sample. Summing up the shopping times and dividing by the sample size of 5, we get (21 + 42 + 23 + 36 + 43)/5 = 33.

2. Calculate the deviation of each shopping time from the mean. Subtract the mean from each shopping time: 21 - 33 = -12, 42 - 33 = 9, 23 - 33 = -10, 36 - 33 = 3, 43 - 33 = 10.

3. Square each deviation. (-12)² = 144, 9² = 81, (-10)² = 100, 3² = 9, 10² = 100.

4. Calculate the variance. Add up the squared deviations and divide by the sample size: (144 + 81 + 100 + 9 + 100)/5 = 86.8.

5. Calculate the standard deviation. Take the square root of the variance: √86.8 ≈ 9.18.

Therefore, the standard deviation of the sample of shopping times is approximately 9.18 minutes.

To learn more about standard deviation  here:

https://brainly.com/question/29115611

#SPJ4