Try It
Complete the square.
y²-20y
Find the missing term that completes the square.
y²-20y +
(Simplify your answer. Type an integer or a fraction.)

The largest lampshade Hillary can wrap laces around has an estimated diameter of [tex]14.32[/tex] inches.

The better measure across the edge of the circle is its diameter. The radius of a circle is the farthest from to any place on the edge. The diameter and radius are inversely proportional, or 2r=d2 r=d.

For instance, if a circle has a circumference of 25 cm, its diameter is 25 cm/, or 7.96 cm. For instance, calculate the square root of 12cm2 if that is the circle's area. Hence, the circle's diameter becomes 1.95 x 2 Equals 3.90 cm.

[tex]C = 2pir[/tex]

where [tex]C[/tex] is the circumference, π (pi) is a mathematical constant approximately equal to [tex]3.14[/tex], and r is the radius of the circle.

We can do this by rearranging the formula for the circumference:

[tex]C = 2pir[/tex]

[tex]r = C / (2pi)[/tex]

We are given that Hilary has [tex]45[/tex] inches of lace, which is the circumference of the circle.

[tex]r = 45 / (2pi) =7.16 inches[/tex]

Finally, we can find the diameter of the circle by doubling the radius:

[tex]d = 2r = 14.32 inches[/tex]

Therefore, the approximate diameter of the largest lampshade Hilary can put lace around is [tex]14.32[/tex] inches.

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We can start by rearranging the equation 5 sin x + 4 cos x = 0 by dividing both sides by cos(x):

5

sin

⁡

�

cos

⁡

�

+

4

=

0

5

cosx

sinx

​

+4=0

Recall that $\frac{\sin x}{\cos x} = \tan x$. So we can substitute this in:

5

tan

⁡

�

+

4

=

0

5tanx+4=0

Now we can solve for $\tan x$:

\begin{align*}

5 \tan x + 4 &= 0 \

5 \tan x &= -4 \

\tan x &= \frac{-4}{5}

\end{align*}

Therefore, the value of $\tan x$ is $\boxed{\frac{-4}{5}}$.

The probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.

To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means is approximately normal for large sample sizes.

First, we need to calculate the standard error of the mean (SEM) using the formula

SEM = standard deviation / sqrt(sample size)

SEM = 29.5 / sqrt(45) = 4.4

Next, we can standardize the sample mean using the formula

z = (x - μ) / SEM

where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.

For the lower limit, we have

z = (185.7 - 193.2) / 4.4 = -1.70

For the upper limit, we have

z = (206.5 - 193.2) / 4.4 = 3.02

We can use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.

The probability of z being between -1.70 and 3.02 is approximately 0.9429 or 94%. Therefore, the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.

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Answer:Sin and cosine of the acute angle are complementary trigonometric functions. This means that between these trigonometric functions, the rule of complementary acute angles applies: sin64° = cos(90°-64°) = cos26°

So, if we have given cos64° = cosx  and we want to determine the value of the acute angle x, given the complementarity of the angles to 90 degrees, the required value of the angle x is 26°.

The answer is: x = 26°

Step-by-step explanation:

4. The transformation by Mrs. Selcer of the function f(x) = x² to create g(x) = 6·x², is a vertical stretch of the function f(x), therefore;

The transformation of a function is a function that results in a variation in the graph of the parent function.

The rules for the transformation of a function indicates that a transformation of a function f(x) to a·f(x), transform the coordinates of the points of f(x) as follows;

(x, y) → (x, a·y)

Therefore;

The transformation is a vertical stretch when a > 1

The transformation is a horizontal compression when a < 1

Since f(x) = x², and g(x) = 6·x², we get;

g(x) = 6·f(x)

Therefore, comparing, we get; a = 6 > 1, which indicates that the function is vertically stretched.

Therefore, Jane is correct.

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Answer: Let's say the total number of students surveyed is "x".

We know that 65% of the students surveyed said their favorite color was red, which means that 325 students said their favorite color was red.

We can set up a proportion to solve for "x":

65/100 = 325/x

To solve for "x", we can cross-multiply:

65x = 32500

Dividing both sides by 65, we get:

x = 500

Therefore, Hakeem surveyed 500 students in total.

Step-by-step explanation:

a. The probability that the top-selling Red and Voss tire wears out before 60,000 miles can be found by calculating the Z-score and using a standard normal distribution table. The Z-score formula is: Z = (X - μ) / σ, where X is the distance (60,000 miles), μ is the mean (71,000 miles), and σ is the standard deviation (5,000 miles).

Z = (60,000 - 71,000) / 5,000 = -11,000 / 5,000 = -2.2. Using a standard normal distribution table, the probability is approximately 0.0139 or 1.39%.

b. To find the probability that a tire lasts more than 81,000 miles, calculate the Z-score: Z = (81,000 - 71,000) / 5,000 = 10,000 / 5,000 = 2. Using the standard normal distribution table, the probability of a Z-score less than 2 is approximately 0.9772. Since we want the probability of the tire lasting more than 81,000 miles, we need to find the complement: 1 - 0.9772 = 0.0228 or 2.28%.

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Step-by-step explanation:

To find the price of one tire patch, you could use the equation:

4x = 22.2 + 1.9

which simplifies to:

4x = 24.1

Then divide both sides by 4 to isolate x:

x = 6.025

So the equation that applies here is:

4x = 22.2 + 1.9

The area of the rectangle has a width of 5 1/3 yards long and 2 1/6 yards wide is 104/9 square yards or 11.56 square yards.

When calculating a rectangle's area, we multiply the length by the breadth of the rectangle.

A mixed fraction is one that is expressed by its quotient and remainder.

Area = length * breadth

Given: Length = [tex]5 \frac{1}{3}[/tex] yards

           breadth = [tex]2 \frac{1}{6}[/tex] yards

First, we need to convert a mixed number into the improper fraction

[tex]5 \frac{1}{3}[/tex] = [tex]\frac{(5*3) + 1}{3}[/tex] = [tex]\frac{16}{3}[/tex]

[tex]2 \frac{1}{6} = \frac{(2*6) +1}{6} =\frac{13}{6}[/tex]

Therefore the area of the rectangle = Length * width

= [tex]\frac{16}{3} * \frac{13}{6}[/tex]

=[tex]\frac{104}{9}[/tex]

=[tex]\frac{104}{9} yards^{2}[/tex]

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Complete question:

The rectangle has [tex]5\frac{1}{3}[/tex] yards long and [tex]2 \frac{1}{6} \\[/tex] yards wide. What’s the area

Answer:

30% of students do not plan to attend college.

Flow rate =[tex]V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex] gallons per hour (rounded to the nearest gallon) will be circulated.

What is meant by rate?

In general, a rate is a measure of how quickly something changes over time or with respect to some other quantity. It is typically expressed as a ratio of two quantities, where the numerator represents the amount of change and the denominator represents the time or other quantity over which the change occurs.

If the new exhibit is 3 1/2 times larger than the old one, then its volume is:

[tex]V_{new} = 3.5 * V_{old[/tex]

We know that in the old exhibit, 576,000 gallons of water circulated over 24 hours. Therefore, the flow rate of water in gallons per hour is:

576,000 gallons / 24 hours = 24,000 gallons per hour

To find the flow rate in the new exhibit, we need to divide the total volume of water by the number of hours. Since we want the flow rate in gallons per hour, we can write:

Flow rate = [tex]V_{new[/tex] / time

Plugging in the values we have:

Flow rate = (3.5 * [tex]V_{old[/tex]) / time

We don't know the time yet, but we do know that the flow rate should be the same as in the old exhibit, which was 24,000 gallons per hour. So we can set up an equation:

24,000 = (3.5 * [tex]V_{old[/tex]) / time

To solve for time, we can multiply both sides by time:

24,000 * time = 3.5 * [tex]V_{old[/tex]

Then we can divide both sides by 24,000:

time = (3.5 * [tex]V_{old[/tex]) / 24,000

Plugging in [tex]V_{old[/tex] = 576,000, we get:

time = (3.5 * 576,000) / 24,000 = 84 hours

Therefore, in the new exhibit, 3.5 times larger than the old one, the flow rate of water in gallons per hour will be:

[tex]Flow rate = V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex]gallons per hour (rounded to the nearest gallon).

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Answer:

To find out how many gallons per hour will be circulated in the new exhibit, we need to first determine the volume of the old exhibit. Given that 576,000 gallons of water circulated through the old tank over 24 hours, we can calculate the amount of water circulated per hour.

To do this, we divide the total gallons by the number of hours:

576,000 gallons / 24 hours = 24,000 gallons per hour

Now, we know that the new exhibit is 3 1/2 times larger than the old one. To find the volume of the new exhibit, we multiply the volume of the old exhibit by 3 1/2.

Let's assume the volume of the old exhibit is x gallons.

The volume of the new exhibit is 3 1/2 times larger than the old one, so the volume of the new exhibit is 3 1/2 * x.

To calculate the new volume, we need to convert the mixed fraction 3 1/2 into an improper fraction. It equals 7/2.

So, the volume of the new exhibit is 7/2 * x.

Now, we can determine the amount of water circulated per hour in the new exhibit.

To find this, we multiply the volume of the new exhibit by the rate of circulation per hour in the old exhibit (24,000 gallons/hour):

(7/2 * x) * 24,000 gallons/hour = (7 * 24,000 * x) / 2 gallons/hour = 168,000x gallons/hour

Therefore, the number of gallons per hour that will be circulated in the new exhibit is 168,000x, where x represents the volume of the old exhibit.

Please note that the actual value of x (the volume of the old exhibit) is not given in the question, so we can't determine the exact number of gallons per hour. However, we can express it as a multiple of the volume of the old exhibit.

Step-by-step explanation:

<3

The density of the lobster population in the area labeled NBHK is C) 9.02 lobsters/mi^2.

Population density refers to the number of people living in a given area, usually expressed as the number of individuals per square mile or kilometer.

To calculate population density, you can divide the total population of a given area by its land area. For example, if a city has a population of 1 million people and an area of 100 square miles, its population density would be 10,000 people per square mile.

The figure has two trapezoid and the areas are 306 and 756. Total area will be 1062 miles².

Lobster population will be:

= 6817 / 756

= 9

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The greatest power of "p" in this situation is 4, which is the coefficient of p4. Consequently, the polynomial has a degree of 4.

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates.

This equation is provided:

1) [tex]$2p^{4}+p^{3}$[/tex]

The greatest power of the polynomial's variable "p" must be identified to categorize this polynomial by degree.

Therefore, the polynomial [tex]$2p^{4}+p^{3}$[/tex] is a polynomial of the fourth degree.

2) [tex]$2x^{2}$[/tex]

The greatest power of the polynomial's variable "x" must be identified to categorize this polynomial by degree.

The greatest power of "x" in this situation is 2, which is the coefficient of . Consequently, the polynomial has a degree of 2.

Therefore, the polynomial [tex]2x^2[/tex] is a polynomial of the second degree.

3) [tex]$-5n^{4}+10n-10$[/tex]

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The greatest power of "n" in this situation is 4, which is the coefficient of . Consequently, the polynomial has a degree of 4.

Therefore, the polynomial [tex]n^4[/tex] is a polynomial of the fourth degree.

4) 6n

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The greatest power of "n" in this situation is 1, which is the coefficient of [tex]n^1[/tex]. Consequently, the polynomial has a degree of 1.

Therefore, the polynomial [tex]n^1[/tex] is a polynomial of one degree.

5) -6

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The polynomial in this instance doesn't have a component. It has a value of 6 and is a constant word. A constant word is thought to have a degree of zero.

Therefore, equation 6 is a zero-degree polynomial.

6) [tex]$x^{3}-3$[/tex]

The greatest power of the polynomial's variable "x" must be identified to categorize this polynomial by degree.

The greatest power of "x" in this situation is 3, which is the coefficient of . Consequently, the polynomial has a degree of 3.

Therefore, the polynomial [tex]x^3[/tex] is a polynomial of the third degree.

7) [tex]$2n^{5}$[/tex]

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The greatest power of "n" in this situation is 5, which is the coefficient of . Consequently, the polynomial has a degree of 5.

Therefore, the polynomial [tex]n^5[/tex] is a polynomial of the fifth degree.

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Answer:

m = 5

n = 2

c = 7

Step-by-step explanation:

Use the property of degrees (when dividing two same based numbers with different degree indicators, the degree indicators are subtracted)

[tex] \frac{ {9}^{ - 3} }{ {9}^{2} } = \frac{1}{ {9}^{m} } [/tex]

[tex] {9}^{ - 3 - 2} = {9}^{ - 5} [/tex]

[tex] {9}^{ - 5} = \frac{1}{ {9}^{m} } [/tex]

If the degree indicator is negative, the number is written as a fraction (1 in the numerator) and the degree indicator is raised to the denominator with a positive sign:

m = 5

.

[tex] \frac{ {x}^{ - 4} }{ {x}^{ - 6} } = {x}^{n} [/tex]

[tex] {x}^{ - 4 - ( - 6) } = {x}^{ - 4 + 6} = {x}^{2} [/tex]

n = 2

.

[tex] \frac{ ({ - 11})^{7} }{ ( { - 11})^{0} } = ( { - 11})^{c} [/tex]

Raising any number to the zero power makes it one

[tex] \frac{ ({ - 11})^{7} }{1} = ({ - 11})^{c} [/tex]

When dividing by 1, the number does not change

[tex]( { - 11})^{7} = ({ - 11})^{c} [/tex]

c = 7

The estimated relationship may not hold for all levels of TV advertising, and there may be non-linearities or interactions with other variables that should be taken into account in a more sophisticated model.

What is the interpretation of this relationship?

To develop an estimated regression equation to estimate weekly gross revenue with the amount of television advertising as the independent variable, we would need a dataset that includes information on both variables. Assuming we have such a dataset, we could use linear regression to estimate the relationship between the two variables.

The estimated regression equation would take the form:

Weekly Gross Revenue = [tex]b_0 + b_1[/tex]×Amount of TV Advertising + error

where [tex]b_0[/tex] is the intercept (the value of weekly gross revenue when the amount of TV advertising is zero), [tex]b_1[/tex] is the slope (the estimated increase in weekly gross revenue associated with a one unit increase in TV advertising), and error represents the random variation in the relationship between the two variables that is not explained by the model.

The interpretation of the relationship between weekly gross revenue and amount of TV advertising would depend on the sign and magnitude of the slope coefficient

[tex](b_1)[/tex]. If [tex]b_1[/tex] is positive, it would suggest that an increase in TV advertising is associated with an increase in weekly gross revenue. The magnitude of [tex]b_1[/tex] would indicate the strength of this relationship - a larger positive value of[tex]b_1[/tex] would indicate a stronger relationship between TV advertising and weekly gross revenue.

If [tex]b_1[/tex] is negative, it would suggest that an increase in TV advertising is associated with a decrease in weekly gross revenue. This could occur if the advertising is perceived as irritating or offensive to viewers, leading them to avoid the advertised product or service.

It is important to note that correlation does not imply causation, and there may be other factors that affect weekly gross revenue that are not captured in the model.

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45% is greater than 40%

With only two hours left, it's important to stay focused and work efficiently. Take breaks as needed to avoid burnout, but don't procrastinate or get distracted by other tasks.

Hi there! I'd be happy to help you with your math on your profile. Could you please provide me with more specific information about the assignment? What topics does it cover and what kind of problems do you need help with? It's difficult to provide a comprehensive answer without more information.

In the meantime, I can offer some general tips for tackling math problems. First, read the problem carefully and make sure you understand what it's asking. Look for key words or phrases that indicate what type of problem it is. Next, identify the relevant formulas or concepts that you'll need to solve the problem. If you're unsure, check your textbook or notes for guidance.

As you work through the problem, be sure to show your work and label each step clearly. This will help you avoid mistakes and make it easier to check your work later. If you get stuck, don't be afraid to ask for help from a teacher or tutor.
Good luck, and let me know if you have any more specific questions or concerns!

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Answer:

Los dos números naturales son 12 y 58.

Step-by-step explanation:

Llamemos al número más pequeño "x" y al número más grande "y".

Del problema sabemos que:

x + y = 70 (ya que la suma de los dos números naturales es 70)

Cuando el número mayor se divide por el número menor, el cociente es 4 con un resto de 10. Esto se puede escribir como:

y = 4x + 10 (ya que 4 es el cociente y 10 es el resto)

Ahora podemos sustituir la segunda ecuación en la primera ecuación:

x + (4x + 10) = 70

Simplificando esta ecuación, obtenemos:

5x + 10 = 70

Restando 10 de ambos lados, obtenemos:

5x = 60

Dividiendo ambos lados por 5, obtenemos:

x = 12

Ahora que conocemos x, podemos volver a sustituirlo en una de las ecuaciones anteriores para encontrar y:

y = 4x + 10 = 4(12) + 10 = 58

Por lo tanto, los dos números naturales son 12 y 58.

Answer:

The first box is 4 and the second box is 4

The solution is
([tex]\frac{3}{2}[/tex],1)

Step-by-step explanation:

y = 2x -2  Subtract 2x from both sides

-2x + y = -2  Multiply all the way through by - 2

4x - 2y = 4  You are doing this so that you can add it to the first equation 4x + 2y = 8

     4x + 2y = 8

(+) 4x - 2y = 4

       8x       = 12  Divide both sides by 8

x = [tex]\frac{12}{8}[/tex] = [tex]\frac{3}{2}[/tex]

To find y substitute [tex]\frac{3}{2}[/tex] for x and solve for y

y = 2x - 2

y = [tex]\frac{2}{1}[/tex] x [tex]\frac{3}{2}[/tex] - 2

y = 3 - 2

y = 1

Helping in the name of Jesus.

Answer:

Part A = 4x - 2y = 4

Part B = (1.5, 1)

Step-by-step explanation:

Part A:

y = 2x - 2

2y = 4x -4

4x - 4 = 2y

4x - 2y = 4

Part B:

4x + 2y = 8

2y = 8 - 4x

y = (8 - 4x)/2

y = 2x -2

(8 - 4x)/2 = 2x -2

8 - 4x = 4x - 4

8x = 12

x = 1.5

4x + 2y = 8

4(1.5) + 2y = 8

6 + 2y = 8

2y = 2

y = 1

(1.5, 1)

Therefore, the value of tan N rounded to the nearest hundredth is approximately 0.85.

A triangle is a basic geometrical shape that is formed by connecting three non-collinear points in a plane using straight line segments. The three points are called the vertices of the triangle, and the line segments connecting them are called the sides. The angles formed between the sides of a triangle are also an important characteristic of the triangle. Triangles come in many different shapes and sizes, and they have many interesting properties and applications in mathematics, science, engineering, and other fields.

Since the opposite side of angle N is √67 and the adjacent side is √92, we can use the following formula for tangent:

tan(N) = opposite / adjacent

tan(N) = √67 / √92

We can simplify this expression by rationalizing the denominator:

tan(N) = (√67 / √92) * (√92 / √92)

tan(N) = √(67*92) / 92

tan(N) = √6164 / 92

tan(N) = 78.43 / 92

tan(N) ≈ 0.85 (rounded to the nearest hundredth)

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The sampling method described in the question is called "quota sampling."

Quota sampling is a non-probability sampling technique in which researchers select participants based on pre-determined quotas or characteristics, such as age or gender. In this case, the researchers are selecting participants between the ages of 20 and 40.

However, this method may not be representative of the entire population as it does not guarantee that all subgroups within the population have an equal chance of being selected. Therefore, the results may be biased and not accurately reflect the opinions of the entire population.

Therefore, it is important to consider the limitations of quota sampling when interpreting the results

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The equation Y=8.35x represents a proportional relationship between Y and x.

What is proportion?

In mathematics, two quantities are said to be proportional if they vary in a way that can be expressed as a ratio or fraction. Specifically, if two quantities x and y are proportional, this means that as x increases or decreases, y also increases or decreases by the same factor.

The equation Y=8.35x represents a proportional relationship between Y and x.

In a proportional relationship, when one variable (x) increases or decreases, the other variable (Y) changes by a constant factor. This constant factor is known as the constant of proportionality.

In the given equation, Y and x are directly proportional to each other, with a constant of proportionality of 8.35. This means that if x is multiplied by any factor, Y will also be multiplied by the same factor. For example, if x is doubled, Y will also be doubled (since 2 times 8.35 is 16.7).

Therefore, the equation Y=8.35x represents a proportional relationship between Y and x.

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Polynomial expressions of [tex]2^{nd}[/tex] degree with one unknown (only [tex]x[/tex]) have [tex]2[/tex] roots. We use the formula below to determine these roots;

This formula is valid for equations of the form [tex]ax^2+bx+c[/tex]. We can convert the equation given in the question into this format to get the result;

Hence, the value of [tex]a[/tex]: [tex]8[/tex],

the value of [tex]b[/tex]: [tex]16[/tex],

the value of [tex]c[/tex]: [tex]3[/tex].

Now, we can find the roots of this equation by using this formula;

a) The null and alternative hypothesis are defined as

[tex]H_0 : p = 0.80 [/tex]

[tex]H_a : p > 0.80[/tex]

So, right choice is option (iii) here.

b) The test statistic value is equals to the 1.25.

c) The p-value of distribution is equals to the 0.1056. So, option(b) is right one here.

d) Conclusion: a fail to reject the null hypothesis, that is p = 0.80. So, there is no evidence to support the claim.

The claim about the population proportion that the proportion is more than 80% is tested under the null and the alternative hypothesis at the 5% level of significance. To calculate the P-value and the test statistic value, we will use Z-test. . We have a random sample of 100 people. So, sample size, n = 100

Number of people who favored candidate from the sample = 85

level of significance, [tex] \alpha[/tex]

= 0.05

Population proportion, [tex] \hat p[/tex]

= 85% = 0.85

a) The null hypothesis is,

[tex]H_0 : p = 0.80[/tex]

The alternative hypothesis is,

[tex]H_a : p>0.80[/tex]

(Right-Tailed)

Therefore, Option (iii) is correct.

b)Now, we determine the z statistic value : z-test statistic is defiend as:

[tex]z= \frac{\hat p−p}{\sqrt{\frac{p(1−p)}{n}}}[/tex]

=> [tex]z = \frac{0.85 - 0.80}{\sqrt{\frac{0.80(1 - 0.80)}{100}}}[/tex]

=> z = 0.05/0.04 = 1.25

so, Z-statistic value is 1.25.

c) Using the Z-distribution table, the value of P( z = 1.25 ) is 0.1056.

d) As we see, p-value (0.1056) > 0.05, so we fail to reject the null hypothesis. There is no evidence to reject null hypothesis.

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Complete question:

a random sample of 100 people was taken. eighty-five of the people in the sample favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 80%.

a) The correct set of hypothesis for this problem is I)H0:p=0.85 and

HA:p>0.85

ii. H0:p>0.80 and

HA:p=0.80

iii.) H0:p=0.80 and

HA:p>0.80

iv.) H0:p=0.80 and HA:p≥0.80

b) find out the Z-statistic value?

c)the p-value is ? group of answer choices 0.2112 0.05 0.1056 0.025

d) What is your conclusion?

Rectangle ABCD was translated 8 units left and then 7 units down.

We can see vertex A(2,4) of rectangle ABCD moves to A"(-6,-3), in a way that A translated 8 units left (-8)and 7 units down(-7) to A".

A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

Vertex is a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet. The plural of a vertex is vertices.

A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints.

that is (2-8,4-7)=(-6,-3)

Similarly the other vertices of rectangle ABCD moves to form rectangle A"B"C"D"

B (2,2) → B" (-6,-5)

C (6,2) → C" (-2,-5)

D(6,4) → D" (-2,-3)

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The measure of IJ is 29, when IJ is dilated by a scale factor of 2 to form I' J', and I' J' measures 58. Geometric figures in two or three dimensions can be expanded and contracted using dilation mathematics.

Dilation refers to the change in size without a change in shape of an object. The scale factor may also cause the object's size to either increase or decrease.

Dilation is hence the process of resizing or altering an object. It is a transformation that makes the objects smaller or larger by applying the provided scale factor. It is a transformation that makes the objects smaller or larger by applying the provided scale factor. The pre-image is the original figure, while the image is the new figure created as a result of dilation. Dilation comes in two varieties:

As an object experiences expansion, its size expands.

Contraction is the process of a thing getting smaller.

Given:

I'J' is IJ with the scale factor of 2.

so (IJ) × 2= (I'J)

(IJ) × 2 = 58

58 ÷ 2 = 29

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Note that given the perimeter of the Rhombus above, KN will be 35.03 inches

Since JKLM is a rhombus, all sides have the same length. Let's call this length "x".

Also, since JL and KM are diagonals of the rhombus, they bisect each other at point N. This means that JN = NL and KN = NM.

We know that JN = 16 inches, and we need to find KN. To do this, we need to first find x, the length of the sides.

The perimeter of the rhombus is 72 inches, so we can write:

4x = 72

Dividing both sides by 4, we get:

x = 18

Now we can use the Pythagorean theorem to find NM (which is equal to KN):

(NM)² = (JN)² + (JM)²

We know that JN = 16, and we can find JM using the fact that JL and KM are perpendicular bisectors of each other:

JM = √[(2x)² - x²] = sqrt(3x²) = x √(3)

Substituting x = 18 and simplifying, we get:

(NM)² = 16² + (18 √(3))²

(NM)² = 256 + 972

(NM)² = 1228

NM = √(1228) = 35.03

Therefore, KN is approximately 35.0 inches (to the nearest tenth).

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