A box with a square base and open top must have a volume of 13,500 cm^3. Find the dimensions of the box (in cm) that minimize the amount of material used.
There are 2 answer, the height and the sides of the base.

The "Angle-Angle (AA) Similarity Theorem" should be used as the justification in #6 based on the assertions made in the proof.

According to the Angle-Angle-Angle (AAA) criterion, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are similar."

The "Angle-Angle (AA) Similarity Theorem" should be used as the justification in #6 based on the assertions made in the proof.

This is due to the proof demonstrating the congruence of two sets of corresponding angles in the triangles ABC and EDC: ACB  DCE and BDE  DBA.

According to the AA Similarity Theorem, two triangles are similar if two sets of corresponding angles in each triangle are congruent.

As a result, the AA Similarity Theorem leads us to the conclusion that ABC equals EDC.

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Let's assume that the number of diners at the Italian restaurant is "x" and the number of diners at the Mexican restaurant is "y". Then, we can write the following equations based on the given information:

Italian restaurant:

Donation = $462 + $1 per diner

Donation = $462 + $1x

Mexican restaurant:

Donation = $235 + $2 per diner

Donation = $235 + $2y

Since both restaurants will donate the same total amount, we can set their donations equal to each other:

$462 + $1x = $235 + $2y

Simplifying this equation, we get:

$2y - $1x = $227

We know that the number of diners has to be a whole number, so we can try different values of x and see which one gives us a whole number for y.

For example, if we try x = 200, then we can solve for y:

$2y - $1(200) = $227

$2y = $427

y = 213.5

Since y is not a whole number, we need to try a different value of x. If we try x = 250, then we get:

$2y - $1(250) = $227

$2y = $477

y = 238.5

Again, y is not a whole number, so we try another value of x. If we try x = 300, then we get:

$2y - $1(300) = $227

$2y = $527

y = 263.5

Still not a whole number, so we try x = 350:

$2y - $1(350) = $227

$2y = $577

y = 288.5

Finally, we get a whole number for y, so we have our solution:

Italian restaurant: x = 350 diners, donation = $812

Mexican restaurant: y = 289 diners, donation = $812

Therefore, 350 diners promised to participate and each restaurant would donate $812.

Answer:

Area = π+4

Perimeter = 4π+4

Step-by-step explanation:

1) The two semi-circles make one whole circle

2) one square.

Area

1) formula for the area of a circle = [tex]r^{2}\pi[/tex]

The diameter is 2 which means the radius is 1

so the area of the circle is equal to π

2) to find the area of a square you multiply the sides

2x2=4

So to find the total area you add [tex]\pi +4[/tex]

which leaves us with [tex]\pi +4[/tex]

Perimeter

1) the formula for the perimeter of a circle = [tex]2\pi r[/tex]

Since the radius is 1

the perimeter of both circles is 4π

2) to find the perimeter of only part of the square (two sides), you have to add them together

2+2=4

So the total perimeter is 4π+4

Answer:

The quotient will have a larger value than the dividend.

Step-by-step explanation:

Example:

15 ÷ [tex]\frac{1}{2}[/tex]

[tex]\frac{5}{\frac{1}{2} }[/tex]

[tex]\frac{\frac{15}{1} }{\frac{1}{2} }[/tex]  x [tex]\frac{\frac{2}{1} }{\frac{2}{1} }[/tex] = [tex]\frac{\frac{30}{1} }{1}[/tex] = 30

Our quotient of 30 has a larger value than the dividend of 15.

Helping in the name of Jesus.

A circle graph would be best to display the data.

A circle graph, also known as a pie chart, is useful for displaying categorical data where the parts represent a percentage of a whole. In this case, the whole is the total number of purchases, which is 125. The different types of items purchased can be represented as sections of a circle, with the size of each section proportional to the percentage of purchases that fall into that category. A circle graph would allow the viewer to easily see the relative frequency of each category in the data set.

Box plots, scatter plots, and histograms are all graphical representations that are better suited for displaying continuous data, rather than categorical data.

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1. The reason is that E bisects line AC and is perpendicular to line AC.

2. The reason is that the angles are alternate interior angles.

What are alternate interior angles?

Alternate interior angles are made when a transversal joins two co-planar lines. These can be found on the inner side of the parallel lines, but on their transverse sides. The transversal goes through the two co-planar lines at two separate points.

1. We are given a statement that E is the midpoint of AC.

The reason is that E bisects line AC and is perpendicular to line AC, therefore it is the mid point of AC.

2. We are given that ∠D ≅ ∠B.

The reason is that DC ║ AB. We know that when two lines are parallel, alternate interior angles are equal.

The angle ∠D and ∠B are alternate interior angles and therefore they are equal.

Hence, the required solutions have been obtained.

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The complete question has been attached below.

Answer:

Change 6 1/3 into a mixed number so 19/3 then multiply 19 * 4 then divide by 4. So C

Step-by-step explanation:

C(N(x)) = 45 + 15(150 - x) = 45 + 2250 - 15x = 2295 - 15x. C(N(x)) = 2295 - 15x, which equals $2295 minus $15 for each guest fewer than 150. Therefore, $795 would be needed to prepare for 50 guests.

A group of terms joined with the operations +, -, x, or  form an expression, such as 4 x 3 or 5 x 2  3 x y + 17. A statement that starts with an equals sign, such as 4 b 2 = 6, says that two statements are equal in value and is known as an equation.

The functions are: C(x) = 45 plus 15x (Cost per guest)

N(x) = 150 - x (Number of guests)

We must simplify and replace the formula for N(x) with C(x) in order to evaluate C(N(x)):

C(N(x)) = 45 + 15(150 - x) = 45 + 2250 - 15x = 2295 - 15x

The expense of catering for x guests who are less than 150 is denoted by the expression 2295 - 15x.

The expense of catering a celebration for x guests fewer than 150 is denoted by the formula: C(N(x)) = 2295 - 15x, which equals $2295 minus $15 for each guest fewer than 150. This expression provides the total expense of catering for the number of guests defined by the function N.(x). For instance, if the event has 50 guests, then x = 100 and the expense of catering for 50 guests.

C(N(100)) = 2295 - 15(100)

= 2295 - 1500

= 795

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Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is essentially what probability means.

The die has 10 faces, with numbers 1 through 10, but we are interested in the number of times it will land on a number less than 10. That means, there are 9 possible outcomes for each roll to be less than 10.

The expected number of times the die will land on a number less than 10 can be calculated by multiplying the probability of getting a number less than 10 on each roll by the total number of rolls.

The probability of getting a number less than 10 on each roll is 9/10, since there are 9 faces with numbers less than 10 out of the total of 10 faces.

Therefore, the expected number of times the die will land on a number less than 10 is:

E = (9/10) x 40 = 36

Therefore, Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

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☆ 36 times.

— your in college ? im in seventh grade and got this question !

There were 21 quarters, 26 dimes, and 10 nickels in the piggy bank.

Quarters are a type of coin used as currency in many countries, including the United States, Canada, and Mexico. In the United States, quarters are worth 25 cents each and have a diameter of 0.955 inches (24.26 mm). Quarters feature the image of George Washington, the first president of the United States, on the obverse (front) side, and an eagle on the reverse (back) side.

Let's use variables to represent the number of each type of coin. Let:

q be the number of quarters

d be the number of dimes

n be the number of nickels

From the problem statement, we have the following information:

The total value of the coins is $8.50, so we can write:

0.25q + 0.10d + 0.05n = 8.50

There were twice as many quarters as nickels, so:

q = 2n

There were 5 less quarters than dimes, so:

q = d - 5

We can use the third equation to substitute for q in the first two equations:

2n = d - 5

n = (d - 5)/2

q = d - 5

Now we can substitute these expressions for n and q in the first equation:

0.25(d-5) + 0.10d + 0.05((d-5)/2) = 8.50

Simplifying and solving for d:

0.25d - 1.25 + 0.10d + 0.025d - 0.125 = 8.50

0.375d = 9.875

d = 26.333...

Since we can't have a fraction of a coin, we need to round this to the nearest whole number. We also know that q = d - 5 and n = (d-5)/2, so:

d = 26

q = 21

n = 10

Therefore, there were 21 quarters, 26 dimes, and 10 nickels in the piggy bank.

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The base and height could also be converted to meters to maintain consistency in units, resulting in an area of 0.3 square meters

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

To calculate the area of the shaded triangle, we can use the formula for the area of a triangle:

Area = 1/2 * base * height

Given that the base of the triangle is the width of the rectangle, which is 6 cm, and the height is the diagonal line connecting the top corners of the rectangle, which is 10 m, we can now substitute these values into the formula and calculate the area of the shaded triangle.

Converting the height to centimeters for consistency:

Height = 10 m * 100 cm/m = 1000 cm

Plugging in the values:

Area = 1/2 * 6 cm * 1000 cm = 3000 cm²

So, the area of the shaded triangle is 3000 square centimeters. Please note that it's important to use consistent units when performing calculations, so make sure to convert measurements to the same unit if necessary. In this case, we converted the height to centimeters to match the units of the base, which was given in centimeters.

Therefore, the base and height could also be converted to meters to maintain consistency in units, resulting in an area of 0.3 square meters.

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The probability is [tex]0.0922 approx[/tex] [tex]9.22%[/tex]%

Probability theory is an area of mathematics that determines the likelihood that an event will occur or a claim will be true.

The probability of an event is a number between[tex]0[/tex] and [tex]1[/tex], where [tex]0[/tex] is the likelihood of the event occurring and [tex]1[/tex] is the chance that it will happen.

The probability that a certain event will occur is simply represented numerically as a probability.

The percentages [tex]0%[/tex]% to [tex]100%[/tex]% or even[tex]0[/tex] to[tex]1[/tex] can be used to express probabilities.

The probability of occurrence in an entire set of equally likely possibilities that results in a particular event divided by the number of outcomes.

We need to know the standard deviation of the sampling distribution of the mean in order to calculate the likelihood that the sample mean will be within one week of the population mean.

The standard error of the mean can be calculated as follows if the population standard deviation is known:

These steps are used to compute standard error: sample size squared / standard deviation of the population

If the sample standard deviation is unavailable, we can estimate the population standard deviation and compute the standard error of the mean as follows:

These steps are used to compute standard error: sample size squared / standard deviation of the population

If we assume that the population's standard deviation is [tex]1[/tex], we can use the standard error of both the mean formula to determine

The probability  that a simple random sample of [tex]55[/tex] unemployed people will somehow generate a sample mean that is within one week of the population average. In this context, "within one week" means within one standard error of something like the population mean, or one.

The standard error of the mean for a sample size of [tex]55[/tex]

Standard error =[tex]\frac{1}{\sqrt{55} }[/tex]

 error                 ≈[tex]0.1348[/tex]

To find the probability that a sample mean is within one standard deviation of the population mean, we can use the standard normal distribution with a mean of [tex]0[/tex] and a standard deviation of [tex]1[/tex].

We want to find the probability that a z-score is between [tex]-1 and 1[/tex], which represents one standard deviation from the mean.

This chance is roughly [tex]0.6827[/tex], as determined by a calculator or a conventional normal distribution table.

In light of this, the probability  that a straightforward random sample of [tex]55[/tex] unemployed people will yield a possession of tiny sums that is close to the population mean in just one week is approximately:

[tex]0.6827*0.1348= 0.0922[/tex](rounded to four decimal places) (rounded to four decimal places)

Therefore , the probability is [tex]0.0922[/tex], or roughly[tex]9.22%[/tex]%.

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Answer:

5x + 12

Step-by-step explanation:

3(x + 2) + 2(x + 3)

= 3x + 6 + 2x + 6 (distributing the coefficients)

= 5x + 12 (combining like terms)

Answer:5x+12

Step-by-step explanation:

3(x+2)= 3x+6

2)x+3) = 2x+6

3x+2x+6+6=5x+12

HOPE I HELPED :)

Answer:

Each bag of spinach weighs 0.833 kg or approximately 833 grams

Step-by-step explanation:

Fiona had 3 kg of spinach. She sold 1/2 kg of spinach to Mrs. Simon, which leaves her with:

3 kg - 1/2 kg = 2.5 kg

Fiona packed the remaining 2.5 kg of spinach equally into 3 bags. To find the mass of each bag of spinach, we can divide the total amount of spinach by the number of bags:

2.5 kg ÷ 3 = 0.833 kg

therefore, Each bag of spinach weighs 0.833 kg or approximately 833 grams

Answer:

C

Step-by-step explanation:

Helping in the name of Jesus.

In Converse: a positive integer is a prime if it has no divisors besides 1 and itself. A positive integer has other divisors besides 1 and itself if it is not a prime; this is Contrapositive. Inverse: A positive integer is not a prime if it has divisors other than 1 and itself.

The conditional statement reads, "A positive integer is a prime only if it has no divisors other than 1 and itself."

In converse: "a positive integer is a prime if it has no divisors other than 1 and itself." This is not always the case, however, as some composite numbers, like 15, have only themselves and the number one as divisors.

Contrapositive: "If a positive integer is not a prime, then it has divisors other than 1 and itself," is the contrapositive. This is true because a prime number cannot have any divisors than itself and the number 1, which means that any number that is not a prime must have other divisors.

Inverse: "A positive integer has divisors other than 1 and itself is not a prime." This is also true since a prime number is defined as having no divisors besides itself and 1. Hence, any number with divisors other than 1 and itself cannot be a prime number.

The converse, contrapositive, and inverse of a conditional statement are typically not logically identical to the original statement and may or may not be true.

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We can conclude after answering the presented question that As a probability result, the likelihood of discovering a package that deviates from the target weight by more than 12 grammes is around 0.4014.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

The mean of the box's overall weight is:

n * mu X = mu Y

With a mean weight of 500/n grammes for each chocolate, we get:

mu Y =n * (500/n) = 500

The standard deviation of the box's total weight is:

sqrt(n) * sigma X = sigma Y

When we substitute the provided values, we get:

= 2 * P(Z > 0.8485)

= 2 * (1 - P(Z < 0.8485))

= 2 * (1 - 0.7993) (1 - 0.7993)

= 0.4014 (rounded to four decimal places) (rounded to four decimal places)

As a result, the likelihood of discovering a package that deviates from the target weight by more than 12 grammes is around 0.4014.

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It appears that the "adjusted balance method" would be best for Judy, as it results in no interest charged for this billing cycle.

What is an interest ?

To calculate the interest charged by each method, we need to determine the average daily balance for the billing cycle, which is calculated as the sum of each day's balance divided by the number of days in the billing cycle.

For the opening balance of $930 that remained for the first 10 days, the average daily balance is:

($930 x 10 days) / 30 days = $310

For the balance of $1480 that remained for the next 10 days, the average daily balance is:

($1480 x 10 days) / 30 days = $493.33

For the balance of $690 that remained for the last 10 days, the average daily balance is:

($690 x 10 days) / 30 days = $230

Part III: Previous balance method

The previous balance method calculates the interest charged on the balance at the end of the previous billing cycle. For Judy's last 30-day billing cycle, the previous balance was $930. Therefore, the interest charged for the previous balance method would be:

$930 x (26%/365) x 30 days = $16.44

Part IV: Adjusted balance method

The adjusted balance method calculates the interest charged on the balance at the end of the billing cycle after subtracting any payments made during the billing cycle. For Judy's last 30-day billing cycle, the adjusted balance would be:

$690 - $790 = -$100

Since Judy made a payment that exceeded her balance, there is no balance on which to charge interest for the adjusted balance method.

Based on these calculations, it appears that the adjusted balance method would be best for Judy, as it results in no interest charged for this billing cycle.

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According to given graph, the equation of the blue graph is [tex]G(x)=(x+3)^3[/tex].

What is graph?

Graph is a mathematical and computer science concept that consists of nodes or vertices, connected by edges to represent the relationships between objects.

Let's plug in x = -3 into both options and see which one gives the y-value of the blue graph at x = -3:

For g(x) = [tex](x+3)^3[/tex], when x = -3, we have g(-3) = ( -3 + 3 )^3 = 0.

For g(x) = [tex](x-3)^3[/tex], when x = -3, we have g(-3) = ( -3 - 3 )^3 = (-6)^3 = -216.

Since the blue graph passes through (-3,0), the correct option is g(x) = [tex](x+3)^3[/tex].

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1. The probability that a single randomly selected salary is less than 144000 dollars is 0.5129. 2. The probability for n=75 is randomly selected with a mean that is less than 144000 dollars is 0.8781.

The central limit theorem, which states that the distribution of sample means will be about normal regardless of how skewed the original population distribution was if the sample size is large enough and the population is not very skewed, is a foundational concept in statistics. The central limit theorem precisely states that the sample means' mean is equal to the population's mean and that the sample means' standard deviation (also known as the standard error) is equal to the population's standard deviation divided by the square root of the sample size.

The z-score us given by the formula:

z = (x - μ) / σ

1. For salary less than 144000 dollars:

z = (144000 - 143000) / 31000 = 0.0323

Using the z-table:

z-score < 0.0323 = 0.5129

Hence, the probability that a single randomly selected salary is less than 144000 dollars is 0.5129.

2. For n = 75:

z = (x - μ) / (σ / √(n))

z = (144000 - 143000) / (31000 / √(75)) = 1.164

Using z-table:

z-score is less than 1.164 = 0.8781.

Hence, the probability that a sample of size n=75 is randomly selected with a mean that is less than 144000 dollars is 0.8781.

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According to the question the value of the test statistic [tex]0.55[/tex]

Data variation from the mean is referred to as "standard deviation." If the standard deviation appears low, the data tend to cluster around the mean; on the other hand, if it appears large, the data are widely spread.

The data deviate from the mean value is indicated by the standard . It is useful for contrasting huge datasets with distinct ranges but the same mean.

The other, though, is without a doubt more spread. The standard deviation reveals the degree of data dispersion. It describes how far away from the mean each number obtained is.

We must compute the t-score, which is represented by: in order to determine the value of the test statistic.

[tex]t = x -[/tex] μ[tex]/(s/\sqrt{n}[/tex]

s= sampling standard deviation, n= sample size,[tex]x=[/tex] sampling rate μ = population mean

[tex]x = 69.5 bpm,[/tex] μ[tex]= 69 bpm, s = 11.4 bpm, n = 154[/tex]

[tex]t = (69.5- 69)/ 11.4/\sqrt{154} \\t = 0.5/ (11.4/12.4)\\t = 0.5/ 0.917\\t = 0.546[/tex]

Therefore the value of the test statistics is [tex]0.55[/tex]

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The value of x in the given equation of the quadrilateral is 20.

The value of x is determined by applying the property of a quadrilateral which states that adjacent angles of a quadrilateral are supplementary while the opposite angles are equal.

(2x + 14) + 126 = 180

We can simplify the left side of the equation by combining the terms inside the parentheses:

2x + 140 = 180

Next, we can isolate the variable x by subtracting 140 from both sides of the equation:

2x = 40

Finally, we can solve for x by dividing both sides of the equation by 2:

x = 20

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The rectangular pyramid's surface area therefore approximates 622.6 in2, which is closest to option 4.

A rectangular is a four-sided polygon in geometry with opposite sides that are parallel and of equal length. It contains four diagonals that cross one another at 90 degree angles. A rectangle is also a rhombus, a rectangle with all sides of equal length, and a parallelogram, a trapezoid with the opposite sides parallel. In the formula A = l w, where l stands for length and w for width, the area of such a rectangle is determined. P = 2l + 2w is a formula that yields the perimeter. In the fields of engineering, design, and architecture, rectangles are used frequently.

given

The Pythagorean theorem can be used to determine the base of the smaller triangle, which equals the pyramid's slant height.

Slant height is equal to (12.5 + 12.9) in (rounded to one decimal place)

Hence, the smaller triangle's area is:

A(small triangular) = 1/2 x 17.8 in, 17.8 in, and 12.9 in, or 115.1 in2.

By summing the areas of all the pyramid's faces, we can determine the overall surface area of the structure:

A (base) + 2 x A (big triangle) + A Equals total surface area (small triangle)

Surface area total = 238 in2 + 2 x 84 in2 + 115.1 in2

Surface area total = 622.1 in2 (rounded to one decimal place)

The rectangular pyramid's surface area therefore approximates 622.6 in2, which is closest to option 4.

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Answer:

L= 18j^5k^10

Step-by-step explanation:

A = L x W

144j⁹k¹⁵=8j⁴k⁵(L)

L= 144j⁹k¹⁵

8j⁴k⁵

L= 18j^5k^10

Answer:

[tex]18 {j}^{5} {k}^{10} [/tex]

Step-by-step explanation:

Given:

[tex]a (area) = 144 {j}^{9} {k}^{15} [/tex]

[tex]w(width) = 8 {j}^{4} {k}^{5} [/tex]

Find: l (length) - ?

.

In order to find the length, we have to divide the area from the width (since a = w × l):

.

[tex]l = \frac{144 {j}^{9} {k}^{15} }{8 {j}^{4} {k}^{5} } = \frac{18 {j}^{9} {k}^{15} }{ {j}^{4} {k}^{5} } = 18 {j}^{5} {k}^{10} [/tex]

Use power properties (when dividing equal bases raised to different powers, power indicators are subtracted)

If good is worth K2 500 cash and it can also be purchased by K200 deposit and monthly instalments of K103.50 for 2 years in hire purchase, the interest charged on hire purchase is K184.

To find the interest charged on the hire purchase, we need to compare the total amount paid through hire purchase to the cash price of the good.

The monthly instalments are K103.50 and the hire purchase term is 2 years, so the total amount paid through hire purchase is:

K103.50/month × 24 months = K2,484

In addition, there is a deposit of K200, so the total amount paid through hire purchase and deposit is:

K2,484 + K200 = K2,684

Since the cash price of the good is K2,500, the interest charged on hire purchase is:

K2,684 - K2,500 = K184

In summary, if someone wants to purchase the good through hire purchase, they need to pay a deposit of K200 and monthly instalments of K103.50 for 2 years. The total amount paid through hire purchase and deposit is K2,684, and the interest charged on hire purchase is K184.

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Answer:

38.4 megabytes for 16 electronic books

Step-by-step explanation:

2.4 megabytes per electronic book

2.4 megabytes x 16 electronic books = 38.4 megabytes

-3 ≤ x ≤ 5 and -4 ≤ y ≤ 2. gives the correct range for the graph.

The correct range for the graph can be determined by looking at the minimum and maximum values of the x and y coordinates of all the points on the graph.

For the given coordinate plane with two line segments, the x-coordinates range from -3 to 5, which means -3 ≤ x ≤ 5. The y-coordinates range from 1 to 2 (on the first segment) and from -4 to 1 (on the second segment), which means -4 ≤ y ≤ 2.

Therefore, the correct range for the graph is -3 ≤ x ≤ 5 and -4 ≤ y ≤ 2.

So, the answer is -3 ≤ x ≤ 5 and -4 ≤ y ≤ 2.

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Answer:

The correct option is C. The best approximate for the given graph is [tex]\sqrt{28}[/tex].

Step-by-step explanation:

From the given graph it is noticed that the point lies between 5 and 6.

Let the square root of x is the best approximate for the given graph.

[tex]5 < \sqrt{x} < 6[/tex]

Taking square on each side.

[tex]5^2 < (\sqrt{x})^2 < 6^2[/tex]

[tex]25 < x < 36[/tex]

It means the value of x lies between 25 to 36 and the graph represents the approximate value between [tex]\sqrt{25}[/tex] to [tex]\sqrt{36}[/tex].

Therefore best approximate for the given graph is [tex]\sqrt{28}[/tex]. Option C is correct.