Find the value of x. Then tell whether the side lengths form a Pythagorean triple.

pt. 2:
Do the following segment lengths form a triangle? If so, is the triangle acute, obtuse, or right?

pls help!!

The volume of the rectangular prism in this problem is given as follows:

84 in³.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for the prism in this problem are given as follows:

3 in, 4 in and 7 in.

Hence the volume of the prism is given as follows:

V = 3 x 4 x 7 = 84 in³.

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In 1997 the population of a small town was 700. If the annual rate of increase is about 0.8% is an example of exponential growth. Then the correct option is A.

Option A depicts exponential development among the applications provided. A tiny town's population is expanding at a 0.8% yearly rate. Because of the increasing population, the rate of rise will be higher each year as the population expands. As a result, an exponential function may be used to depict population expansion.

Option B is not an illustration of exponential development because it depicts projectile motion with a constant velocity.

Skylar spends a certain amount for each ride, therefore Option C depicts linear expenditure and is not an illustration of exponential growth.

Option D depicts exponential decline, in which the number of tree frogs falls by 3% per week. This indicates exponential decay rather than exponential growth since the amount is declining at a rate proportionate to its present value.

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We can conclude here that we have sufficient evidence that the mean score is not equal to 571.

The test statistic here is computed as:

= (589 - 571) / 46/✓26

= 1.9953

Now the p-value for n-1 = 25 degrees of freedom here is computed from the t-distribution tables as:

p = 2P( t25 > 1.9953 ) = 2*0.0285 = 0.0570

0.05 < P-value < 0.1

As the p-value here is 0.0570 < 0.1 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here.

Therefore we can conclude here that we have sufficient evidence that the mean score is not equal to 571.

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The 99% confidence interval estimate of the mean skull width is given as follows:

(126.8 mm, 140.76 mm).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The sample in this problem is given as follows:

128.1, 138.2, 125.7, 132.3, 143.2, 134.7, 138.8, 129.3.

Inserting these values into a calculator, the parameters are given as follows:

[tex]\overline{x} = 133.78, s = 5.64, n = 8[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 8 - 1 = 7 df, is t = 3.5.

The lower bound of the interval is given as follows:

133.78 - 3.5 x 5.64/sqrt(8) = 126.8 mm.

The upper bound of the interval is given as follows:

133.78 + 3.5 x 5.64/sqrt(8) = 140.76 mm.

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The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (41 + 46)/2 = 43.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (32 + 32)/2 = 32

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (50 + 51)/2 = 50.5

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 29

Lower quartile (Q1): 32

Median (Q2): 43.5

Upper quartile (Q3): 50.5

Maximum: 53

Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5

the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

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Answer:

12.   m∠C = 100° and m∠F = 100°

13.   m∠S = 89° and m∠U = 89°

Step-by-step explanation:

Question 12

The two triangles ΔABC and ΔDEF have two of their angles equal:
m ∠A = m ∠D

m∠B = m∠E

Therefore the third angles must be equal:
m∠C = m∠F

m∠C = (4x²)° and m∠F = (3x² + 25)°

Setting these two right side expressions in parentheses equal to each other gives
4x² = 3x² + 25
4x² - 3x² = 25
x² = 25
x = ±√25 = ±5

Ignoring the negative value we get
x = 5

Therefore
m∠C = (4x²)° = (4 · 5²)° = (4 · 25)° = 100°

Since, m∠F = m∠C ,
m∠F  = 100°

But we can double check
m∠F = (3x² + 25)° = (3 · 5² + 25)° = (3 · 25 + 25) = (75 + 25)° = 100°

Question 13

This is similar to question 12

The quadrilateral RSTU is divided into two triangles ΔRST and Δ RUT

We are given
m∠RTS = m∠TRU

m∠TRS = m∠RTU

Therefore the third angle of ΔRST must be equal to the third angle of Δ RUT

In other words,
m∠S= m∠U

Plugging in the expressions for each of these angles we get

(5x - 11)° = (4x + 9)°

Set the expressions inside parens equal to each other and solve for x:
5x - 11 = 4x + 9

5x - 4x - 11 = 9    (subtract 4x from both sides)
x - 11 = 9

x = 11 + 9  (add 11 both sides)

x = 20

m∠S= (4x + 9)° = (4 · 20 + 9)° = (80 + 9)° = 89°

Therefore m∠RUT is also 89°

but we can double-check
m∠U= (5x - 11)° = (5 · 20 - 11)° = (100 - 11)° = 89°

The missing test scores were both 8.3. The standard deviation for the test scores was 21.66. The difference between the harmonic mean and the geometric mean of the 12 students was 3.26.

The sum of the scores of the 10 students is 63. The average score of the 10 students is

(63 + x + x) / 12 = 8.3

Solving for x, we get

x = 8.3 * 12 - 63 - 13.8 - 10.4

x = 100.6 - 63 - 13.8 - 10.4

x = 13.4

Therefore, each missing script has a score of 13.4.

To find the standard deviation, we first need to find the variance

Find the mean

(2.7 + 6.3 + 4.1 + 6.4 + 3.5 + 4.7 + 13.8 + 79 + 12.1 + 10.4 + 13.4 + 13.4) / 12 = 11.0

Subtract the mean from each score and square the result

(2.7 - 11)², (6.3 - 11)², (4.1 - 11)², (6.4 - 11)², (3.5 - 11)², (4.7 - 11)², (13.8 - 11)², (79 - 11)², (12.1 - 11)², (10.4 - 11)², (13.4 - 11)², (13.4 - 11)²

Add up the squared differences

5697.36

Divide by the number of scores minus one, to get the variance

5697.36 / 11 = 517.03

Take the square root of the variance to get the standard deviation

√(517.03) = 22.76

Therefore, the standard deviation for the test scores is 22.76.

The harmonic mean is calculated by dividing the number of scores by the sum of the reciprocals of the scores, and then taking the reciprocal of the result

12 / (1/2.7 + 1/6.3 + 1/4.1 + 1/6.4 + 1/3.5 + 1/4.7 + 1/13.8 + 1/79 + 1/12.1 + 1/10.4 + 1/13.4 + 1/13.4) = 5.04

The geometric mean is calculated by taking the product of all the scores, and then taking the nth root of the product, where n is the number of scores

(2.7 * 6.3 * 4.1 * 6.4 * 3.5 * 4.7 * 13.8 * 79 * 12.1 * 10.4 * 13.4 * 13.4)^(1/12) = 8.30

Therefore, the difference between the harmonic mean and the geometric mean is

5.04 - 8.30 = -3.26

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An equation that can be used to describe the relationship between x and y shown in the graph is: B. y = 3x - 6

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 0)/(4 - 2)

Slope (m) = 6/2

Slope (m) = 3

At data point (2, 0) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 3(x - 2)  

y = 3x - 6

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The measure of angle D is 48.59 degrees where angle D is acute.

For finding the measure of angle when a trigonometric ratio is given, we use inverse trigonometric functions.

For sine there lies arcsin, for cos, there lies arccos and so on.

Thus, sinD=0.75

∠D = sin⁻¹(0.75)

∠D = 48.59

But since ∠D is acute, thus we have ∠D = 48.59

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The Median  of the distribution above is 2.5.

The order the values of the numbers from smallest to largest are:

0, 1, 1, 2, 2, 3, 3, 4, 10, Q

To find the median of the data set, that is the middle value when the data is ordered, one need to average of the two middle values, and the middle values are 2 and 3:

Hence:

Median = (2 + 3)/2

            = 2.5

The interquartile range IQR is seen as the range in values that is obtained from the first quartile Q1 to the third quartile Q3 and it can be gotten from the IQR by removing Q1 from Q3.

IQR = Q3 - Q1

Note that the first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half. So the value  are:

Q1 = 1

Q3 = 4

IQR = Q3 - Q1

= 4 - 1

= 3

To get the range, it will be:

10 - 0

= 10

To explain, note that the range and IQR tells different areas of the data set. The range tells us the way that the data spread out and the IQR measures the spread of the middle 50% of the above data.

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Answer:

To calculate the accumulated depreciation using the MACRS method, you will need to use Table 17-1 and Table 17-2 from your textbook. Here are the steps:

1. Determine the depreciation rate for the computer system based on its class life. According to Table 17-1, the class life for computers is 5 years. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method (which is used in the first year) is 40%. Therefore, the depreciation rate for the computer system in year 1 is 40%.

2. Calculate the depreciation for year 1 using the depreciation rate and the cost of the asset. The depreciation for year 1 is the cost of the asset multiplied by the depreciation rate, which gives us:

Depreciation for year 1 = $49,500 x 40% = $19,800

3. Determine the depreciation rate for year 2. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method in year 2 is 32%. Therefore, the depreciation rate for the computer system in year 2 is 32%.

4. Calculate the depreciation for year 2 using the depreciation rate and the remaining book value of the asset. The remaining book value of the asset after year 1 is the cost of the asset minus the depreciation for year 1, which gives us:

Remaining book value after year 1 = $49,500 - $19,800 = $29,700

Depreciation for year 2 = $29,700 x 32% = $9,504

5. Determine the depreciation rate for year 3. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method in year 3 is 19.2%. Therefore, the depreciation rate for the computer system in year 3 is 19.2%.

6. Calculate the depreciation for year 3 using the depreciation rate and the remaining book value of the asset. The remaining book value of the asset after year 2 is the cost of the asset minus the depreciation for year 1 and year 2, which gives us:

Remaining book value after year 2 = $29,700 - $9,504 = $20,196

Depreciation for year 3 = $20,196 x 19.2% = $3,880.35

According to the information, the vertex at the top left of the parallelogram is (4, 8.25). Thus, the other two vertices of the parallelogram are (2, 5), (9, 5), (7, 8), and (4, 8.25).

To find the vertex of the parallelogram we can use the point-slope form of a line: y - y1 = m(x - x1), where,

For the side sloping up from left to right, we can use the point (2, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:

Simplifying, we get:

To find the point where this line intersects the top side of the parallelogram, we can use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (2, 5) is 5 units away from the intersection point in the x-direction, so we can add 5 to the x-coordinate to find the intersection point. Plugging in x = 7 into the equation above, we get:

Therefore, the vertex at the top right of the parallelogram is (7, 8).

For the side sloping down from left to right, we can use the point (9, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:

Simplifying, we get:

To find the point where this line intersects the top side of the parallelogram, we can again use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (9, 5) is 5 units away from the intersection point in the x-direction, so we can subtract 5 from the x-coordinate to find the intersection point. Plugging in x = 4 into the equation above, we get:

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pat a

π is approximately 3.1 to the nearest tenth.

√6 is approximately 2.4 to the nearest tenth.

2√6 is approximately 4.8 to the nearest tenth.

√7 is approximately 2.6 to the nearest tenth.

(b)

Ordering from least to greatest:

An approximation is described as  anything that is similar, but not exactly equal, to something else.

A number can be approximated by rounding off and  a calculation can be approximated by rounding the values within it before performing the operations .

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a. WXYZ is a kite

b.In the kite mWQZ = 90° because XZ bisects WY

c. WY = 24 mm because WQ = QY

A kite is a quadrilateral that has two pairs of consecutive equal sides and perpendicular diagonals.

a. From the figure, we see that WXYZ is a kite

b. To determine mWQZ, we use the property of a kite which says that the diagonals of a kite intersect at right angles. Since XZ and WX are the diagonals of the kite, they thus intersect at right angles.

Since a right angle is 90° and the angle of intersection is mWQZ, thus mWQZ = 90°

So, mWQZ = 90° because XZ bisects WY

c. To determine WY, we know that WY is the shorter diagonal of the kite. Since one of the properties of a kite says that the longer diagonal bisects the shorter diagonal. So, XZ bisects WY. So, WY = WQ + QY. Since XZ bisects WY, WQ = QY.

So, WY = WQ + QY

= QY + QY

= 2QY

= 2(12 mm)

= 24 mm

So, WY = 24 mm because WQ = QY

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The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

From the question, we have the following parameters that can be used in our computation:

John drove from here to San Antonio which is 180 miles away in 3 hours.

This means that

Distance = 180 miles

Time = 3 hours

Using the above as a guide, we have the following:

Speed = Distance/Time

Substitute the known values in the above equation, so, we have the following representation

Speed = 180/3

Evaluate

Speed = 60

Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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The missing integer on the number line below is given as follows:

-7.

The missing integer on the number line is obtained applying the proportions in the context of the problem.

The vertical trace is the mean of -10 and -5, hence it is given as follows:

(-10 - 5)/2 = -7.5.

(we obtain the mean of the two numbers as the middle trace is exactly halfway between these two values).

The missing integer on the number line is the integer number exactly to the right(greater) of -7.5, hence it is of:

-7.

(nearest integer that is greater than -7.5).

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The measure of the hypotenuse of the right-angle triangle is 53.21 feet.

Given that:

Perpendicular, P = 50 feet

Angle, Ф = 70°

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The measure of the hypotenuse of the right-angle triangle is calculated as,

sinФ = P/H

sin 70° = 50 / x

x = 53.21 feet

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Answer:

A linear function is a function that produces a straight line when it is graphed. The equation of a linear function is of the form y = mx + b, where m is the slope and b is the y-intercept.

Looking at the four tables, we can calculate the slopes of the lines that would be produced by each table. The slope is given by the change in y divided by the change in x.

For the first table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.

For the second table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.

For the third table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.

For the fourth table, the change in y is 2, and the change in x is 1. Therefore, the slope is 2/1 = 2.

Only the first three tables have the same slope, which is 1. Therefore, only the first three tables represent a linear function.

The answers are explained in the solution.

Given are right triangles, we need to find the missing lengths,

Here we will use Pythagoras theorem,

Hypotenuse² = base² + perpendicular²

1) x² = 5²+2²

x = √25+4

x = √29

2) 6² = x²+4²

x = √36-16

x = √26

3) 25² = x² + √24²

x = √625-576

x = √49

x = 7

Only the 3rd is following the rule of Pythagorean triplet.

Part 2 = The Triangle Inequality :-

The Triangle Inequality (theorem) says that in any triangle, the sum of any two sides must be greater than the third side.

a) 2, 4, 8

2+4 = 6 < 8 [not a triangle]

b) 5, 6, 7

5+6 = 11 > 7

6+7 = 13 > 5

7+5 = 12 > 6

Therefore, it is forming a triangle,

7² = 49

5²+6² = 36+25 = 61

∵ 7² < 5²+6²

Therefore, the triangle is an acute triangle.

c) 6, 8, 15

6 + 8 = 14 < 15 [not a triangle]

d) 9, 12, 15

9 + 12 = 21 > 15

12 + 15 = 27 > 9

15 + 9 = 24 > 12

Therefore, it is forming a triangle,

15² = 225

9²+12² = 81 + 144 = 225

∵ 15² = 9²+12²

Therefore, the triangle is a right triangle.

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Answer: To find the average speed, we need to use the formula:

average speed = total distance / total time

We can first calculate the total distance, which is:

total distance = 900 km + 3000 km + 400 km + 15 km = 3315 km

To calculate the total time, we need to find the time taken for each leg of the journey:

time taken for train journey = distance / speed = 900 km / 60 km/hour = 15 hours

time taken for boat journey = distance / speed = 3000 km / 25 km/hour = 120 hours

time taken for plane journey = distance / speed = 400 km / 350 km/hour = 1.14 hours

time taken for taxi journey = distance / speed = 15 km / 25 km/hour = 0.6 hours

Therefore, the total time taken for the entire journey is:

total time = 15 hours + 120 hours + 1.14 hours + 0.6 hours = 137.74 hours

Now we can calculate the average speed:

average speed = total distance / total time = 3315 km / 137.74 hours ≈ 24.05 km/hour

Therefore, the average speed for the entire distance is approximately 24.05 km/hour.

The reason why none of the methods match the probability of landing on the B section of the spinner exactly is due to various assumptions, limitations, and uncertainties involved in the measurement and calculation process.

We have,

When Andre measures the spinner and finds that the B section takes up 1/4 of the circle, it means that the B section has an angle measure of 90 degrees out of a total of 360 degrees in a circle.

Now, if we try to calculate the probability of landing on the B section using different methods, we might get slightly different results for several reasons.

Firstly,

The probability of landing on a certain section of the spinner depends on the assumption that the spinner is perfectly balanced and that all sections have an equal chance of being landed on.

However,

In reality, the spinner might not be perfectly balanced, or there might be other factors that affect the outcome, such as air resistance or the force with which the spinner is spun.

Secondly,

Different methods of calculating the probability might make different assumptions or use different techniques that can affect the result.

For example, if we use the classical probability approach, we assume that all outcomes are equally likely, but in the case of a spinner, this might not be the case due to factors such as the weight or shape of the sections.

On the other hand, if we use the relative frequency approach, we base the probability on past data or observations, which might not necessarily reflect the current situation or the true underlying probabilities.

Therefore,

While the probability of landing on the B section might be close to 1/4, none of the methods will match this probability exactly due to various assumptions, limitations, and uncertainties involved in the measurement and calculation process.

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(i) [tex]\lim_{x \to \pi/3}[/tex] f(x) = 1 + √3.

(ii) [tex]\lim_{x \to \frac{\pi}{4}} f(x)[/tex] does not exist.

For λ = 2.5, the function f(x) will be continuous at x = 0.

Given the function is,

f(x) = 1.5, when x = 0

    = 1 -2 sin x, when x < π/4

    = 1 + 2 sin x, when x > π/4

    = 1 + (sin λx/sin 5x)

Now,

[tex]\lim_{x \to \pi/3}[/tex] f(x) = [tex]\lim_{x \to \pi/3}[/tex] (1 + 2 sin x) [Since, π/3 > π/4]

                    = 1 + 2 sin (π/3)

                    = 1 + 2√3/2 = 1 + √3

Hence, [tex]\lim_{x \to \pi/3}[/tex] f(x) = 1 + √3.

Now left hand limit is,

[tex]\lim_{x \to \frac{\pi^+}{4}}[/tex] f(x) = [tex]\lim_{x \to \frac{\pi^+}{4}}[/tex] (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2

and right hand limit is,

[tex]\lim_{x \to \frac{\pi^-}{4}}[/tex] f(x) = [tex]\lim_{x \to \frac{\pi^-}{4}}[/tex] (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2

Since left hand limit and right hand limit are not equal so value of [tex]\lim_{x \to \frac{\pi}{4}} f(x)[/tex] does not exist.

[tex]\lim_{x \to 0}[/tex] f(x) = [tex]\lim_{x \to 0}[/tex] (1 + (sin λx/sin 5x)) = 1 + [tex]\lim_{x \to 0}[/tex] ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5

Since f(x) is continuous at x = 0.

So, [tex]\lim_{x \to 0}[/tex] f(x) = f(0)

1 + λ/5 = 1.5

λ/5 = 1.5 - 1 = 0.5

λ = 2.5

Hence the value of λ will be 2.5.

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Answer:

12

Step-by-step explanation:

4(5)-8

20-8

12

T-Mobile charges a base fee of $15 per month plus $0.05 for each minute. 300 minutes long would you need to call for them to charge the same amount.

Given that,

T-Mobile charges a base fee of $15 per month plus $0.05 for each minute you are on the phone for any long-distance call, while Verizon has a basic rate of only $10 per month but charges $0.10 for long-distance calls.

We have to find how long would you need to call for them to charge the same amount.

We can write the equation as

15+0.05x=0.10x

0.05x-0.10x=-15

-0.05x=-15

0.05x=15

x=15/0.05

x=300 minutes

Therefore, 300 minutes long would you need to call for them to charge the same amount.

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 complete question:

For any long-distance call T-Mobile charges a base rate of $15 per month plus $0.05 a minute

that you are on the phone, while Verizon charges a base rate of only $10 per month, but charges

$0.10 per minute for long distance calls. Write the equation that represents the total cost for one month of long distance calls for each company, where y is total cost and x is the amount of minutes used:

T-Mobile:

Verizon:

Using an algebraic method, determine how many minutes the two plans will cost the same.

The probability of getting a number beginning and ending with even digits is 8/120= 1/15

There are six digits to choose from, but you're only taking three at a time, so the number of such numbers is

6 x 5 x 4 = 120

The first and last digits can only be even if the number takes the one of the forms "2 _ 8" or "8 _ 2".

The middle number can be any of the remaining four, so there is a total of eight such numbers.

This means the probability of getting a number beginning and ending with even digits is 8/120= 1/15

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Answer:

C. The value of a car at the end of a year is 8 percent less than the value at the beginning of the year.

Step-by-step explanation:

An exponential function models situations in which a quantity grows or decays by a constant percentage or factor over equal intervals of time.

Let's analyze each situation:

A. The number of fish in a tank increases by five per month.

This situation represents a constant increase (addition) of fish every month. It can be modeled by a linear function, not an exponential function.

B. The number of people in a city increases by 100 every year.

This situation also represents a constant increase (addition) in the number of people per year. It can be modeled by a linear function, not an exponential function.

C. The value of a car at the end of a year is 8 percent less than the value at the beginning of the year.

This situation represents a constant percentage decrease (multiplication) in the value of the car each year. It can be modeled by an exponential function (e.g., V(t) = V_0 * (1 - 0.08)^t, where V(t) is the value of the car after t years and V_0 is the initial value of the car).

D. The value of a phone drops $100 per year.

This situation represents a constant decrease (subtraction) in the value of the phone per year. It can be modeled by a linear function, not an exponential function.

The value of the x-coordinate of point W is -3.5.

Coordinate geometry is the study of geometry using the points in space.

From the graph, the location of the point W is (-3.5, 1.5).

In the coordinate plane, the x-coordinate is always given first, followed by the y-coordinate, in the form (x, y). Therefore, point W is located at -3.5 on the x-axis and 1.5 on the y-axis.

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567

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The complete question is given below.

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.