100 Points! Geometry question. Photo attached. Find x and y in the right triangle. Please show as much work as possible. Thank you!

Given the relationship, 9r + 8t = 9, the relationship as a function r = f(t) will be (9 - 8t) / 9.

The relationship 9r + 8t = 9 as a function r = f(t), one is needed to isolate the variable r first on one side of the equation.

Taking with the original equation:

9r + 8t = 9

Subtract 8t from both sides in order to isolate the term with r:

9r = 9 - 8t

Divide both sides by 9 in order to solve for r:

r = (9 - 8t) / 9

Therefore, the relationship 9r + 8t = 9 can be written as the function:

r = (9 - 8t) / 9.

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Your question seems incomplete, the probable complete question is:

Consider the relationship 9r + 8t = 9. a. Write the relationship as a function r = f(t).

The value of x in triangle STU is given as follows:

b) 8.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

Applying the Pythagorean Theorem for this problem, the value of x is obtained as follows:

x² + 15² = 17²

x² = 17² - 15²

x² = 64.

x = 8.

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Answer:

0.15 flowers/ ft²

Step-by-step explanation:

area = 12 X 18 = 216.

population density = population/area

= 32/216

= 0.148

= 0.15 flowers/ ft²

Answer:

A. 0.15 flowers/ft²

Step-by-step explanation:

The population density of flowers is the number of flowers per square foot.

To find the population density, we need to know the area of the garden and the number of flowers.

The area of the garden is 12 feet*18 feet =216 square feet.

The number of flowers is 32.

The population density is 32flowers/216square feet = 0.15 flowers/ft².

Therefore, the answer is (A).

The angles in the triangle are as follows:

∠X = 58°

Exterior angle of ∠X = 122°

The sum of angles in a triangle is 180 degrees. The sum of the exterior angle and the interior angle of a triangle is 180 degrees.

Therefore, let's find the measure of ∠X in the triangle XYZ.

Hence,

m∠X = (2g + 16)°

The exterior angle of m∠X  measures 4g + 38 degrees.

Hence,

2g + 16 + 4g + 38 = 180

6g + 54 = 180

6g = 180 - 54

6g = 126

g = 126 / 6

g = 21

Therefore,

∠X = (2(21) + 16)°  = 42 + 16 = 58 degrees

Exterior angle of ∠X =  4(21) + 38 = 84 + 38 = 122

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Answer:

Aprox: 465.4 ms/2

Step-by-step explanation:

To find the magnitude of the acceleration the engine must produce, we'll break down the missile's motion into its horizontal and vertical components.

Given:

Initial velocity (V₀) = 1810 m/s

Launch angle (θ) = 20.0°

Target distance (d) = 19,500 m

Target direction (φ) = 32.0°

Time of flight (t) = 9.20 s

First, let's find the horizontal and vertical components of the missile's initial velocity (V₀x and V₀y).

V₀x = V₀ * cos(θ)

V₀y = V₀ * sin(θ)

V₀x = 1810 m/s * cos(20.0°) ≈ 1712.4 m/s

V₀y = 1810 m/s * sin(20.0°) ≈ 618.8 m/s

Now, let's find the horizontal and vertical displacements (dx and dy) of the missile using the time of flight (t) and the target distance (d).

dx = d * cos(φ)

dy = d * sin(φ)

dx = 19,500 m * cos(32.0°) ≈ 16,402.8 m

dy = 19,500 m * sin(32.0°) ≈ 10,236.8 m

Next, let's calculate the acceleration needed in the x-direction (ax) and y-direction (ay) to cover the horizontal and vertical displacements in the given time.

ax = (2 * dx) / t²

ay = (2 * dy) / t²

ax = (2 * 16,402.8 m) / (9.20 s)² ≈ 391.7 m/s²

ay = (2 * 10,236.8 m) / (9.20 s)² ≈ 257.7 m/s²

Finally, to find the magnitude of the acceleration, we can use the Pythagorean theorem:

acceleration magnitude (a) = √(ax² + ay²)

a = √(391.7 m/s²)² + (257.7 m/s²)² ≈ 465.4 m/s²

Therefore, the magnitude of the acceleration that the engine must produce is approximately 465.4 m/s².

In a math class with 19 students, on a day when a test and an assignment were given, there were 10 students who passed the test and 14 students who completed the assignment.

In a math class with 19 students, a test and an assignment were given on the same day.

Out of the 19 students, 10 of them passed the test and 14 students completed the assignment.

This information allows us to analyze the performance and completion rate of the students in the class.

Firstly, we can determine that there are at least 10 students who demonstrated a satisfactory level of understanding and knowledge in the subject matter, as they successfully passed the test.

This indicates that approximately 52.63% (10 out of 19) of the students achieved a passing grade on the test.

Furthermore, we know that 14 students completed the assignment.

This implies that these students fulfilled the requirements and submitted the necessary work within the given timeframe.

Consequently, we can deduce that approximately 73.68% (14 out of 19) of the students in the class completed the assignment.

It's worth noting that there may be overlap between the students who passed the test and those who completed the assignment, as well as students who did both.

However, without additional information, we cannot determine the exact number of students who passed the test, completed the assignment, or did both.

This data provides insight into the performance and diligence of the students in the math class, indicating the proportions of students who met the criteria for passing the test and completing the assignment.

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The missing side of the right triangle is √57

To find the missing side of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Let's assume the missing side is represented by the variable x.

According to the Pythagorean theorem:

(2√6[tex])^2 + x^2 = 9^2[/tex]

Simplifying, we have:

[tex]4 \times 6 + x^2 = 81\\24 + x^2 = 81\\x^2 = 81 - 24\\x^2 = 57[/tex]

Taking the square root of both sides, we get:

x = √57

Thus, the missing side of the right triangle is √57

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Answer:

The sum of 33, 78, 23, 21, 98, and 32 is 325.

The length of each side of the square base should be approximately 244.95 meters when rounded to the nearest hundredth.

To calculate the length of the sides of the square base of the pyramid, we can use the formula for the volume of a square pyramid:

V = (1/3) * (side length)^2 * height

Given that the volume of the pyramid is 2,000,000 m³ and the height is 100 m, we can substitute these values into the formula:

2,000,000 = (1/3) * (side length)^2 * 100

To isolate the side length, we can rearrange the equation:

(side length)^2 = (2,000,000 * 3) / 100

(side length)^2 = 60,000

Taking the square root of both sides, we find:

side length ≈ √60,000

side length ≈ 244.95

Therefore, the length of each side of the square base should be approximately 244.95 meters when rounded to the nearest hundredth.

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Beth and Kelly were on vacation for 6 days.

Let's assume that Beth and Kelly were on vacation for "x" days.

For Beth:

The cost per day for dog sitting at Rover Sleepover is $24.50.

Beth also paid a fee of $90.50 for food and cleaning.

So the total cost for Beth's dog sitting can be expressed as:

Total cost for Beth = (Cost per day × Number of days) + Cleaning fee

Total cost for Beth = ($24.50 × x) + $90.50

For Kelly:

The cost per day for dog sitting at Pet Palace is $32.

Kelly also paid a fee of $45.50 for cleaning.

So the total cost for Kelly's dog sitting can be expressed as:

Total cost for Kelly = (Cost per day × Number of days) + Cleaning fee

Total cost for Kelly = ($32 × x) + $45.50

Since both Beth and Kelly spent the same total amount of money, we can set up an equation:

($24.50 × x) + $90.50 = ($32 × x) + $45.50

Simplifying the equation, we get:

$24.50x + $90.50 = $32x + $45.50

Moving the variables to one side and constants to the other side:

$32x - $24.50x = $45.50 - $90.50

Combining like terms, we have:

$7.50x = $45

Dividing both sides of the equation by $7.50:

x = $45 / $7.50

x = 6

Therefore, Beth and Kelly were on vacation for 6 days.

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Answer:

The average speed of a particle over a time interval is defined as the total distance traveled divided by the time elapsed. In this case, the average speed of the particle over the time interval [0,4] is represented by options 2 and 3. Option 2 represents the change in position over the time interval [0,4] divided by the time elapsed. Option 3 represents the slope of the secant line connecting the points (0,s(0)) and (4,s(4)), which is equivalent to the average rate of change of position over the time interval [0,4].

the correct answers are, 2 and 3

The complete table for the function are

x  -2  -1  1  3

y  2   3  5  7

The graph is added as an attachment

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

The function equation and the incomplete table of values

This is given as

y = x + 4

From the table, the missing values are at

x = -2, x = -1, 1 and x = 3

So, we have

y = -2 + 4 = 2

y = -1 + 4 = 3

y = 1 + 4 = 5

y = 3 + 4 = 7

The graph is added as an attachment

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The value of an automobile company's stock fell 5 points over the last month.  The integer that represents the change in the stock's value is -5.

In the context of stock market performance, positive values typically indicate an increase in the stock's value, while negative values indicate a decrease. In this case, since the stock's value fell by 5 points, we assign a negative sign to represent the change.

By convention, negative numbers are used to represent decreases or losses, while positive numbers represent increases or gains. When the stock's value decreases, it is common to use negative integers to signify the change.

In this scenario, a decrease of 5 points is denoted by the negative sign (-) followed by the numerical value 5. Therefore, the integer -5 represents the change in the stock's value.

Using this notation helps provide clarity and consistency in understanding the direction and magnitude of changes in stock prices. It allows investors, analysts, and market participants to communicate and interpret market movements accurately and effectively.

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Teresa's result of 95 heads is slightly higher than what she would have expected, it is still reasonably close to the expected value based on the theoretical probability of getting a head when flipping a fair coin.

Teresa's result of 95 heads in 150 coin flips is slightly higher than what she would have expected if the theoretical possibility of getting a head when flipping a coin was exactly 1/2.

When flipping a fair coin, the probability of getting a head is indeed 1/2, and the probability of getting a tail is also 1/2. Therefore, if we assume that the coin is fair and unbiased, we can use the concept of expected value to determine what Teresa would have expected.

The expected value of a single coin flip can be calculated as follows:

Expected value = (Probability of an outcome) * (Value of the outcome)

In this case, the probability of getting a head is 1/2, and the value of getting a head is 1 (since we are interested in the number of heads). Therefore, the expected value of a single coin flip is:

Expected value = (1/2) * 1 = 1/2

To determine what Teresa would have expected in 150 coin flips, we can multiply the expected value of a single coin flip by the number of flips:

Expected number of heads = (Expected value) * (Number of coin flips)

Expected number of heads = (1/2) * 150 = 75

So, if Teresa had flipped the coin 150 times and the coin was fair, she would have expected to get approximately 75 heads.

However, Teresa obtained 95 heads in her actual experiment. This result is slightly higher than the expected value of 75 heads. It's important to note that, due to the inherent randomness of coin flips, there will always be some variation between the expected and actual results. Flipping a coin 150 times is a relatively small sample size, and it is within the realm of possibility to deviate from the expected outcome.

Therefore, while Teresa's result of 95 heads is slightly higher than what she would have expected, it is still reasonably close to the expected value based on the theoretical probability of getting a head when flipping a fair coin.

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Answer: D = 100π square units

Step-by-step explanation:

The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle.

In this case, we have a circumference of 20π units, so we can set up the equation as follows:

20π = 2πr

To find the radius, we can divide both sides of the equation by 2π:

r = (20π) / (2π)

Simplifying further:

r = 10

Now that we have the radius, we can calculate the area of the circle using the formula A = πr^2:

A = π * (10)^2

A = π * 100

A = 100π

Answer: Your line should start at (-1,6) then it should cross (0,0) so, straight down and a small curve. Then you should be at (0 -2), continue the small curve you made. DO not make it a parabola. it is basically just a straight line down, then a really long curve. Make sure you make the curve go across the entire graph.

The correct system of inequalities is 1500x + 1250y ≥ 175,000 and x + y ≥ 200, option A is correct.

We have two carriers: land carriers and air carriers.

The land carriers can transport 1500 pieces of mail per load, and the air carriers can transport 1250 pieces of mail per load.

The loading equipment at the distribution center can handle up to 200 loads per day.

To represent this situation using a system of inequalities, we can define the variables x and y as the number of loads by land carriers and air carriers, respectively.

The first inequality, 1500x + 1250y ≥ 175,000, represents the total number of pieces of mail transported per day.

The second inequality, x + y ≥ 200, represents the total number of loads.

Hence,  the correct system of inequalities is 1500x + 1250y ≥ 175,000 and x + y ≥ 200.

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The  names of the siblings from shortest to longest time are:

Rafael= 75min = 1 hour and 15 minutes.

Leanne= 1 hour and 25 minutes

Ray= 1 3/4 =  1 hour and 45 minutes.

To be able to compare 1 hour and 25 minutes with  1 3/4 (1.75 hours), one need convert the minutes to hours. 1 hour is equal to 60 minutes, so 1 hour and 25 minutes is equivalent to 1.42 hours.

1.42 hours is smaller than 1.75 hours. hence Ray has the longest time.

So according to the given information, note that:

Hence, the siblings' names listed from shortest to longest time are Rafael, Leanne, and Ray.

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The function g(x) in the context of this problem is given as follows:

A. [tex]g(x) = \sqrt[3]{x + 4} + 3[/tex]

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

[tex]f(x) = \sqrt[3]{x}[/tex]

The translated function was moved 4 units left and 3 units up, hence the function is defined as follows:

[tex]g(x) = \sqrt[3]{x + 4} + 3[/tex]

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Susan would have to repay her parents $8,454.96 at the end of 13 months to clear the outstanding balance using the declining balance method.

To calculate the outstanding balance at the end of 13 months, we need to use the declining balance method. This method involves applying the interest rate to the remaining balance after each repayment.

First, let's calculate the interest for the first 4 months. The interest for this period can be calculated using the formula: Interest = Principal × Rate × Time. In this case, the principal is $18,500, the rate is 5.00% per year (or 0.05), and the time is 4 months (or 4/12 years). Thus, the interest for the first 4 months is $18,500 × 0.05 × (4/12) = $308.33.

Next, we subtract the repayment made after 4 months ($5,300) from the outstanding balance ($18,500) and add the interest for the first 4 months ($308.33). This gives us a new outstanding balance of $18,500 - $5,300 + $308.33 = $13,508.33.

Now, let's calculate the interest for the period between 4 and 10 months. The principal remains the same ($13,508.33), the rate is still 5.00% per year (or 0.05), and the time is 6 months (or 6/12 years). Therefore, the interest for this period is $13,508.33 × 0.05 × (6/12) = $337.71.

Subtracting the repayment made after 10 months ($3,800) from the outstanding balance ($13,508.33) and adding the interest for the period gives us a new outstanding balance of $13,508.33 - $3,800 + $337.71 = $10,045.04.

Finally, to determine the last payment required to clear the outstanding balance at the end of 13 months, we subtract the new outstanding balance ($10,045.04) from the principal ($18,500). The last payment is therefore $18,500 - $10,045.04 = $8,454.96.

Therefore, Susan would have to repay her parents $8,454.96 at the end of 13 months to clear the outstanding balance using the declining balance method.

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The statement is saying that a class R is considered an n-ary relation if all its elements are n-tuples.

The symbol R⊂Vⁿ represents that the class R is a subset of Vⁿ, which is the class of all n-tuples.

Here, Vⁿ represents the set of all possible n-tuples, and R is a subset of that set.

The notation Cⁿ is used to denote the set of n-tuples with elements from the set C, and C×D represents the Cartesian product of sets C and D.

The statement defines an n-ary relation as a class where all its elements are n-tuples, and it establishes a connection between the class R and the set of all n-tuples (Vⁿ).

The notation Cⁿ and C×D are used to describe sets of n-tuples and Cartesian products, respectively, in a mathematical context.

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12) Volume of semi - sphere = 261.67 km³

13) Volume of semi - sphere = 8574.29 feet³

We have to given that;

12) Radius of sphere = 5 km

13) Radius of sphere = 16 feet

Since, We know that;

Volume of sphere = 4/3 πr³

Hence, We get;

Volume of semi - sphere = 2/3πr³

12) Here, Radius of sphere = 5 km

Volume of semi - sphere = 2/3πr³

Volume of semi - sphere = 2/3 × 3.14 × 5³

Volume of semi - sphere = 261.67 km³

13) Here, Radius of sphere = 16 feet

Volume of semi - sphere = 2/3πr³

Volume of semi - sphere = 2/3 × 3.14 × 16³

Volume of semi - sphere = 8574.29 feet³

Thus, We get;

12) Volume of semi - sphere = 261.67 km³

13) Volume of semi - sphere = 8574.29 feet³

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Answer:

x intercept at( -2)

y intercept at (4)

The x-intercept and the y-intercept are -2 and 4 respectively.

The X-intercept is the point where the line of an equation intersects the X-axis. While y-intercept is the point where the line of an equation intersects the Y-axis. Here, the X-axis is the horizontal axis, and the Y-axis is the vertical axis.

Since the given graph shows the line intersecting the X-axis i.e. the horizontal axis at -2, the x-intercept of the line would be -2. Whereas, since the line intersects the Y-axis at 4, the y-intercept is 4. The points that show these intercepts are (-2,0) for the x-intercept and (0,4) for the y-intercept.

∴ The intercepts are -2,4 respectively.

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The complete equation is x² + 1/2x -2 = 2 + 2

The given equation can be rewritten as:

x² + (1/2)x + () = 2 + ()

Since the equation involves two missing values, let's consider them one by one.

Solve for the first missing value indicated by (_):

To find the missing value indicated by (_), we equate the quadratic equation to 2:

x² + (1/2)x + (_) = 2

Comparing this with the standard form of a quadratic equation,

ax² + bx + c = 0, we have:

a = 1, b = 1/2, c = (_ - 2)

Using the quadratic formula, x = (-b ± √(b²- 4ac)) / (2a), we can substitute the values:

x = (-(1/2) ± √((1/2)² - 4(1)(_-2))) / (2(1))

x = (-1/2 ± √(1/4 + 8(1)(_-2))) / 2

x = (-1/2 ± √(1/4 + 8(_ - 2))) / 2

Therefore, the first missing value is represented by (_ - 2).

Solve for the second missing value indicated by (_):

To find the missing value indicated by (_), we equate the constant term to 2:

(_) = 2

This indicates that the second missing value is equal to 2.

Putting it all together, the solution to the equation x² + (1/2)x + _ = 2 + _ is:

x = (-1/2 ± √(1/4 + 8(_ - 2))) / 2

with (_ - 2) representing the first missing value, and the second missing value is 2.

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The value of x with the answers in simplest radical form is 18.

We are given that;

The right triangles with dimension

Now,

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2

1. 14^2+14^2=x^2

196+196=x^2

x^2=392

x=19.7

2. x^2+X^2=12^2

2x^2=144

x^2=72

x=8.48

3. 9[tex](\sqrt{2} )^2[/tex]+9[tex]\sqrt{2})^2[/tex]=x^2

162+162=x^2

324=x^2

x=18

Therefore, by pythagoras theorem the answer will be 18.

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Answer:

  (a)  0.75

Step-by-step explanation:

You want the 10th term of the geometric sequence with a1 = 384 and a7 = 6.

The equation for the n-th term can be written ...

  an = a1·b^(n-1)

Using a1 = 384, we can find b from ...

  a7 = 6 = 384·b^(7-1)

  (6/384)^(1/6) = b

Then the 10th term is ...

  a10 = 384·(6/384)^((10-1)/6) = 0.75

The 10th term of the sequence is 0.75.

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The answer to this question: B

Sin 40° = x/16

0.6428 = x/16

x = 0.643 × 16

x = 10.2848

x = 10.28

So, the value of x is 10.28 (C)

That's it :)

The value of the permutation P(5,0) is 1.

To find the value of the permutation P(5,0), we can use the formula:

P(n, r) = n! / (n - r)!

In this case, we have n = 5 and r = 0.

Substituting these values into the formula, we get:

P(5,0) = 5! / (5 - 0)!

Since any number factorial is equal to 1, we have:

P(5,0) = 5! / 5!

Simplifying further:

P(5,0) = 1

Therefore, the value of the permutation P(5,0) is 1.

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Answer: A

Step-by-step explanation: