Find the Fourth vertex

The coordinates of endpoint T are (5,18).

The midpoint formula is expressed as:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.

Let's call the coordinates of point T (x,y).

Since S is the midpoint of RT, we can use the midpoint formula to find the coordinates of S:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

((13+x)/2, (-8+y)/2) = (9,5)

Solving for x:

(13+x)/2 = 9

13 + x = 2 × 9

13 + x = 18

x = 18 - 13

x = 5

Solving for y, we get:

(-8+y)/2) = 5

-8 + y = 5 × 2

-8 + y = 10

y = 10 + 8

y = 18

Therefore, the coordinates  are (5,18).

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The length of Tim's deck is 1/15th of the length of Al's deck.

Finding the expressions for the length of each deck.

For Al's deck:

Area of a rectangle = length × width

60x + 40 = length × 4

length = (60x + 40) / 4

length = 15x + 10 ft

For Tim's deck:

Area of a rectangle = length × width

21x + 14 = length × 7

length = (21x + 14) / 7

length = 3x + 2 ft

Now we can find no. of times the length of Tim's deck is Al's deck by dividing the length of Al's deck by the length of Tim's deck:

(15x + 10) / (3x + 2)

Simplifying this expression:

(3(5x + 3) + 1) / (3x + 2)

(3(5x + 3) / (3x + 2)) + (1 / (3x + 2))

15 + (1 / (3x + 2))

Therefore, the length of Tim's deck is 1/15th of the length of Al's deck.

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The approximate area of the mulch around the merry-go-round is 126.228 feet².

Diameter of the merry go round = 10.4 feet

Radius is half of the diameter.

Radius of the merry go round = 10.4/2 = 5.2 feet

Before the piece can be installed, a solid circular pad of mulch must be put down which extends 3 feet beyond the edge of the merry-go-round.

Radius of the merry go round with mulch = 5.2 + 3 = 8.2 feet

Total area of the merry go round with the mulch is,

Area = π (8.2)² = 67.24π feet²

Area of the merry go round = π (5.2)² = 27.04π feet²

Area of the mulch = 67.24π feet² - 27.04π feet² = 40.2π = 126.228 feet²

Hence the required area is 126.228 feet².

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The box in a box plot represents the middle 50% of the data (E) and the interquartile range (F).

Proposition 3.9 means that if there is a third subgroup that contains the first two subgroups in group G, then when the subgroups are unified, they would still be a subgroup of G.

Put simply, a subgroup collection of Group G is directed if it contains any two subgroups that have a third subgroup containing them both. The subgroup union of this sorted collection is also a subgroup of G.

This definite conclusion occurs because the subgroup criterion states that if any small two subgroups of G are part of a union, then that union is also a subgroup of G. Additionally, a directed subgroup family can be perceived as a series of successive subgroups, with each subgroup being enclosed within the following one.

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Answer:

7120.95^3

Step-by-step explanation:

Using the formula (2/3)πr^3 we get (2/3)π10^3 which equals 2094.4 for the volume of the hemisphere.

The volume for the cylinder would be 5026.55 using the formula of V=πr2h for the volume of a cylinder.

The total volume would amount to 7120.95^3

Result:

Yes, the fifth-grade team will need to ship the order of 325 shirts for Field Day. They will need to package them in 16 boxes to ship them.

To evaluate the number of boxes needed to ship the order, we need to divide the total number of shirts by the number of shirts that can fit in one box.

where:

Number of shirts per box = 21

Total number of shirts = 325

Number of boxes needed = Total number of shirts / Number of shirts per box

Number of boxes needed = 325 / 21

Number of boxes needed = 15.47619

Since we cannot have a fraction of a box, we would round up to the nearest whole number.

Therefore, the fifth-grade team will need to ship the order in 16 boxes.

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Simplifying the expression, (3x - 2y + 7) - (x + 8xy - 1) + (10x - xy), the solution we would get by combing like terms can be expressed as: 12x - 2y + 7xy + 6.

Given the expression, (3x - 2y + 7) - (x + 8xy - 1) + (10x - xy), to simplify it, follow the steps shown below:

(3x - 2y + 7) - (x + 8xy - 1) + (10x - xy) [given]

Open the bracket by applying the distributive property:

3x - 2y + 7 - x + 8xy - 1 + 10x - xy

Combine like terms together:

3x - x + 10x - 2y + 8xy - xy + 7 - 1

12x - 2y + 7xy + 6

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Answer:

22

Step-by-step explanation:

4

The measure of the arc length AB is [tex]\frac{16\pi }{15}[/tex] centimeters.

An arc length is simply the distance between two points along a section of a curve.

The arc length is expressed as:

s = 2πr × (θ/360°)

Where s is the arc length, r is the radius, θ is the angle and π is constant pi.

Given that:

Plug the values into the above formula

s = 2πr × (θ/360°)

s = 2 × π × 3cm × ( 64°/360°)

[tex]s = \frac{16\pi }{15} cm[/tex]

Therefore, the arc length is [tex]\frac{16\pi }{15}[/tex] cm.

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The equation of the line for the given points is y= (1/2)x - 3.

An equation of a line can be written in slope-intercept form, which is:

y = mx + b

where:

y and x are the coordinates of any point on the line.

m is the slope of the line (the rate at which y changes with respect to x).

b is the y-intercept of the line (the y-coordinate of the point where the line intersects the y-axis).

The slope of the line is calculated as,

m = ( y₂ -y₁) / (x₂ - x₁)

m = ( -2+1) / (2-4)

m = 1/2

The y-intercept is calculated as,

y = mx + c

-1 = (1/2)x 4 + c

c = -3

The equation of the line will be,

y = mx + c

y = (1/2)x - 3

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Answer:

[tex](x-6)^2+(y+7)^2=4[/tex]

Step-by-step explanation:

The formula for the equation of a circle is:

[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]

where:

From inspection of the given graphed circle, we can see that the coordinates of its center are (6, -7), and its radius is 2 units. Therefore:

To determine the equation of the graphed circle, substitute these values into the equation of a circle formula:

[tex]\implies (x-6)^2+(y-(-7))^2=2^2[/tex]

[tex]\implies (x-6)^2+(y+7)^2=4[/tex]

Therefore, the equation of the graphed circle is:

[tex]\boxed{(x-6)^2+(y+7)^2=4}[/tex]

The probability of drawing 2 blue marbles in a row is 9/64

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

Marbles = 1 + 3 + 4 = 8

Blue = 3

Selecting the first marble we have

P(Blue) = 3/8

The marble is returned

So, we have the probablility of the second to be

P(Blue) = 3/8

The probability of drawing two blue marbles is

P = 3/8 * 3/8

Evaluate

P = 9/64

Hence, the probability is 9/64

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Answer:

Since the first blue marble is replaced before the second draw, the probability of drawing a blue marble on the second draw is still 3/8, the same as the probability of drawing a blue marble on the first draw.

To find the probability of both events occurring, we can multiply the probabilities of each event:

P(drawing two blue marbles in a row) = P(drawing a blue marble on first draw) x P(drawing a blue marble on second draw)

P(drawing two blue marbles in a row) = (3/8) x (3/8)

P(drawing two blue marbles in a row) = 9/64

Therefore, the probability of drawing two blue marbles in a row is 9/64.

Step-by-step explanation:

a) The height of the stone 5 seconds later is: 90 feet

b) The time at which the stone hits the ground is: 7.66 secs

c) The velocity of the stone when it hits the ground is: 227 ft/sec

We are given:

Height above ground: h = 800 feet

Initial speed: u = 18 feet per second

(A.) Height of the stone at t = 5 seconds.

g = -32feet/sec²

t = 5 sec.

Since the stone is thrown vertically upward from some height X = 800 feet, so the total height will be:

h = X + ut + 1/2at²

h = 800 + (18*5) + ¹/₂ * (-32) * (5²)

h = 90 feet

(B.) At what time did the stone hit the ground, that means height, h = 0.

0 = 800 + (18t) + ¹/₂ * (-32) * (t²)

16t² - 18t - 800 = 0

t = 18 ± √-18² - 4 * 16 * (-800)/2*16

t = 7.66 sec

So at t = 7.66 secs, the stone hits the ground.

(C.) The velocity when the stone hits the ground.

Using the energy conservation theorem,

Initial total energy =  Final total energy.

¹/₂mu² + mgh = ¹/₂mv² + 0

u² + 2gh = v²

v² = 18² + 2*32*800

v=√18² + 2*32*800

v = 227 ft/sec

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The correct fraction that goes in the blank seven over eight > _____> three over five are,

⇒ 2 / 3

We have to given that;

The expression is,

⇒  seven over eight > _____> three over five

Now, We can write as;

⇒ seven over eight > _____> three over five

⇒ 7 / 8 > ___ > 3 / 5

Now, We can fill with fraction as;

⇒ 7 / 8 > 2 / 3 > 3 / 5

Thus, The correct fraction that goes in the blank seven over eight > _____> three over five are,

⇒ 2 / 3

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The volume of the sphere with a diameter of 6cm is 108 cm³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi

Given the data in the question:

Diameter d = 6cm

Radius is half of diameter

Radius r - 6cm/2

Radius r = 3cm

Also, π = 3

Plug the given values into the above formula.

Volume =  (4/3)πr³

Volume =  (4/3)π3³

Volume =  (4/3)(3)(27)

Volume =  108 cm³

Therefore, the volume is 108 cm³.

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There are 6 such paths, so there are 6 outcomes in the sample space that show Casey winning.

We can use a tree diagram to visualize the different outcomes of Casey's rolls:

Each branch of the tree represents one roll of the number cube.

The first two rolls are independent and equally likely to be any of the six numbers.

If the first two rolls are the same number, then Casey gets to roll again. If the third roll is a 6, she wins.

We can count the number of outcomes in the sample space that show Casey winning by counting the number of paths in the tree that lead to a 6 on the third roll.

These are:

1-1-6

2-2-6

3-3-6

4-4-6

5-5-6

6-6 (rolls again)-6

Therefore, the answer is 6.

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The sum of the squares of all the real roots of the polynomials = 1² + (-71) = -70

Using Vieta's formulas, the sum of the roots of the polynomials is 1, so the sum of the two non-positive roots is -1. Let's call these roots r and s. Then we have:

Let r and s be the non-positive roots of the polynomial P(x) = x³ - x² - 18x + k. Then we have:

r + s = -1

rs + k = 18

The sum of the squares of these roots:

r² + s² = (r + s)² - 2rs = 1 - 2(18 - k) = -35 + 2k

For the non-positive roots to be real, the discriminant of the polynomial must be non-negative, i.e.,

D = 18² - 4(1)(-k) = 72 + 4k ≥ 0

Solving for k, we get:

4k ≥ -72

k ≥ -18

So, the smallest value of k that makes the non-positive roots real is -18, and the sum of their squares is:

r² + s² = -35 + 2(-18) = -71

Finally, the sum of the roots of P(x) = 1 (by Vieta's formulas).

Therefore, the sum of the squares of all the real roots of the polynomials = 1² + (-71) = -70

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By evaluating the function related to the second derivative f''(x) = - 25 · sin 5x is equal to f(π / 5) = (14π - 50) / 25.

In this question we find the definition of the second derivative of a function, this function must be found by integrals and initial values. First, write the entire function:

f''(x) = - 25 · sin 5x

Second, determine the first derivative:

f'(x) = (1 / 5) · cos 5x + C₁

f(0) = (1 / 5) · cos 0 + C₁

3 = 1 / 5 + C₁

C₁ = 14 / 5

f'(x) = (1 / 5) · cos 5x + 14 / 5

Third, determine the function:

f(x) = (1 / 25) · sin 5x + (14 / 5) · x + C₂

f(0) = (1 / 25) · sin 0 + (14 / 5) · 0 + C₂

- 2 = (1 / 25) · sin 0 + (14 / 5) · 0 + C₂

- 2 = C₂

f(x) = (1 / 25) · sin 5x + (14 / 5) · x - 2

Fourth, evaluate the function:

f(π / 5) = (1 / 25) · sin π + (14 / 5) · (π / 5) - 2

f(π / 5) = 14π / 25 - 2

f(π / 5) = (14π - 50) / 25

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The equation has a slope of 2/3 and the y-intercept is -1. The graph is aatched with the answer below.

An equation of a line is a mathematical expression that describes the relationship between the x and y coordinates of all the points on a straight line. It takes the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis). This equation allows us to easily calculate the y-coordinate of any point on the line, given its x-coordinate.

A linear graph, also known as a straight-line graph, is a graph that represents a linear equation. The x and y coordinates of each point on the line are plotted on a graph, with the x values on the horizontal axis and the y values on the vertical axis.

The resulting graph is a straight line that passes through the y-intercept (the point where the line intersects the y-axis) and has a slope equal to the coefficient of x in the equation.

Linear graphs are useful in many fields, including mathematics, science, engineering, economics, and business, as they allow us to visualize and analyze relationships between two variables that are directly proportional to each other.

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Answer:

Step-by-step explanation:

20% of 80 is 16.

6% of 150 is 9.

30% of 200 is 60.

65% of 400 is 260.

50% of 150 is 75.

1 Let x be the unknown number. Then we have the equation:

0.04x = 28

Solving for x, we divide both sides by 0.04:

x = 28 ÷ 0.04 = 700

Therefore, 28 is 4% of 700.

2. Let x be the unknown number. Then we have the equation:

0.25x = 100

Solving for x, we divide both sides by 0.25:

x = 100 ÷ 0.25 = 400

Therefore, 25% of 400 is 100.

3 Let x be the unknown number. Then we have the equation:

0.75x = 69

Solving for x, we divide both sides by 0.75:

x = 69 ÷ 0.75 = 92

Therefore, 69 is 75% of 92.

4 Let x be the unknown number. Then we have the equation:

0.15x = 9

Solving for x, we divide both sides by 0.15:

x = 9 ÷ 0.15 = 60

Therefore, 15% of 60 is 9.

5. Let x be the unknown number. Then we have the equation:

0.12x = 60

Solving for x, we divide both sides by 0.12:

x = 60 ÷ 0.12 = 500

Therefore, 12% of 500 is 60.

(3)

1 Let x be the percent, then we can set up the equation:

x/100 * 200 = 50

Solving for x, we get:

x = 25

Therefore, 50 is 25% of 200.

2 Let x be the percent, then we can set up the equation:

x/100 * 50 = 40

Solving for x, we get:

x = 80

Therefore, 40 is 80% of 50.

3 Let x be the percent, then we can set up the equation:

x/100 * 10 = 6

Solving for x, we get:

x = 60

Therefore, 6 is 60% of 10.

4. 200 is 100% of itself, so the percent is 100.

5. Let x be the percent, then we can set up the equation:

x/100 * 800 = 200

Solving for x, we get:

x = 25

Therefore, 200 is 25% of 800.

The measure of v is 61 degree.

We have,

Interior angle = (v - 19) or v

Exterior angle = v + 42

Using exterior Angle Property

Exterior angle= Sum of opposite interior angle

v + 42 = v - 19 + v

v + 42 = 2v - 19

v - 2v = -19 - 42

-v = -61

v= 61

Thus, the value of v is 61.

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The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.

First, the rate of change

= (483 - 210) / (23 - 10)

= 273 / 13

= 21

So, the equation for the relationship between the number of bracelets made and the number of beads used.

(y - 210) = 21 (x-  10)

y - 210 = 21x - 210

y = 21x

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Result:

The probability of getting a sum greater than 25 = 1/9.

The answer is not among the given options.

To find the probability, we would need to consider the possible combinations of the spinner and number cube that result in a sum greater than 25.

First, note that the highest possible sum we can get is 12 (that is 6 from the spinner and 6 from the number cube). Therefore, we can remove all combinations that result in a sum of 24 or less.

Next, we can consider the combinations that result in a sum of 25 like this:

Spinner lands on 6, number cube lands on 5

Spinner lands on 5, number cube lands on 6

Spinner lands on 6, number cube lands on 4

Finally, we can consider the combinations that result in a sum greater than 25:

Spinner lands on 5, number cube lands on 5

Spinner lands on 6, number cube lands on 5

Spinner lands on 5, number cube lands on 6

Spinner lands on 6, number cube lands on 6

Here, 4 possible combinations can result in a sum greater than 25 from a total of 6 x 6 = 36 possible outcomes.

So, the probability of getting a sum greater than 25 is 4/36 = 1/9.

Therefore, none of the given answer choices matches this result.

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La madre canguro saltó una distancia total de 6 millas para llegar al lago.  .

The volume of the packing material that luke will need is: 11 cubic feet

The formula for the volume of a box is expressed as:

V = length * width * height

Now, we are given:

Area of base = 15 square feet

height = 3 feet

Thus:

Volume of box = 15 * 3 = 45 cubic feet

If he is going to ship a toy that is 34 cubic feet, then it means that:

Volume of packing material Luke needs = 45 - 34 = 11 cubic feet

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Answer:So the instantaneous velocity at t = 0 is -20. This means that the object is moving in the negative direction at a rate of 20 units per second at t = 0.

Look at the Photo

The length of ZL and IL is 297.72 ft and 283.15 ft respectively.

The lengths of ZL and IL is calculated by applying trigonometry ratio as follows;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The hypothenuse side = ZL and the adjacent side = IL.

tan 18 = 92/IL

IL = 92/tan (18)

IL = 283.15 ft

sin 18 = 92/ZL

ZL = 92/si 18

ZL = 297.72 ft

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