In the diagram shown, BC, EF, DK, and AK intersect at point K. Determine the values
of x and y

(a).The volume of the cylinder is 216π [tex]cm^{3}[/tex]

(b). The volume of the cone is 72π [tex]cm^{3}[/tex]

(c). The volume of the hemisphere is 144π [tex]cm^{3}[/tex]

(a). Volume of the cylinder:

The volume of the cylinder is 216π [tex]cm^{3}[/tex]  

Since the hemisphere fits snugly inside the cylinder, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.

So, the volume of the cylinder V = [tex]\pi r^{2} h[/tex] where

r = radius of cylinder = 6 cm and

h = height of cylinder = radius of hemisphere = 6 cm

So, V = [tex]\pi r^{2} h[/tex]

=[tex]\pi r^{2}[/tex]× r

=[tex]\pi r^{3}[/tex]

= π(6 cm)³

= 216π [tex]cm^{3}[/tex]

So, the volume of the cylinder is 216π [tex]cm^{3}[/tex]  

(b). Volume of the cone

The volume of the cone is 72π [tex]cm^{3}[/tex]  

Since the cone fits snugly inside the same hemisphere, the radius and height of the cone equals the radius of the hemisphere.

So, the volume of the cone V' = [tex]\frac{\pi r^{2} h}{3}[/tex] where

r = radius of cone = 6 cm and

h = height of cone = radius of hemisphere = 6 cm

So, V' = [tex]\frac{\pi r^{2} h}{3}[/tex]

= [tex]\frac{\pi r^{2} *r}{3}[/tex]

= [tex]\frac{\pi r^{3} }{3}[/tex]

=[tex]\frac{ \pi(6 cm)^{3} }{3}[/tex]

[tex]= \frac{216 \pi}{3}cm^{3} = 72 \pi cm^{3}[/tex]

So, the volume of the cone is 72π [tex]cm^{3}[/tex]

(C). Volume of hemisphere

The volume of the hemisphere is 144π cm³  

Since the volume of hemisphere, V" equals the averages of the volume of the cylinder, V and volume of the cone, V'

So, V" =[tex]\frac{ (V + V')}{2}[/tex]

V" =[tex]\frac{ (216\pi cm^{3} + 72\pi cm^{3})}{2}[/tex]

V" = [tex]\frac{288\pi cm^{3} }{2}[/tex]

V" = 144π [tex]cm^{3}[/tex]

So, the volume of the hemisphere is 144π [tex]cm^{3}[/tex].

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A possible formula for the trigonometric function whose values are in the given table is u(x) = 3cos(πx/2)

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The code of the puzzle is 75.5 which is the sum of all the sides of the missing triangles.

Pythagorean triples are a collection of three positive numbers that fit into the Pythagorean theorem formula, which is written as, a² + b² = c², where a, b, and c are positive integers.

1.

Substitute the known values in the Pythagorean theorem formula, and solve for a:

a² + 8² = 12²

a² + 64 = 144

a² = 144 - 64

a² = 80

a = √80

a = 8.9

Similarly, solve the length of the missing side of the other triangles.

2. The missing side b = 14.5

3. The missing side c = 10.3

4. The missing side a = 18.8

5. The missing side b = 8

6. The missing side c = 15

Now, the sum of all the sides of the missing triangles as:

8.9 + 14.5 + 10.3 + 18.8 + 8 + 15 = 75.5

Thus, the code of the puzzle is 75.5.

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The number of terms in the expression -11 - 7c + 5 - 2x - 13b - 7 is 6

Algebraic expressions are defined as expressions that are composed with coefficients, terms, factors, constants and variables.

They are also known to consist of mathematical operations, such as;

From the information given, we have the algebraic expression as;

-11 - 7c + 5 - 2x - 13b - 7

The terms are either single number or variables in the expression. They are six

Hence, the number is 6

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The value of the expression xy - x² - 5x - 4 when x = -1 and y = 6 is -6.

Given the expression in the question;

xy - x² - 5x - 4

To find the value of the expression; substitute in x = -1 and y = 6 for all occurrence of x and y in the expression and simplify.

xy - x² - 5x - 4

Plug in  x = -1

(-1)y - (-1)² - 5(-1) - 4

Plug in y = 6

(-1)(6) - (-1)² - 5(-1) - 4

Simplify

-6 - 1 + 5 - 4

Add -6 and -1

-7 + 5 - 4

Add -7 and 5

-2 - 4

Add -2 and -4

-6

Therefore, the value of the expression is -6.

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6.29117647059

This is the answer

Answer: 6.29117647059

Step-by-step explanation:

divide the problem :)

Answer:

The variable "y" is a placeholder for a value in mathematics and can represent many different things depending on the context. To find the value of y, you need to know the equation or expression that relates y to other variables. For example, if y = 2x + 1, then y is equal to the sum of 2 times the value of x and 1. To find the value of y for a particular value of x, you would substitute the value of x into the equation and solve for y.

In general, the value of y can represent anything from a dependent variable in an equation to a coordinate on a graph. To determine what y represents in a specific context, you need to understand the context and the equation or expression that defines y.

Step-by-step explanation:

By applying the algebra concept, it can be concluded that p = 3x or p = 2 - 3x.

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.

We want to express p in terms of x of this equation:

9x² – 6x + 5 = p² – 2p + 5

First, we have to eliminate 5, so we have:

9x² – 6x = p² – 2p

Then we add 1 on each side, so we have:

9x² – 6x + 1 = p² – 2p + 1

       (3x - 1)² = (p - 1)²

            p - 1 = √(3x - 1)²

Thus the solutions are:

p - 1 = 3x - 1      ⇔     p = 3x

or

p - 1 = -(3x - 1)   ⇔     p = 2 - 3x

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The rate of change picking the apples is 8 bushels of apples per hour.

Rate of change is used to mathematically describe the percentage change in value over a defined period of time, the formula for rate of change is: R = (D2 - D1)/T. where: R = rate of change.

Given that, you and your best friend are picking apples at a local orchard. there were already 12 bushels of apples on the tractor when you began at 8:00 am and you picked apples until noon, we are asked to find, what was your rate of change if there were 44 bushels filling the tractor when you stopped,

So, the rate change = total apples picked in 8 am to noon / number of hours.

Therefore, the total apples picked in 8 am to noon =

Since, it was 44 bushels at the end and when they started there were already 12 bushels, so the number of bushels of apples filled between given hours = 44 - 12 = 32 bushels.

The number of hours in picking 32 bushels of apples = 12 noon - 8 am

= 4 hours

Therefore,

The rate of change = 32 / 4

= 8

Hence, the rate of change picking the apples is 8 bushels of apples per hour.

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Answer:

Step-by-step explanation:

We got two equations.

First modeling the total money using x for nickels and y for quarters.

0.05x + 0.25y = $8.80

Our second equation is modeling the total coins.

x + y = 68

Which we can change to substitute for x.

x = 68 - y

Substitute for x to find the answer.

0.05(68 - y) + 0.25y = 8.80

3.4 - 0.05y + 0.25y = 8.80

3.4 + 0.20y = 8.80

0.20y = 5.4

y = 27.

So, there is 27 quarters and 41 nickels.

Therefore, we can see that equation the only y-value that is part of all four lines is y = 1. Therefore, the y-coordinate of the solution is 1.

In arithmetic equations, the exact symbol (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12.

Here,

The given system of equations is:

y = -2

y = 3

y = 1

y = 0

To graph this system, we plot the horizontal lines y=-2, y=3, y=1, and y=0 on the same coordinate plane:

lua

Copy code

   |     *   <-- y=3

 4 +    

   |           <-- y=1

 3 +     *   <-- y=0

   |    

 2 +          

   |     *   <-- y=-2

 1 +    

   |      

   +----------------

        1   2   3   4

From the graph, we can see that the only y-value that is part of all four lines is y = 1. Therefore, the y-coordinate of the solution is 1.

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Julian has $10,824.32 at the end of the year and $14,859.47 after 5 years.

Compound interest is the interest paid by the bank for both of principle amount and the interest the account has already earned.

Julian starts bank with principle amount $10,000.

Bank compounds the interest quarterly at an annual interest rate 8%.

Then, total amount in the end of the year.

     [tex]A = p(1+\frac{r}{n} )^{nt}[/tex]

         = [tex]10,000(1+\frac{0.08}{4} )^{4}[/tex]

         = $10,824.32.(at the end of the year)

After 5 years,

    [tex]A=10000(1+\frac{0.08}{4} )^{(4)(5)}[/tex]

        = $14,859.47(after 5 years)

Hence, Julian has $10,824.32 at the end of the year and $14,859.47 after 5 years.

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Answer:

1. 4

2. $52

3. $20

4. 58

5. 30

6. 2

7. 132

8. 24

Step-by-step explanation:

1. If he needs 10 feet all together, and only has 6, you can put it in an equation as “6+x=10” because 10 would be the final amount, and he already had 6 feet, so he needs x feet. Then you need to get the x alone in the equation, so you would subtract 6 from both sides. 10-6 is 4, which means x=4. So Phil needs 4 more feet of lumber.

2. Emmet paid $64 in total. Within that total, $12 is for the case. You can set up an equation as either 12+x=64 or 64-12=x, both get the same answer, as shown in the first problem. 64-12 is 52, so that would be your answer.

3. So if he paid $x, 6+14=x. 6 from how much money was spent, 14 from how much was returned. 6+14=20. In total, brandy gave the cashier $20.

4. If the temprature dropped 15 degrees, and it is now 43, all you need to do is undo the dropping. If it didnt drop, it rose. To you need to add 15 to 43, giving you 58. The starting temperature was 58.

5. Her rate per hour is $12. That means if she worked x hours, you would set it up as 12x=m, m being the amount of money she earns. If she earns $360, you plug that in, making it look like 12x=360. Then you do the opposite of multiplication, on both sides, so you decide both sides by 12. On the left it cancels out, on the right 360/12 is 30. That means that Cindy worked for 30 hours.

6. If she used 32 cups and there is 16 cups in a gallon, all you need to do is divide 32 by 16. 32/16 is 2. So Mary used 2 gallons of juice.

7. You can write an equation for this one that looks like x/12=11. X is the total number. From there, you multiply 12 on both sides, giving you 132. That means there are 132 students in the gym class.

8. If there are 4 ping-pong balls in each package and there are 6 packages, all you need to do it multiply 6 by 4. 6 times 4 is 24. So Matthew has 24 ping-pong balls.

The  required solution to the system of equations using elimination, as follows:

18. The solution is (x, y) = (40/11, -17/11).

19. The solution is (x, y) = (6, 1).

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

To solve the system of equations using elimination, we can multiply one equation by a scalar so that one of the variables has the same coefficient in both equations.

18.

-6x + 4y = -28

6x + 7y = 11

Add the two equations to eliminate x:

11y = -28+11

11y = -17

y = -17/11

Now that y is known, we can substitute back into either equation to find x:

-6x + 4(-17/11) = -28

-6x - 68/11 = -28

x = 40/11

So the solution is (x, y) = (40/11, -17/11).

19.

2x + 3y = 15

x - 3y = 3

Add the two equations to eliminate y:

3x = 18

x = 18/3

x = 6

Now that x is known, we can substitute back into either equation to find x:

2(6) + 3y = 15

12 + 3y = 15

3y = 3

x = 1

So the solution is (x, y) = (6, 1).

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Answer: B. (5b-6)2

Step-by-step explanation:

Answer:

600g Butter, 2000g Flour, 200g Sugar

Step-by-step explanation:

First we divide the final number of cakes by the initial

[tex]72 \div 18 = 4[/tex]

Then we multiply each of the ingredients by 4

[tex]150 \times 4 = 600[/tex]

[tex]500 \times 4 = 2000[/tex]

[tex]50 \times 4 = 200[/tex]

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

The ratio for this problem is:

(Ingredients: number of cakes)

Therefore, we need to know how many times 18 can fit into 72.

Now, if we know that 18 can be multiplied by 4 to get 72, we need to multiply all of the ingredients by 4.

Therefore, if the recipe stays proportional, we will need 600g butter, 200g flour and 200g sugar to make 72 cakes.

The equation represents the rule is y = 2x-5

The best fits the terms x and y is y=2x-5

In function rules, the output of the function depends on the input of the function. This makes the output of the function the dependent variable and the input the independent variable. This means that the output depends on the values of the inputs, and we can create a function with inputs that give a given output.

The definition of a function in mathematics can also be interpreted as a relation that connects each member of x in a set called the domain (domain) with a single value f(x) from a second set called the codomain (codomain).

The set of values obtained from these relations is called the range. A function is a rule that connects each element in a set, so that a function can be said to be a special part of a relation.

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The length of the ramp, which is the hypotenuse of a right triangle, can be found using the formula:

length = horizontal distance / sin(angle)

Plugging in the given values, we get:

length = 14 feet / sin(9º)

Using a calculator, we find:

length ≈ 85.67 feet (rounded to two decimal places)

Therefore, the length of the ramp is approximately 85.67 feet.

Given a parallelogram ABCD with points B and D, we draw two lines such that line BM intersects CD at point M and line DN intersects BC at point N, and BM = DN. The intersection of these lines is point I. Our goal is to prove that IA is a bisector of angle BID.

To prove this, we first note that since ABCD is a parallelogram, AB is parallel to CD and AD is parallel to BC. This means that ∠BAD and ∠CDA are congruent, and ∠BAC and ∠DCB are congruent.

Next, we consider triangle ABM. Since BM is perpendicular to AB, we have ∠BAM = 90°. By the same reasoning, we have ∠BID = 90°. This means that IA is perpendicular to both AB and BD.

Since IA is perpendicular to AB and BD, it follows that IA bisects ∠BAD and ∠BDC. Additionally, we know that AB = BD and ∠BAD = ∠BDC, so it follows that IA bisects ∠BID.

This completes the proof that IA is a bisector of ∠BID. The key idea here is that a line perpendicular to two parallel lines bisects the angles formed by the intersection of the two parallel lines with a third line.

In conclusion, given a parallelogram ABCD with points B and D, the intersection of lines BM and DN, point I, is the bisector of angle BID. This result can be used to prove various geometric theorems and helps to understand the properties of parallelograms and their related figures.

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Answer:

y=-2x+1

Explanation:

you can see that the x goes up by 1 every time. Y goes down by 2 every time, because 1-2=-1, -1-2=-3, etc. So the -2 goes in your m part of y=mx+b. Then you need to figure out what y is when x is 0, for your y-intercept, or your b part of y=mx+b. The picture makes it simpler, showing that when x is 0, y is 1. Therefore, 1 is your b part of y=mx+b. If you put it all together, it looks like this:

Y=-2x+1

Step-by-step explanation:

It looks Iike the equation is in slope intercept form

[tex]y = mx + b[/tex]

m is the slope

b is the y intercept

Finding B is easy, it's just where X = 0. On this table, Y is 1 when X is 0.

Finding the slope. We'll take two different (X,Y) coordinates. Let's do the first two rows (0,1) and (1,-1)

Next we apply the slope formula. That being

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

So plugging that in

[tex] = \frac{ - 1 - 1}{1 - 0} [/tex]

That gives you -2/1, also known as -2

Now that we have everything, we can put the forumla together

[tex]y = - 2x + 1[/tex]

Where -2 is the answer that belongs in the [?]

The feet the bicycle will it cover in 30 seconds is 306 feet

When we talk about speed, it is often expressed in miles per hour (mph). However, in this problem, we must determine the distance covered in feet per second. To convert mph to feet per second, we can use the following formula:

1 mph = 5280 feet/hour = 5280/3600 feet/second

Therefore, to convert 14 mph to feet per second, we multiply 14 by the conversion factor of 5280/3600:

14 mph * (5280/3600 feet/second/mph) = 14 * 5280/3600 feet/second = 10.2 feet/second

So, the bicycle is traveling at a speed of 10.2 feet per second. To find the distance covered in 30 seconds, we multiply the speed by the time:

10.2 feet/second * 30 seconds = 306 feet

Finally, rounding to the nearest tenth of a foot, we have:

306 feet ≈ 306.0 feet to the nearest tenth.

Therefore, the bicycle covers 306.0 feet in 30 seconds, rounded to the nearest tenth of a foot.

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The table to show the depreciation over time for the first three years is:

Year (x) Depreciation (y)

1         $15,000

2         $13,500

3        $12,000

It should be noted that in order to generate a table to show the depreciation over time for the first three years, we can use the given equation:

y = 16,500 - 1,500x

where y is the depreciation and x is the number of years since the car was purchased new.

Substituting x = 1, 2, and 3 into the equation, we get:

When x = 1, y = 16,500 - 1,500(1) = 15,000

When x = 2, y = 16,500 - 1,500(2) = 13,500

When x = 3, y = 16,500 - 1,500(3) = 12,000

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The length of the shorter arc from vertex P to vertex N is 37.68 inches.

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which means numerous) and gon (which means sides).

To create a closed figure, at least three line segments must be connected end to end.

Given an equilateral polygon, PENTA is inscribed in a circle of radius 15 inches,

The central angle of the polygon leaning to the shortest chord is

α = 2π/5

α = 2*360/5 = 72°

The central angle of the polygon leaning to the shorter arc from vertex P to vertex N is

β = 2(2π/5)

β = 144°

The length of the corresponding arc is

= r*β

here r = 15 inches, and π = 3.14

length = r*2*2π/5

length = 15*2*2(3.14/5)

length = 37.68 inches.

Hence length is 37.68 inches.

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Answer:y + 6 = 1/3 (x - 4)  

Step-by-step explanation:Replace the second y (y1) and the 2nd x (x1) with the new points and then -3 become 1/3 due to perpendicular meaning opposite reciprocal (2/3 reciprocal is 3/2 and the opposite would be its negative, -3/2, for example

The probability of the event that the second dice is not smaller than the first dice is 15/36.

It's simple to rule out every option:

First die is a 1, and the second die wins 5/6.

First die is a 2, and the second die wins 4/6.

First die is a 3, and the second die wins 3/6.

First die is a 4, and the second die wins 2/6.

First die is a 5, and the second die wins 1/6.

First die is a 6, winning with a score of 0/6.

In total, 15 out of the 36 results favor the second die. All of these might be tabulated.

So the probability of the event that the second dice is not smaller than the first dice = 15/36

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The order of the steps in the iterative problem-solving process is: a) collect information, b) formulate and test hypothesis, c) analyze results, and d) consider alternative explanations. (option c)

The iterative problem-solving process is a cycle that involves gathering information, forming hypotheses, testing hypotheses, analyzing the results, and then considering alternative explanations.

The second step is to formulate and test hypotheses. Hypotheses are educated guesses about what might be causing the problem or why the problem is occurring.

The third step is to analyze the results. This involves interpreting the data and determining if the hypothesis was correct or incorrect.

The final step is to consider alternative explanations. This involves looking at the data and considering other potential causes for the problem.

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Complete Question:

Which of these sequences is the order of the steps below in the iterative problem-solving process? a) formulate and test hypothesis b) collect information c) analyze results d) consider alternative explanations.

Option:

Answer: 8 micrograms, y=40-(8)4

Step-by-step explanation: after four hours, 8 (4) micorgrams will stil be in her body

Answer:

the answer is y=40(0.8)^x

16 micrograms