Help me please please I have to get a good grade on it Otherwise, my grade is going down

Help Me Please Please I Have To Get A Good Grade On It Otherwise, My Grade Is Going Down

Answers

Answer 1

The total surface area of the cylinder is 62.8 ft². And the right option is D. 62.8.

What is a cylinder?

A cylinder is a solid shape that is made up of a rolled surface with a circular top and a circular base.

To calculate the total surface area of the cylindrical drum, we use the formula below.

Formula:

SA = 2πr²+2πrh......................... Equation 1

Where:

SA = Total surface area aof the cylinderr = Radius of the circular baseh = Height of the cylinder

From the question,

Given:

r = 2 feeth = 3 feetπ = 3.14

Substitute these values into equation 1

SA = (2×3.14×2²)+(2×3.14×2×3)SA = 25.12+37.68SA = 62.8 ft²

Hence the total surface area is 62.8 ft².

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Related Questions

Evaluate

+
(


)

2
p+(−q)−2p, plus, left parenthesis, minus, q, right parenthesis, minus, 2 where

=

3
p=−3p, equals, minus, 3 and

=
5
q=5q, equals, 5.

Answers

The value of the expression  p + (-q) - 2p for the value p = -3 and q = 5 is equals to -2.

The expression is equal to,

p + (-q) - 2p

Where 'p' and 'q' are the two variables.

To evaluate p + (-q) - 2p with p = -3 and q = 5,

Substitute the values into the given expression, we get,

= p + (-q) - 2p

= ( -3 ) + ( -5 ) - 2 × ( -3 )

As minus multiply by minus is plus.

And minus multiply by plus is minus.

= -3 - 5 + 6

= -8 + 6

Put the sign of greatest integer.

= -2

Therefore, value of p + (-q) - 2p = -2 when p = -3 and q = 5.

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The above question is incomplete, the complete question is:

Evaluate p+(−q)−2p where p = -3 and q = 5.

You move up 9 units. You end at (-3, 4). Where did you start?

Answers

Answer:

The x-coordinate stays the same, so the starting point is at (-3, -5) since 4 - 9 = -5.

Module 10 Test
17) Kendra flips a coin and spins the spinner with 8 equal-size sections shown below once. After
40 trials of the experiment, the relative frequency of flipping tails and spinning blue is.

What is the difference between the number of actual outcomes and the number of expected
outcomes?
Pic below

Answers

The difference between the number of actual outcomes and the number of expected outcomes is given as follows:

3 outcomes.

How to calculate a probability?

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probabilities are given as follows:

Tails: 1/2 -> fair coin.Spinning blue: 1/4 -> 2/8 of the spinner.

Hence the composite probability of the two independent events is given as follows:

1/2 x 1/4 = 1/8.

The expected number of outcomes in 40 trials is given as follows:

1/8 x 40 = 5 outcomes.

Hence the difference is of:

8 - 5 = 3 outcomes.

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I dont nkow wht to do here
pls answer
woth 20 point!!

Answers

The circumference of a circle is pi times diameter. 8.1 * 3.14159… = 25.4 (rounding to 3 sf)

Find the equation of a line that passes through the point (5,3) and has a gradient of -2. Leave your answer in the form y=mx+c​

Answers

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{5}) \\\\\\ y-3=-2x+10\implies {\Large \begin{array}{llll} y=-2x+13 \end{array}}[/tex]

8, find the surface area of the composite solid. (See Example 4.)
4 yd
ft
2 ft
16.
3 yd
8yd

18. 10cm 12cm

Answers

The figures can be evaluated as composite figures, which indicates;

16. The surface area composite solid is about 125.65 yd²

17. The surface area of the composite solid is about 210·π yd²

What is a composite solid?

A composite solid is a solid that comprises of two or more regular solids.

16. The formula for the surface area the pyramid are;

Surface area, S.A. = π·r·l + Base Area

Where;

Base Area = π·r²

l = The slant height

r = The radius of the base = 3 yd

l = √(4² + 3²) = 5

S.A. = π × 3 × 5 = 15·π

Area of the pyramid at the bottom is therefore;

l = √(8² + 3²) = √(73)

S.A. = π × 3 × √(73) = 3·√(73)·π

The surface area is therefore; 15·π + 3·√(73)·π ≈ 127.65

The surface area of the solid is about 127.65 yd²

18. The surface area of the cylinder = π × 10²/4 + π × 10 × 12 = 145·π

The surface area of the circular pyramid is therefore;

S.A. = π × r × l

l = √((10/2)² + 12²) = 13

r = 10/2 = 5

S.A. = π × 5 × 13 = 65·π

The surface area of the figure is therefore; 145·π + 65·π = 210·π

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What is the volume of a sphere with a radius of 41.8 in, rounded to the of a cubic inch?

Answers

Answer:

402,124 cubic inches

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.

Substituting the given radius of 41.8 inches into the formula, we get:

V = (4/3)π(41.8 in)^3

V = (4/3)π(75,927.832 in^3)

V = 402,123.732 in^3

Step-by-step explanation:

Volume of a sphere = 4/3 pi r^3  = 4/3 pi (41.8)^3 = 305,926.7511 in^3

     (round as needed)

Find the indefinite integral​

Answers

The integral of the rational expression is equal to I = - 1.414 · ㏑ |x + 3.372| + 2.194 · ㏑ |x - 2.372| + 0.219 · ㏑ |x - 1| + C.

How to find the integral of a rational expression

In this problem we find the case of a rational expression, whose integral must be determined. This can be done by means of partial fractions method, that is, decompose the rational expression into a sum of fractions. First, write the entire rational expression and use partial fractions method:

(x² - 9) / (x³ - 9 · x + 8)

[(x - 3) · (x + 3)] / [(x + 3.372) · (x - 2.372) · (x - 1)]

A / (x + 3.372) + B / (x - 2.372) + C / (x - 1)

(x - 3) · (x + 3) = A · (x - 2.372) · (x - 1) + B · (x + 3.372) · (x - 1) + C · (x + 3.372) · (x - 2.372)

x² - 9 = A · (x² - 3.372 · x + 2.372) + B · (x² - 2.272 · x - 3.372) + C · (x² + x + 7.998)

x² - 9 = (A + B + C) · x² + (- 3.372 · A - 2.272 · B + C) · x + (2.372 · A - 3.372 · B + 7.998 · C)

Solve the system of linear equations:

A + B + C = 1

- 3.372 · A - 2.272 · B + C = 0

2.372 · A - 3.372 · B + 7.998 · C = - 9

(A, B, C) = (-1.414, 2.194, 0.219)

(x² - 9) / (x³ - 9 · x + 8) = - 1.414 / (x + 3.372) + 2.194 / (x - 2.372) + 0.219 / (x - 1)

Second, integrate the resulting equation:

I = - 1.414 ∫ [1 / (x + 3.372)] dx + 2.194 ∫ [1 / (x - 2.372)] dx + 0.219 ∫ [1 / (x - 1)] dx

I = - 1.414 · ㏑ |x + 3.372| + 2.194 · ㏑ |x - 2.372| + 0.219 · ㏑ |x - 1| + C

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Solids A and B are similar. Use the given information and scale factor k from solid A to solid B to find the volume of solid B.
Round your answer to the nearest hundredth if necessary.
The volume of cone A is 167 cubic centimeters and k =
3
2
The volume of cone B is cubic centimeters.
4

Answers

The volume of cone B is of 2.37π cubic centimeters.

What is a dilation?

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The scale factor in this problem is given as follows:

k = 3/2.

Hence:

A/B = 3/2.B/A = 2/3.

The scale factor measures the ratio of the side lengths, in units, while the volume is given in cubic units, hence the ratio of the volumes is given as follows:

Vb/Va = (2/3)³

Vb/Va = 4/27

Hence the volume of solid B is given as follows:

Vb = 4/27 x 16π

Vb = 2.37π.

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Answer:

Answer:

169.65

Step-by-step explanation:

Solving ones like these, I use the formula: Volume b/Volume a=k^3. I will be using “•” to represent multiplication, “^” is used for exponent. 16•pie is the volume for shape A, and k is 3/2. The reason why k is exponent by 3 is because this is for volume. Then, plug in the values, Volume B/16•pi=3/2^3 is what we have. With the piwer of inverse operations, we can isolate for Volume B. By multiplying 16•pi by each side, Volume B=16•pi•3/2^3. Lets do 3/2^3 first since it is following the order of PEMDAS. To recall what PEMDAS is, it is a method my school uses for solving equations. Parentheses first, Exponent next, then Multiply, Divide, Add, and subtract. Basically the order of solving any equation. 3/2^3= 27/8. Now, back to multiplying! I use desmos scientific calculator. 27/8•16•pi= =169.6460033. The qeustion says to round to the nearest hundreth, so it would be 169.65. Have a great day everybody

Step-by-step explanation:

HELP PLEASEE

01 yards
01/15
04 yards
yards
yards
Question 6(Multiple Choice Worth 2 points)
(Factoring MC)

Answers

The requried total amount of metal needed for the project is 4 1/2 yards.

The first piece of metal measures 1 1/5 yards, which is equivalent to 6/5 yards. The second piece of metal measures 3/10 yards. To find the total amount of metal needed, we need to multiply the sum of the two pieces by 3:

Total amount of metal = 3 x (6/5 + 3/10) yards

Simplifying the expression inside the parentheses, we have:

Total amount of metal = 3 x (12/10 + 3/10) yards

Total amount of metal = 3 x 15/10 yards

The total amount of metal = 9/2 yards

Total amount of metal = 4 1/2 yards

Therefore, the total amount of metal needed for the project is 4 1/2 yards.

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Find the missing angle

Answers

Answer:

D - 37 degrees

Step-by-step explanation:

Sin = opp / hyp

Cos = adj / hyp

Tan = opp / adj

Tan(x) = 29/38

~37.34 degrees

The answer is D - 37 degrees

Which value of b satisfies both inequalities for b?
2b-8>5
3b-13 < 9
Use substitution to find the answer.

Answers

Answer:

  B.  7

Step-by-step explanation:

You want the value of b from the choices {5, 7, 8, 10} that will satisfy both inequalities ...

2b -8 > 53b -13 < 9

Substitution

You are asked to find the answer by substitution. This means you put the offered value of 'b' into the inequality where 'b' is, then simplify and see if you have a true relation.

A. b=5

In the first inequality, this is ...

  2·5 -8 > 5

  10 -8 > 5

  2 > f . . . . . . . false — not a solution

B. b=7

In the first inequality, this is ...

  2·7 -8 > 5

  14 -8 > 5

  6 > 5 . . . . . . True

In the second inequality, we have ...

  3·7 -13 < 9

  21 -13 < 9

  8 < 9 . . . . . . True — this is the solution you want

The choice b = 7 satisfies both inequalities.

__

Additional comment

We generally find it easier to compare to zero, rather than some constant. In the attached, we evaluated the left-side expressions ...

2b -8 -5 > 03b -13 -9 < 0

The first inequality is true for b = {7, 8, 10}. The second inequality is true for b = {5, 7}. The only value of b that satisfies both inequalities is b=7.

You will notice we also find it easier to try all the choices at once, rather than retype the calculator input for each one.

I’m completely lost pls help

Answers

The probability that exactly 2 of the pencils in the package are painted green is given as follows:

p = 9/30.

How to calculate a probability?

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

In this problem, we have a set of 30 outcomes, in which the number of outcomes in which the letter G appears exactly twice is given as follows:

9.

Hence the probability that exactly 2 of the pencils in the package are painted green is given as follows:

p = 9/30.

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Marguerite draws a net of a solid figure.
The net has 1 square face and
4 triangular faces. For which polyhedron did Marguerite draw a net?

Answers

The polyhedron Marguerite get from the net diagram is square based pyramid.

Given that, the net has 1 square face and 4 triangular faces.

A square pyramid characterized by a square base is a three-dimensional shape having five faces, thus called a pentahedron. The most famous example of such a square pyramid is the Great Pyramid of Giza.

Marguerite drew a net of a tetrahedron; a polyhedron with four faces, all of which are triangles. A net is a two-dimensional figure that can be folded to form a three-dimensional shape. A tetrahedron has four faces, all of which are triangles, and four vertices. It is one of the simplest polyhedral and is comprised of four triangular faces that meet at a single point, called the vertex.

Therefore, the polyhedron Marguerite get from the net diagram is square based pyramid.

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Find the dimensions in feet of the Great Pyramid of Khufu and solve for the volume. Show work

Answers

Answer:

The volume of the pyramid is approximately 25,920,000 cubic feet.

Step-by-step explanation:

The Great Pyramid of Khufu is one of the most famous pyramids in Egypt, located in Giza. Its original height was 146.7 meters (481 feet), but due to erosion and the loss of its outer casing, it now stands at a height of 138.8 meters (455 feet). The base of the pyramid is a square with sides measuring 230.4 meters (755.9 feet).

To find the volume of the pyramid, we can use the formula:

V = (1/3)Bh

where V is the volume, B is the area of the base, and h is the height of the pyramid.

First, we need to convert the dimensions of the pyramid to feet. The height of the pyramid is 455 feet, and the base of the pyramid is a square with sides of 755.9 feet.

The area of the base is:

B = side^2 = (755.9 ft)^2 = 571536.81 sq ft

The volume of the pyramid is:

V = (1/3)Bh = (1/3) × 571536.81 sq ft × 455 ft ≈ 2.592 × 10^7 cubic feet

Therefore, the dimensions of the Great Pyramid of Khufu are approximately 755.9 feet for each side of the base, and 455 feet for the height. The volume of the pyramid is approximately 25,920,000 cubic feet.

30kg of clay divided to portions of 5/8kg each and enough to distribute to all students. how many students are there

Answers

There are 48 students.

To find the number of students, we need to divide the total amount of clay by the weight of each portion.

We are given that there are 30kg of clay. We are also told that the clay is divided into portions of 5/8kg each.

To divide one quantity by another, we can use the following formula:

quantity ÷ weight per portion = number of portions

In this case, we can write:

30kg ÷ (5/8)kg per portion = number of portions

30kg × (8/5) portions per kg = number of portions

Simplifying, we get:

48 portions = number of portions

Therefore, there are 48 portions of clay in total. To find the number of students, we need to divide the number of portions by the number of portions per student.

Since each portion weighs 5/8kg, we can write:

1 portion = 5/8kg

number of portions per student = 1 portion/student

So, the number of students would be:

48 portions ÷ 1 portion per student = 48 students

Therefore, there are 48 students.

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Find the answer about the given situation
using the given chart.
Daniel recorded the number of
hummingbirds (B) and the number of red
flowers (F) for each quarter of a field.
The chart on the right shows his
observations.
What is the constant of variation for the
number of hummingbirds per flower?
f
B
Hummingbirds
6
8
12 16
12
24
20
40

Answers

The constant of variation for the

number of hummingbirds per flower is 0.75.

How to find the constant

From the information, Daniel recorded the number of hummingbirds (B) and the number of red flowers (F) for each quarter of a field.

For the first observation, we have 6 hummingbirds and 8 flowers. So the ratio of hummingbirds to flowers is 6/8 = 0.75.

For the second observation, we have 12 hummingbirds and 16 flowers. So the ratio of hummingbirds to flowers is 12/16 = 0.75.

Hence, the constant of variation for the

number of hummingbirds per flower is 0.75.

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Solve x² + 6x = 16
by graphing.

Answers

Answer:-8 and 2

Step-by-step explanation:

graph it

Use the Echelon method 4p+9p=-15 3p-7q=30

Answers

Solution of system is p = 3 and q = -3.

The given system of equation is

4p+9q = -15

3p-7q = 30

The augmented matrix of this system be

[tex]\left[\begin{array}{ccc}4&9&-15\\3&-7& 30\\\end{array}\right][/tex]

Now use echelon method to convert it into reduced form,

So perform [tex]R_{2}[/tex] ⇒ 3x[tex]R_{1}[/tex] - 4x[tex]R_{2}[/tex]

 [tex]\left[\begin{array}{ccc}4&9&-15\\0&55& -165\\\end{array}\right][/tex]

Now the reduced system be

4p+9q = -15  ...(i)

   55q = -165

⇒     q = -165/55 = -3

Put   q = -3 into equation (i)

⇒ 4p + 9x(-3) = -15

⇒   p = 3

Hence p = 3 and q = -3

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8. Which of these graphs are connected?

Answers

In the given graphs, the second graph is a connected graph.

What are connected graphs:  

A connected graph is a type of graph in which there is a path between every pair of vertices. In other words, it is a graph in which every vertex is reachable from any other vertex.

A graph is composed of vertices, which are points or nodes, and edges, which are the lines connecting the vertices.

In a connected graph, there are no isolated vertices or disjoint subsets of vertices, and every vertex is connected to at least one other vertex.

Here we have 3 graph

In the first graph, there are 3 individual graphs that are not connected.

Hence, The first graph is not connected graph

In the second graph, there are no isolated nodes or vertices as the graph is connected at every node

Hence, The Second graph is connected graph

In the third graph, there are 2 graphs that are not connected,

Hence, The third graph is not a connected graph.  

Therefore,

In the given graphs, the second graph is a connected graph.

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Solve the inequality 3x - 3 < 9
+

Answers

Answer:

[tex]3x - 3 < 9[/tex]

[tex]3x < 12[/tex]

[tex]x < 4[/tex]

Graph this system of equations and determine the number of solutions. y= 1 2 x–6 y= 1 2 x–4 Line A passes through the points (6,1) and ( – 4,6). Line B passes through the points (14,3) and ( – 10, – 9).

Answers

The graph of the system is on the image at the end, there we can see that it has no solutions.

Which statement is true?

The two linear equations are:

y = (1/2)*x - 6

y = (1/2)*x - 4

First we can see that the two lines are parallel, thus, the lines never do intercept, so that is enough to know that the system of equations has no solutions.

We can graph both of the lines in the same coordinate axis and we wil see that the lines never intercept, as you can see in the graph at the end of this answer.

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a student evaluated 5x-6/x^2 for x=2 and got a result of 1 is this correct explain

Answers

Answer:

it's correct because when you plug in the value of 2 and check, you get 1. try it yourself and you'll see!

Step-by-step explanation:

Find all solutions of the equation in the interval [0, 2).
sin x-1= cos x
Write your answer(s) in radians in terms of π.
If there is more than one solution, separate them with commas.
x=

Answers

Answer: The solutions to the equation sin x - 1 = cos x in the interval [0, 2) are x = -π/2 and x = 3π/4, in radians in terms of π.

Step-by-step explanation:sin x - 1 = cos x

Subtracting cos x from both sides:

sin x - cos x - 1 = 0

Using the identity sin(x - π/4) = sin x cos π/4 - cos x sin π/4, we get:

sin(x - π/4) = -1/√2

Taking the inverse sine of both sides, we get:

x - π/4 = -π/4 - π/2 = -3π/4

or

x - π/4 = π/2 + π/4 = π/2

Adding π/4 to both sides:

x = -3π/4 + π/4 = -π/2

or

x = π/2 + π/4 = 3π/4

Note that the interval [0, 2) contains 0, π/2, and π, but none of these values satisfy the equation. Therefore, the solutions in the given interval are:

x = -π/2 and x = 3π/4.

Hence, the solutions to the equation sin x - 1 = cos x in the interval [0, 2) are x = -π/2 and x = 3π/4, in radians in terms of π.

What is the domain of the equation?

Answers

The domain of the equation include the following: D. all real numbers.

What is a domain?

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

How to identify the domain any graph?

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-4, ∞}

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A pottery class, 30kg of clay are divided into portion of 5/8kg each, and it just enough to distributes to all the students. how many students are there in the class?

Answers

There are 48 students in the pottery class

30kg of clay is divided into 5/8kg chunks, and there is just enough for all of the kids. To find the number of students in the class, we need to divide the total amount of clay by the amount of clay per student.

The amount of clay per student is 5/8kg.

So, number of students = (total amount of clay) / (amount of clay per student)

Dividing the total amount of clay by the amount of clay per student, we get:

30 / (5/8) = 30 x 8/5

= 48

Therefore, there are 48 students in the pottery class

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Find the missing information for both parts below.
Please help!!!

Answers

Applying the angle of intersecting secants theorem, the missing information is: a. m(XY) = 42°       b. m(PR) = 18°

How to Find the Missing Information Using the Angle of Intersecting Secants Theorem?

To find the missing information, use the angle of intersecting secants theorem to create an equation, then solve accordingly.

a. 31 = 1/2(104 - m(XY)) [based on the angle of intersecting secants theorem]

31 * 2 = 104 - m(XY)

62 = 104 - m(XY)

62 - 104 = -m(XY)

-42 = -m(XY)

m(XY) = 42°

b. 34 = 1/2(m(PR - 50) [based on the angle of intersecting secants theorem]

34 = 1/2(m(PR - 50)

68 = m(PR) - 50

68 - 50 = m(PR)

m(PR) = 18°

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Help plsss!!!
Quadrilateral A' B' C' D' is the image of quadrilateral A B C D under a translation.

Answers

Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a translation of 2 units to the right and 5 units to left.

Given information:

Quadrilateral A'B'C'D' is the image of quadrilateral ABCD.

In Euclidean geometry, a translation is a geometric transformation that entails shifting each point in a figure, shape, or space by the same amount in one direction.

A translation may also be conceived of as changing the coordinate system's origin or as adding a constant vector to each point.

As per the diagram:

A(-5, 3) translates to A'(-3, -2).

As per the translation rule:

A translates to A' as per the rule of 2 units to the right and 5 units to left.

Similarly, all the remaining coordinates follow the same translation rule.

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Explain why a square with the same area as the parallelogram and with its vertices at the intersections of grid lines cannot be drawn

Answers

A square cannot be drawn with the same area as the parallelogram and with its vertices at the intersections of grid lines because the sides of the square would have to be diagonal to the grid lines.

What is square?

A square is a geometrical shape with four equal sides and four equal angles, each of which is a right angle (90 degrees).

A parallelogram can be drawn on a grid by connecting its vertices with line segments that are parallel to the grid lines. However, a square cannot be drawn with the same area as the parallelogram and with its vertices at the intersections of grid lines because the sides of the square would have to be diagonal to the grid lines.

This means that the sides of the square cannot be parallel to the grid lines. If the sides of the square are not parallel to the grid lines, then it cannot be drawn on the grid in a way that all of its vertices lie at the intersections of grid lines.

Therefore, a square with the same area as the parallelogram and with its vertices at the intersections of grid lines cannot be drawn.

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In triangle PQR, let X be the intersection of the angle bisector of angle P with side QR, and let Y be the foot of the perpendicular from X to side PR. If PQ = 9, QR = 9, and PR = 9, then compute the length of XY.

Answers

In the triangle PQR, let X represent the point where angle P and side QR connect, and let Y represent the foot of the perpendicular that runs from X to side PR. The length of XY is  2.25 × √(3) units.

What are triangles?

By drawing straight lines from three non-collinear points, a triangle is a three-sided polygon.

It is a basic geometric shape having several properties and applications in science, technology, engineering, and other fields.

Depending on the size of their angles and side lengths, triangles can be divided into different categories.

Due to the fact that PQ = QR = PR, triangle PQR is an equilateral triangle.

Let's write x as the length of each angle in this triangle. Since the angle P is divided into two equal halves by the angle bisector, the measures of the angles PXQ and QXR are both x/2.

Let's write d to represent XY's length. Trigonometry can be used to determine the length of XY since triangle PXY is a right triangle. Specifically, we have

tan(30) = XY / PY

Since PY = PQ - QY and PQ = QR = 9, we have PY = 9 - QY. Therefore:

tan(30) = XY / (9 - QY)

Solving for XY, we get:

XY = (9 - QY) tan(30)

QY needs to be located. The Pythagorean theorem can be used to determine QY because triangle QYX is also a right triangle:

QY² + XY² = QX²

Triangle QRX being a 30-60-90 triangle gives us:

QX = QR / 2 = 4.5

Therefore:

QY² + XY² = 4.5²

QY² + (9 - QY)² tan²(30) = 4.5²

The result of simplifying and solving for QY is:

QY = 2.25

Inputting this value into the XY expression yields the following result:

XY = (9 - 2.25) tan(30) = 2.25 × √(3)

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