Let’s begin with a 30°-60°-90° triangle. A 30°-60°-90° triangle with a hypotenuse of 2 units is shown.

If another right triangle contains a 30° or a 60° angle but is a different size, what can you say about the side lengths of that triangle in terms of the given triangle? Explain your answer.

Answer:

y = -3x + 4

Step-by-step explanation:

y = mx + c

y = gradient(x intercept) + y intercept

y = -3x + 4

It looks like the boundaries of [tex]R[/tex] are the lines [tex]y=\dfrac23x [/tex] and [tex]y=3x[/tex], as well as the hyperbolas [tex]xy=\frac23[/tex] and [tex]xy=3[/tex]. Naturally, the domain of integration is the set

[tex]R = \left\{(x,y) ~:~ \dfrac{2x}3 \le y \le 3x \text{ and } \dfrac23 \le xy \le 3 \right\}[/tex]

By substituting [tex]x=\frac uv[/tex] and [tex]y=v[/tex], so [tex]xy=u[/tex], we have

[tex]\dfrac23 \le xy \le 3 \implies \dfrac23 \le u \le 3[/tex]

and

[tex]\dfrac{2x}3 \le y \le 3x \implies \dfrac{2u}{3v} \le v \le \dfrac{3u}v \implies \dfrac{2u}3 \le v^2 \le 3u \implies \sqrt{\dfrac{2u}3} \le v \le \sqrt{3u}[/tex]

so that

[tex]R = \left\{(u,v) ~:~ \dfrac23 \le u \le 3 \text{ and } \sqrt{\dfrac{2u}3 \le v \le \sqrt{3u}\right\}[/tex]

Compute the Jacobian for this transformation and its determinant.

[tex]J = \begin{bmatrix}x_u & x_v \\ y_u & y_v\end{bmatrix} = \begin{bmatrix}\dfrac1v & -\dfrac u{v^2} \\\\ 0 & 1 \end{bmatrix} \implies \det(J) = \dfrac1v[/tex]

Then the area element under this change of variables is

[tex]dA = dx\,dy = \dfrac{du\,dv}v[/tex]

and the integral transforms to

[tex]\displaystyle \iint_R 9xy \, dA = \int_{2/3}^3 \int_{\sqrt{2u/3}}^{\sqrt{3u}} \frac{dv\,du}v[/tex]

Now compute it.

[tex]\displaystyle \iint_R 9xy \, dA = \int_{2/3}^3 \ln|v|\bigg|_{v=\sqrt{2u/3}}^{v=\sqrt{3u}} \,du \\\\ ~~~~~~~~ = \int_{2/3}^3 \ln\left(\sqrt{3u}\right) - \ln\left(\sqrt{\frac{2u}3}\right) \, du \\\\ ~~~~~~~~ = \frac12 \int_{2/3}^3 \ln(3u) - \ln\left(\frac{2u}3\right) \, du \\\\ ~~~~~~~~ = \frac12 \int_{2/3}^3 \ln\left(\frac{3u}{\frac{2u}3}\right) \, du \\\\ ~~~~~~~~ = \frac12 \ln\left(\frac92\right) \int_{2/3}^3 du \\\\ ~~~~~~~~ = \frac12 \ln\left(\frac92\right) \left(3-\frac23\right) = \boxed{\frac76 \ln\left(\frac92\right)}[/tex]

Answer:1.166 reams of paper.

Step-by-step explanation:

Just use simple division and divide 7/6.

Each classroom will get  [tex]\dfrac{7}{6}[/tex]  paper when there are 6 fifth grade classrooms that share 7 packs of paper.

A fraction is defined as a part of a whole. The upper part of the fraction is called the numerator, and the lower part is called the denominator.

Given that:

Number of fifth grade classrooms = 6

Number of packs of paper = 7

The number of paper each classroom get in fractions can be obtained by dividing the number of packs of paper by the number of fifth grade classrooms.

Each classroom get = [tex]\dfrac{Number \ of \ packs \ of \ paper}{ \ Number \ of \ fifth \ grade \ classrooms}[/tex]

Each classroom get = [tex]\dfrac{7}{6}[/tex]

Each classroom will get  [tex]\dfrac{7}{6}[/tex]  paper.

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Answer:

Each Person:

-In tips: $2

-Food Bill: $7.50

Step-by-step explanation:

Let's find the tip amount for each person. $16 for the whole group. Each person will give in $2 for the tips, for a total of $16 in tips.

Now that tips are done, we must subtract the amount of tips from the food bill, to see how much each person pays. $76 - $16 = $60.

Divide 60 by 8 to get.. 60/8= 7.5.

With 7.5 as an answer, we can conclude that each person paid $7.50 for the food bill.

I see you need to select solutions, may I see them to help you out? The description is pretty vague..

G is the matrix representation of the four colored graph.

According to the statement

we have given that a graph is colored with one of the four colors red, blue, yellow, or green.

And we have to represent the edges of this graph using a variation of the adjacency matrix structure

So, Adjacency Matrix Structure is a way of representing a graph as a matrix of booleans (0's and 1's). A finite graph can be represented in the form of a square matrix on a computer, where the boolean value of the matrix indicates if there is a direct path between two vertices.

And in this graph representation the Adjacency Matrix Structure denoted by a matrix G.

so, there are a four colors used that's why there are 4 into 4 matrix is formed to represent the edges.

G =  [tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]

And this is the matrix representation of the graph which is colored with four graphs.

So, G is the matrix representation of the four colored graph.

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Answer: 384 feet

Step-by-step explanation:

     We will simplify and solve -16t² + 160t when t is equal to 4.

-16t² + 160t

-16(4)² + 160(4)

384 feet

Answer:

Step-by-step explanation:

**Note: The polynomial in question is -16t² + 160t, as clarified in the discussion under the question.**

Since there is a polynomial to find the height given a certain time, the height is a function of time.

This function would be h(t) = -16t² + 160t, so plugging in 4 for t would give the height.

[tex]h(4) = -16(4)^2+160(4)[/tex]

[tex]-16(16)+160(4)[/tex] [Squaring 4]

[tex]-256 + 640[/tex] [Multiplying]

[tex]384[/tex] [Combining both terms]

Hence, the height of the firework after 4 seconds is 384 feet.

Answer:

I think that is is C

Step-by-step explanation:

The Vertical Line Test determines whether or not a curve on the graph is a function. This one passes the vertical line test because no vertical line can intersect the curve more than once. I hope that helps!

Answer:

No, L and S are parallel.

Step-by-step explanation:

Perpendicular lines go directly opposite from each other, making a + looking arrangement. While parallel lines go in the exact same direction, making a = looking arrangement. The only way both S and L can both be perpendicular to R is if they are both parallel to each other. An illustration by yours truly is placed below to represent it visually.

                    L                                              |

_______________________________|_____

                                                                    |

                                                                    |

                                                                    |   R

                                                                    |

_______________________________|_____

                     S                                             |  

                                                                    |

Now, if this were on the outside of a sphere, then it would be totally possible to have three lines all be parallel, because they can curve with the sides of the sphere and create a triangle with all right angles.

Answer: There are only 90 two-digit numbers. It shouldn’t take long to write them out and count them

Step-by-step explanation:

Answer:

45 numbers

Step-by-step explanation:

The 10-digit numbers are 10-99. We can manually write them out to start and see if we can find a pattern.

We can start 10-19: The numbers that have one odd digit and one even digit at 10, 12, 14, 16, 18 (since 1 is odd, we can only pick the numbers that have an even unit digit)

Next, we move on to 20-29: The numbers that follow the property are 21, 23, 25, 27, 29

Both of these examples have 5 numbers that follow the property. We can notice that all of the subsequent clusters (30-39, 40-49, 50-59, 60-69, 70-79, 80-89, 90-99) will also have 5 each. The numbers that start with an odd number will have the same unit digits as the 10-19 cluster, and the numbers that start with an even number will have the same unit digits as the 20-29 cluster. Observe:

30-39: 30, 32, 34, 36, 38

40-49: 41, 43, 45, 47, 49

50-59: 50, 52, 54, 56, 58

60-69: 61, 63, 65, 67, 69

70-79: 70, 72, 74, 76, 78

80-89: 81, 83, 85, 87, 89

90-99: 90, 92, 94, 96, 98

In all, there are 9 clusters of numbers, and each one has 5 numbers that follow the property. Therefore, the total is 9*5 or 45 numbers

a. The mean, median and mode for this plot are 70.8, 70 and 60 respectively.

b. Mean best represents the data for this plot.

c. When there are outliers, the mean might be a deceptive center tendency measure.

Mean, Median, and Mode

Mean = Sum of prices / Total number of sunglasses

Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25

Mean = 70.8

Median is equal to (n/2 + 1) when n is an odd number.

Here, the number of sunglasses is represented by n.

⇒ (25/2 + 1)th term is the median

Median = 13th term

Median = 70

Mode is the most frequent data from the plot.

⇒ Mode = 70

Mean Being the Best Central Measure

The mean is often the ideal measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data are normally distributed. So, mean here denotes the typical cost of the sunglasses.

Misleading Measure

When there are outliers, the data mean is significantly impacted. As a result, it may be inaccurate when examining the data's average price.

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Considering the sum of the internal angles of the triangle, the angle of elevation from point L to point J is of 37º.

The sum of the internal angles of a triangle is of 180º.

In this problem, the angles are:

90º, 53º, x

Hence:

90 + 53 + x = 180

x = 180 - 143

x = 37º

The angle of elevation from point L to point J is of 37º.

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Answer:

53*

Step-by-step explanation:

took on edge

Answer:

B. 54π units ²

Step-by-step explanation:

solution:

given,

Radius (r) = 3

(l) = 15

we know that,

T.S.A. of cone = πr( r + l )

= π × 3(3 + 15)

= π × 3 × 18

= π × 54

= 54π units ²

We can identify that the missing reason in the proof is: Definition of Congruent angles.

We know that an angle measure of 90° of ∠ABC in the triangle means that it is a right angle triangle.

We also see that ∠ADB is also a right angle and is equal to 90°.

Now, since they have exactly the same measure, these angles are congruent. Then we can say that the angles are congruent and as such:

∠ABC ≅ ∠ABD

Thus, we can identify that the missing reason is: Definition of Congruent angles.

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Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.  This can be obtained using finding y intercept of both parabolas and vertex of parabola A.

Parabola A, (x + 3)² = y = x² + 6x + 9

Parabola B, y = mx + 9

x=0, y = 9

y coordinate of parabola A is (0,9)

⇒The vertex coordinate,

(-b/2a , -(b²-4ac)/4a) = (-3,0)          

x=0, y = 9  

y coordinate of parabola B is (0,9)    

Isabel claims one solution to the system of two equations must always be the vertex of parabola A which is wrong.  

Hence Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Parabola A can be represented using the equation (x + 3)2 = y, while line B can be represented using the equation y = mx + 9. Isabel claims one solution to the system of two equations must always be the vertex of parabola A. Which best describes the reasonableness of her claim?

88e interprets the total cost for all the economy class seats, as all seats are sold, where 88 is the number of economy class seats and e dollars is the cost of each economy class seat.

In the question, we are given an equation, C = 24f + 88e, and are informed that the cost, C, in dollars from an airplane flight given that the average cost of a first class seat is f dollars and the average cost of an economy seat is e dollars is given by the equation above if all seats are sold.

We are asked for the interpretation about the 88e as shown in the equation.

The equation given to us is a cost equation.

A cost equation comprises of two parts:

In the given equation, we have two types of quantities:

Thus, both these quantities must be having a per unit price, multiplied by the number of units sold.

Now, we are informed that e dollars is the per unit price for an economy class seat.

Thus, 88e interprets the total cost for all the economy class seats, as all seats are sold, where 88 is the number of economy class seats and e dollars is the cost of each economy class seat.

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For complete question, refer to the attachment.

The thousand of miles across the United states from the east coast to the west coast.

In order to find the number of miles across the United states from the east coast to the west coast.

Hence, the thousand of miles across the United states from the east coast to the west coast.

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Answer:

Both A and B

Step-by-step explanation:

A set of ordered pairs is not a function if there is a repeating output (Y value.)

Y values of A= 5, 2, -2, -5.

Y values of B= 2, -2, 4, -3.

There are no repeating outputs.

The area of the plate covered by the napkin is (C) [tex]56cm^{2}[/tex].

What is an area of a triangle?

To find the area of the plate covered by the napkin:

Given :

The following steps can be used in order to determine the area of the plate covered by the napkin:

Step 1 - The formula of the perimeter of a triangle is given below:

P = a + b + c   --- (1)

where a, b, and c are the length of the sides of the triangle.

Step 2 - According to the given data, the triangle is isosceles.

Therefore, the two sides are similar and the length of the base is 8 cm.

Step 3 - Now, substitute the values of the known terms in the above formula.

38 = 2L + 8

38 - 8 = 2L

L = 15 cm

Step 4 - The area of the plate covered by the napkin is given below:

[tex]A=\frac{1}{2} * 15 * 15 *Sin30[/tex]

Step 5 - Simplify the above expression.

[tex]A=56.25cm^{2}[/tex]

Rounding off to the nearest whole number, which is [tex]56cm^{2}[/tex].

Therefore, the area of the plate covered by the napkin is (C) [tex]56cm^{2}[/tex].

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The question you are looking for is here:

A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters. To the nearest square centimeter, how many square centimeters of the plate is covered by the napkin?

(A) 16 square centimeters

(B) 30 square centimeters

(C) 56 square centimeters

(D) 60 square centimeters

Outliers are sample values that lie very far away from the majority of the other sample values.

We know that, an outlier is an observation that lies an abnormal distance from other values in a random sample from a population.

It differs significantly from other observations in a sample values.

Outlier is a value that is distant from the majority of the values in a data set.

For a scatter plot, an outlier is the point or points that are farthest from the regression line.

For example in the record of marks 25, 29, 7, 32, 85, 33, 27, 28 both 7 and 85 are outliers.

Therefore, outliers are sample values that lie very far away from the majority of the other sample values.

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Answer:

[tex]\huge\boxed{\sf A = 78.5\ ft\²}[/tex]

Step-by-step explanation:

Circumference = C = 31.4 ft

We know that,

Where, r is the radius

31.4 = 2(3.14)r

31.4 = 6.28(r)

Divide 6.28 to both sides

31.4/6.28 = r

5 ft. = r

Now,

A = πr²

A = (3.14)(5)²

A = (3.14)(25)

[tex]\rule[225]{225}{2}[/tex]

Answer:

324[tex]\pi[/tex] units³

Step-by-step explanation:

Surface Area of Sphere = 4[tex]\pi[/tex]r²; where 'r' is the radius of the sphere.

4[tex]\pi[/tex]r² =

4[tex]\pi[/tex]9² =

4[tex]\pi[/tex]81 =

324[tex]\pi[/tex] units³

Answer:

324[tex]\pi[/tex] unit^2

Step-by-step explanation:

The formula for finding the surface area of a sphere is: [tex]A = 4\pi r^2[/tex]

--> A = Surface area of the sphere

--> r = Radius of the sphere

The image shows that the radius of the sphere is 9.

All we need to do is to replace r with 9.

--> A = 4[tex]\pi[/tex]9^2

--> A = 4[tex]\pi[/tex]81

--> A = 324[tex]\pi[/tex]

So that is your final answer! 324[tex]\pi[/tex] unit^2

--> It is unit^2 since it is an area, not a volume.

+ I'm leaving this as [tex]\pi[/tex], since the question is asking for the exact value, not the ones that are rounded up.

The total amount in the investment account is $3031.00

The given parameters are

Principal, P = $2800

Rate, r = 5.5%

Time = 18 months i.e. 1.5 years

The amount is then calculated as:

A = P + PRT

This gives

A = 2800 + 2800 * 5.5% * 1.5

Evaluate

A = 3031

Hence, the total amount in the investment account is $3031.00

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The solution to the system of inequalities x < 2y + 3 and -2x < y + 1 is the darker region shown in the graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequality is an expression that shows the non equal comparison of two or more numbers and variables.

The solution to the system of inequalities x < 2y + 3 and -2x < y + 1 is the darker region shown in the graph.

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The system of inequalities x > 2 · y + 3 and - 2 · x < y + 1 includes the point (x, y) = (10, 0).

The solution area of the two inequalities given in the statement does not contain the point (x, y) = (10, 0) as we can see in the first figure.

But if we change the sign "<" for ">" in the first inequality, then the solution area includes the point mentioned above. Please see the second figure for further details.

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The inequality that represents the height that is displayed by the graph is: 10 ≤ h ≥ 50.

In an inequality graph, we the small circle at any end is shaded or full, the inequality sign used is either "less than or equal to" or "greater than or equal to" ("≤" or "≥"). If the circle is empty or not shaded, we use "less than" or "greater than" ("<" or ">").

In the graph showing Jeremy’s height above the ground at any time during the ride, we have a full circle (shaded) starting from 10, and another on the right at 50.

This implies that the range of height is from 10 to 50. Since the circle is full (shaded), then we would use "less than or equal to" and "greater than or equal to" ("≤" and "≥") in writing the inequality that represents the height.

Thus, where h is the height, the inequality would be: 10 ≤ h ≥ 50.

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Answer:

there will be 17 integers!

List :

1

4

9

16

25

36

49

64

81

100

121

144

169

196

225

256

289

They're all squares, like for example, 1^2, 2^2, 3^2, etc

Answer:

cheapt

Step-by-step explanation:

It means the probability of a random permutation of n numbers gets sorted after 1 pass of bubble sort is n!

According to the statement

we have to find the probability of random permutation of the N numbers.

So, according to the definition of A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable.

In this we order of select the objects randomly.

So, Let There are n−1 comparisons, so 2n−1 possible sequences of actions - swap or don't swap.

To find the permutations, start with 1,2,3,4,5 and undo a sequence.

For example, if let n=5, there are 24=16 out of 5!

which is 5! =120 that end after one round of bubble sort.

So, It means the probability of a random permutation of n numbers gets sorted after 1 pass of bubble sort is n!

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The arc length of [tex]y=2\cos(3x)[/tex] on the interval [tex][a,b][/tex] is

[tex]\displaystyle \int_a^b \sqrt{1 + (y')^2} \, dx = \int_a^b \sqrt{1 + (-6\sin(3x))^2} \,dx = \boxed{\int_a^b \sqrt{1+36\sin^2(3x)} \, dx}[/tex]

Answer:

10

Step-by-step explanation:

It's just symmetry. You see that the geometrical construction above has been rotated, so its properties will remain the same.

Answer:

(-2, -0.5)

Step-by-step explanation:

1. add the x-coordinates and then either divide by 2 or multiply by 1/2

2. add the y-coordinates and then either divide by 2 or multiply by 1/2

(-7+3)/2 = -2

(-10+9)/2 = -0.5

Have a blessed day!

Answer:369

Step-by-step explanation:

all you have to do is multiply 18 and 22 its easy

18 x 22 = 369.