boiling point of water

The polar coordinates (r, θ) for the given rectangular coordinates are

(10, π/3)

To convert rectangular coordinates (5, 5√3) to polar coordinates (r, θ), we can use the following formulas:

r = √(x² + y²)

θ = arc tan (y/x)

Given the rectangular coordinates (5, 5√3), we have:

x = 5

y = 5√3

let's calculate the values

r = √(5² + (5√3)²

= √(25 + 75)

= √100

= 10

θ = arctan(5√3/5)

= arctan (√3)

= π/3 (since θ is in the interval [0,2π))

Therefore, the polar coordinates (r, θ) for the given rectangular coordinates are (10, π/3).

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Angle 4 is equal to the sum of the measures of the two nonadjacent interior angles because of the corresponding angles theorem for parallel lines and a transversal.

Angle 4 can be considered as the sum of two nonadjacent interior angles because of the properties of parallel lines and a transversal line. When a transversal line intersects two parallel lines, it creates several pairs of corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.

In this case, we have two parallel lines and a transversal line that intersects them.

Angle 4 is formed by the intersection of the transversal line with one of the parallel lines.

The two nonadjacent interior angles that we are interested in can be identified as the adjacent angles on the other parallel line, corresponding to the same transversal line.

According to the corresponding angles theorem, when two parallel lines are cut by a transversal line, the corresponding angles formed are congruent.

Therefore, the two nonadjacent interior angles that correspond to angle 4 are congruent.

Since congruent angles have the same measure, we can conclude that the measure of angle 4 is equal to the sum of the measures of the two nonadjacent interior angles.

This property holds true for any pair of parallel lines intersected by a transversal line.

It is a fundamental concept in geometry that helps us understand the relationships between angles formed by parallel lines and transversals, and it is useful in solving various geometric problems and proofs.

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As per the given image, the surface area of the composite figure is 1996 square meters.

Calculating the surface areas of the rectangular prism and the prism at the top separately and adding them together will yield the surface area of the composite figure.

The rectangular prism's surface area is as follows:

Surface Area = 2(length x width + length x height + width x height)

Surface Area of rectangular prism = 2(15m x 10m + 15m x 25m + 10m x 25m)

= 2(150m² + 375m² + 250m²)

= 2(775m²)

= 1550m²

Surface Area = 2(length x width) + perimeter of base x height

Surface Area of prism = 2(8m x 6m) + (8m + 6m) x 25m

= 2(48m²) + 14m x 25m

= 96m² + 350m²

= 446m²

Total surface area = Surface Area of rectangular prism + Surface Area of prism

= 1550m² + 446m²

= 1996m²

Thus, the answer is 1996m².

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The correct matches are:

-10u³ ⇒ -15u³ + 5u³

  5u³ ⇒ 10u³ + (-5u³)

 15u³ ⇒ 10u³ + 5u³

 -5u³ ⇒ 5u³ + (-10u³)

For the expressions:

Expression 1:

-15u³ + 5u³

To add these expression taking u³,

⇒ (-15 + 5)u³

⇒ -10u³

Expression 2:

⇒ 10u³ + (-5u³)

To add these expression taking u³

⇒ (10 - 5)u³

⇒ 5u³

Expression 3:

⇒ 10u³ + 5u³

To add these expression taking u³

⇒ 15u³

Expression 4:

⇒ 5u³ + (-10u³)

To add these expression taking u³

⇒ (5 - 10)u³

⇒ -5u³

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The complete question is attached below:

While one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

In a race between two runners, one of them had a personal best time, while the other runner neither trained nor had a personal best time.

The runner who had a personal best time implies that they had trained and put in effort to improve their performance. A personal best time suggests that they have achieved their highest level of performance in a race. This indicates that the runner has dedicated time and effort to their training regimen, focusing on improving their speed and endurance.

On the other hand, the runner who neither trained nor had a personal best time implies that they did not invest effort in training or actively seek to improve their performance. They may have participated in the race casually or without specific training goals in mind. As a result, they did not achieve a personal best time, indicating that they did not put in the necessary effort to reach their full potential.

In summary, while one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

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The slope of the line passing through the points (-6, 1) and (8, -7) is -4/7.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Point A: ( -6,1 )

x₁ = -6

y₁ = 1

Point B: ( 8,-7 )

x₂ = 8

y₂ = -7

Now, plug the given x and y values into the slope formula above and simplify:

[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{-7 - 1}{8 - (-6)} \\\\Slope\ m = \frac{-7 - 1}{8 + 6} \\\\Slope\ m = \frac{-8}{14} \\\\Slope\ m = -\frac{4}{7}[/tex]

Therefore, the slope of the line is -4/7.

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The Probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

To find the probability that the randomly chosen coin is gold, given that it is small, we need to determine the number of small gold coins and the total number of small coins.

From the given information, Marco has 12 small gold coins and 3 small silver coins, making a total of 12 + 3 = 15 small coins.

The probability that the coin is gold, given that it is small, can be calculated as the ratio of the number of small gold coins to the total number of small coins:

P(Gold|Small) = Number of Small Gold Coins / Total Number of Small Coins

P(Gold|Small) = 12 / 15

Simplifying the fraction, we have:

P(Gold|Small) = 4 / 5

Therefore, the probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

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Answer:

It takes 135 of the 1/3 unit cubes to fill the prism.

Step-by-Step Explanation:

The volume of the prism is 5 cubic units. This means the prism can be filled with five 1×1×1 unit cubes

How many cubes with 1/3 unit side lengths can fit in a cube with 1-unit side lengths?

There are 27 cubes with 1/3 unit side lengths in 1 cubic unit.

Since the rectangular prism is made up of 5 cubic units, we would have 5×27 total cubes with 1/3 unit side lengths.

It takes 135 of the 1/3 unit cubes to fill the prism.

Answer:

The polynomial 2x^3 + x^2 - 2x - 1 can be factored as (x + 1)(2x^2 - x - 1).

Step-by-step explanation:

To find the factors of the polynomial 2x^3 + x^2 - 2x - 1, we can use synthetic division or long division to divide the polynomial by the factor x + 1.

Using synthetic division:

-1 | 2 1 -2 -1

| -2 1 1

___________________

2 -1 -1 0

The result of the division is 2x^2 - x - 1.

So, the polynomial 2x^3 + x^2 - 2x - 1 can be factored as (x + 1)(2x^2 - x - 1).

Answer:

Step-by-step explanation:

Solution

verified

Verified by Toppr

given, 2x

3

+x

2

−2x−1

=x

2

(2x+1)−1(2x+1)

=(x

2

−1)(2x+1)

=(x+1)(x−1)(2x+1)

The value of x is 94 degree.

we know that

The inscribed angle measures half that of the arc comprising

So, <K = 1/2 (80+92)

<K = 1/2 x 172

<K = 86 degree

Now, inscribed quadrilateral, the opposite angles are supplementary

So, <K + x= 180

86 + x = 180

x = 180- 86

x= 94 degree

Thus, the value of x is 94 degree.

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The first three pairs are of vertically opposite angles.

Given figure,

Vertical angles are the angles that are opposite to each other.

Hence the pairs of vertical angles will be opposite to each other as well as will be equal to each other.

So,

Vertical opposite angles are :

Option A

Option B

Option C

Thus 3 pairs will be considered for vertical angles .

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The number of Cheetos you can buy in the supermarket is 7.

You have $16 and a coupon for a five dollar discount at a local

supermarket . One bag of hot Cheetos cost 3 dollars. Therefore, the

number  of bag of Cheetos you can buy can be calculated as follows:

Therefore, altogether he has 16 + 5(coupon discount)  = 21 dollars to spend

in the super market.

Therefore,

number of Cheetos worth 3 dollars one can buy = 21 / 3

number of Cheetos worth 3 dollars one can buy = 7

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The function that describes the table of values is y = 1/2x + 2

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

x= (-8) (-4) (4) (8)

y= (-2) (0) (4) (6)

From the table, we can see that

As x increases by 4

The y values increase by 2

So, we have

m = Slope = 2/4 = 1/2

The equation is calculated as

y = mx + c

So, we have

y = 1/2x + c

Using the other points, we have

1/2 * -4 + c = 0

So, we have

c = 2

This gives

y = 1/2x + 2

Hence, the function that describes the table of values is y = 1/2x + 2

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Answer:

Hi

Please mark brainliest ❣️

Step-by-step explanation:

-3 1/4 ÷ 2 1/3

Change to improper fraction

-13/4 ÷ 7/3

-13/4 × 3/7

-39/28 or -1 11/28

The  best measure of center for the data shown is the median, and its value is 17.

The median is the best measure of center for the given data set. To find the median, we arrange the numbers in ascending order:

10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Since the data set has an odd number of values, the median is the middle value, which in this case is 17.

Therefore, the best measure of center for the data shown is the median, and its value is 17.

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Based on the information provided, the triangle ABC is an Isosceles triangle.

If triangle ABC is equal to triangle DEF and AB is equal to EF, it means that the corresponding sides and angles of the two triangles are congruent.

Based on the information given, we can conclude that triangle ABC is an isosceles triangle. An isosceles triangle is a triangle that has two sides of equal length. In this case, sides AB and EF are equal in length, making triangle ABC isosceles.

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Answer: 48

Step-by-step explanation:

This isn't college

J=2S

J+S=72

3S=72

S=24

24*2=48

Juan has 48

The surface area of the triangular prism is 137ft².

To get the surface area of a triangular prism, we will calculate the area of each face and then sum them up.

Base area = (4 ft * 5 ft) / 2

Base area = 20ft/2

Base area = 10 ft²

Since triangular prism has two triangular bases, the total area of the triangular bases is:

= 2 * Base area

= 2 * 10 ft²

= 20 ft².

Perimeter of the triangular base:

= 4 ft + 5 ft + 4 ft

= 13 ft

Face area = Perimeter * Height

Face area = 13 ft * 3 ft

Face area = 39 ft²

The total area of the rectangular faces is:

= 3 * Face area

= 3 * 39 ft²

= 117 ft².

The Surface area of the triangular prism will be:

= Total area of triangular bases + Total area of rectangular faces

= 20 ft² + 117 ft²

= 137 ft².

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The required answer are :

a. Odds in favor of drawing a spade: 13:39 or simplified as 1:3.

b.the odds against drawing a five are:

Favorable outcomes: 4 Unfavorable outcomes: 48

Odds against drawing a five: 48:4 or simplified as 12:1.

Given that, suppose one card is drawn at random from a standard deck.

To find the odds in favor of drawing a spade, we need to determine the number of favorable outcomes (spades) and the number of unfavorable outcomes (non-spades).

In a standard deck of 52 cards, there are 13 spades (A♠, 2♠, 3♠, ..., 10♠, J♠, Q♠, K♠) and 39 non-spades (all other cards).

The odds in favor of drawing a spade can be expressed as the ratio of favorable outcomes to unfavorable outcomes. Therefore, the odds in favor of drawing a spade are:

Favorable outcomes: 13 Unfavorable outcomes: 39

Odds in favor of drawing a spade: 13:39 or simplified as 1:3.

(b) To find the odds against drawing a five, we need to determine the number of favorable outcomes (non-fives) and the number of unfavorable outcomes (fives).

In a standard deck of 52 cards, there are 48 non-fives (all cards except 5♠, 5♥, 5♦, and 5♣) and 4 fives (5♠, 5♥, 5♦, and 5♣).

The odds against drawing a five can be expressed as the ratio of unfavorable outcomes to favorable outcomes.

Therefore, the odds against drawing a five are:

Favorable outcomes: 4 Unfavorable outcomes: 48

Odds against drawing a five: 48:4 or simplified as 12:1.

Hence, the answer are:

a. Odds in favor of drawing a spade: 13:39 or simplified as 1:3.

b.the odds against drawing a five are:

Favorable outcomes: 4 Unfavorable outcomes: 48

Odds against drawing a five: 48:4 or simplified as 12:1.

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Answer:

  (a)  Multiply (200.96)(22).

Step-by-step explanation:

You want the volume of the cylinder with base area 200.96 mm² and height 22 mm.

The volume is found using the formula ...

  V = Bh

where B is the base area, and h is the height.

For base area 200.96 mm² and height 22 mm, the volume is ...

  V = (200.96)(22) mm³

You find the volume by multiplying 200.96 and 22.

<95141404393>

La respuesta: 20-(-40)=60. 50-(-50)=100.

Para 20-___=60, tienes que restar 60 de 20. 20-60=-40

Para 50-___=100. tienes que restar 100 de 50. 50-100=-50.

Un negativo menos un negativo es igual a un positivo.

The points on the scatter plot show the different predictions. The straight line drawn is called the line of regression.

Errors in prediction for each point can be determined by drawing a vertical line from the point to the line of regression. As seen in the image, all of the prediction points are found on the line except for points (14,25) and (16,25). Therefore, these points contain errors in prediction.

The graph that represent this data using the points is added as an attachment

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

The x and y values

Where

x = stars

y = price

To determine the graph that represent the data, we enter the x and y values in a graphing tool to create the graph

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The measure of central angle DBC is 68 degree.

Hence, option C is correct.

In the given figure,

Measure of intercepted arc = 68 degree,

We have to find the measure of central angle DBC

We know that,

When two circle radii intersect in the center of a circle, they produce a vertex. These circle arms may begin at two distinct positions along the arc of such a circle. The two radii cross to produce a central angle, which serves to divide a circle into separate sectors.

A central angle is generated in the center of a circle when two radii within the circle overlap. As previously stated, a central angle in geometry is one whose vertex forms at the canter of the circle and whose arms cross the circle at two separate positions.

By connecting these two locations, an arc on the circle is formed. As a result, a central angle is the angle formed by an arc in the center of a circle.

Thus by property of central angles,

central angle = measure of intercepted arc

Hence,

⇒ m ∠DBC = 68 degree.

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Solving a system of equations we can see that each pound of trail mix costs $3.50, and each pound of jelly beans costs $1.50

Let's define the variables:

Then we can write a system of equations so we will get:

5x + 3y = 22

2x + 12y = 25

To solve this, we can subtract 4 times the first equation fom the second one:

2x + 12y - 4(5x + 3y) = 25 - 4*22

2x + 12y - 20x - 12y = -63

-18x = -63

x = -63/-18

x = 3.5

That is the cost of each pound of trail mix, and replacing that in one of the equations:

2*3.5 + 12y = 25

y = (25 - 2*3.5)/12

y = 1.5

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The inequality to solve for p is 6p > 600 and the solution is p > 100

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

Selling price = $6 per apple

So, we have

Total = 6p

Also, we have

Spendings = $600

To make profit, we have

6p > 600

Divide by 6

p > 100

Hence, the inequality to solve for p is 6p > 600 and the solution is p > 100

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Option 2 is the correct graph for the function f(x) = [tex]4[(1/2)^{x}][/tex] .

Given ,

f(x) = [tex]4[(1/2)^{x}][/tex]

Mathematically the graph will of exponential in nature.

So,

Let us assume few values to understand the nature of graph.

Firstly,

Let x= 1

f(x) = [tex]4[(1/2)^{1}][/tex]

f(x) = 2

Let x = 2

f(x) = [tex]4[(1/2)^{2}][/tex]

f(x) = 1

Let x = 3

f(x) = [tex]4[(1/2)^{3}][/tex]

f(x) = 0.5

Thus from these values of f(x) corresponding to the values of x second graph will be correct .

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Lucio is 64 meters from the starting point.

The square has four sides of equal length, so Lucio has walked half the length of one side.

To return to the starting point, he needs to walk the other half of the side, which is 64 meters.

The angle Lucio turns is irrelevant, as long as he turns 180 degrees in total.

With this in mind, it can be seen that based on the parameters and the conditions, Lucio is 64 meters from the starting point because the angle to which he turns is irrelevant.

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The question in English:

In a square Lucio walks in straight sections, starting from the flagpole, at one point he changes direction turning 150º to his left, advances 64 meters and stops. To return to the pole you have to turn 75º to the left. How far are you from the starting point?

Using the distributive property, the boxes would be filled as follows;

(4 × 3 ) + (4 × 7 )

Mathematicians use the distributive property to explain how multiplication distributes across addition or subtraction. It offers a rule for expanding terms and condensing expressions.

With the help of the distributive property, we can factor polynomials, simplify expressions, and solve equations more quickly in algebra and arithmetic.

We know that;

4 × (3 + 7) =(4 × 3 ) + (4 × 7 )

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Answer:

Step-by-step explanation this is a tough one but i know everything the answer is 69