A set of points S is called convex if whenever two points P and Q are in S, the entire segment PQ is contained in S. Prove that the interioir of a triangle ABC is a convex set.

Answer:

12x^9 is the area

Step-by-step explanation:

3x^3 × 4x^6 = 12 x 9

Answer:

2 m.

Step-by-step explanation:

T = 8.0 s is the period of the pendulum

g = 9.81 m/s^2 is the acceleration due to gravity

Answer: x > 3

Step-by-step explanation:

The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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Answer:

True

Step-by-step explanation:

Linear equations are often used to model the relationship between the dependent variable that is affected by changes in the independent variable.  

For instance, the linear function: f(x) = 2x + 3, where f(x) is the output (dependent variable) depends on the value of the input, x (independent variable).  

Therefore, the correct answer is True.      

Step-by-step explanation:

square root 3 divided by

2

The side that will be in palce of Questionmark by Similarity of Triangle is LM.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are described as items with the same shape but varying sizes, such as two or more figures. A hula hoop and the wheel of a bicycle are two examples of things whose forms are similar to one another.

Properties:

in Triangle LMO and LON:

Angle LON = angle LMO = 90 degrees

Angle OLM is a common angle .

Therefore , angle LNO = angle LOM

So triangle LMO and LON are similar (AAA similarity)

So, the ratio of sides are equal.

Therefore,

\(\frac{LN}{LO} = \frac{LO}{LM}\).

The side that will be in palce of Questionmark is LM.

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The side that will be in place of Question mark by Similarity of Triangle is LM.

What is Similarity of Triangle ?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are described as items with the same shape but varying sizes, such as two or more figures. A hula hoop and the wheel of a bicycle are two examples of things whose forms are similar to one another.

Properties:
Despite having the same form, each might have different sizes.
There are no matching angles that are not equal.
Similar equivalent side ratios exist.
in Triangle LMO and LON:
Angle LON = angle LMO = 90 degrees
Angle OLM is a common angle .
Therefore , angle LNO = angle LOM
So triangle LMO and LON are similar (AAA similarity)
So, the ratio of sides are equal.
Therefore,
The side that will be in palce of Questionmark is LM.

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The volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L, calculated using the ideal gas law equation.

To compute this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the initial temperature of 25 °C to Kelvin:

T1 = 25 + 273.15 = 298.15 K

Next, we can rearrange the ideal gas law equation to solve for V2:

V2 = (P1 * V1 * T2) / (P2 * T1)

We have:

P1 = 1.08 atm (initial pressure)

V1 = 50.0 L (initial volume)

P2 = 0.855 atm (final pressure)

T2 = 10.0 °C (final temperature)

Converting the final temperature to Kelvin:

T2 = 10 + 273.15 = 283.15 K

Substituting the values into the equation:

V2 = (1.08 * 50.0 * 283.15) / (0.855 * 298.15)

V2 ≈ 42.81 L

Therefore, the volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L.

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Answer:

-816

Step-by-step explanation:

-12*68= -816 this is probably wrong but this is what i got

Answer:

-816

Step-by-step explanation:

you subtract 9-21 to get -12 then you take 7+61 which is 68 and then you multiply them to get -816

To provide a detailed answer to your question, we first need to have the data for morning (AM) and afternoon (PM) dog groups. Since you didn't provide any data, I will explain the steps to perform the analysis for each part of your question. Create frequency tables:


2. Create frequency tables:
- Collect the dog weights for AM and PM groups
- Divide the weights into classes (ranges of 10 pounds)
- Count the number of dogs in each class for both groups
3. Median of AM and PM groups:
- Sort the dog weights in each group
- Find the middle value for each group
4. First quartile (Q1) of AM and PM groups:
- Find the middle value between the lowest value and the median
5. Third quartile (Q3) of AM and PM groups:
- Find the middle value between the median and the highest value
6. Comparative box plot:
- Create a box plot for each group, showing the five-number summary (minimum, Q1, median, Q3, and maximum)
7. Interquartile range (IQR) of AM and PM groups:
- Calculate IQR by subtracting Q1 from Q3 for both groups
8. Easier group to walk:
- Compare the box plots and IQRs of the two groups
- The group with a smaller IQR and less variation in weights would likely be easier to walk as one group.

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By applying the distributive property of multiplication, the students that are correct in their approach to solving the problem are: Nico, Raj and Sandra.

In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 5/2 as follows:

2/5(5 + x) = 8

Multiplying both sides by 5/2, we have:

5/2 × 2/5(5 + x) = 8 × 5/2

5 + x = 40/2

5 + x = 20

Subtracting 5 from both sides, we have:

5 + x - 5 = 20 - 5

x = 15

In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 1/2 and then 5 as follows:

2/5(5 + x) = 8

Multiplying both sides by 1/2, we have:

1/2 × 2/5(5 + x) = 8 × 1/2

1/5(5 + x) = 4

Multiplying both sides by 5, we have:

5 × 1/5(5 + x) = 4 × 5

5 + x = 20

Subtracting 5 from both sides, we have:

5 + x - 5 = 20 - 5

x = 15

In order to open the bracket and isolate the variable x, we would apply the distributive property of multiplication:

2/5(5 + x) = 8

2/5 × 5 + 2/5 × x = 8

2 + 2x/5 = 8

Subtracting 2 from both sides, we have:

2 - 2 + 2x/5 = 8 - 2

2x/5 = 6

Multiplying both sides by 5/2, we have:

5/2 × 2x/5 = 5/2 × 6

x = 30/2

x = 15.

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Answer:

When there are 2 answers there will be a crown you can click and that will give brainlest

Step-by-step explanation:

=  

a + b + c

2

=  

8 + 10 + 5

2

=  11.5 inches

Area =  √s(s-a)(s-b)(s-c)

=  √11.5×(11.5 - 8)×(11.5 - 10)×(11.5 - 5)

=  19.810035335658 inches

Answer:

the answer is 19.81 inches

Answer:

Step-by-step explanation: Let's solve for b.

m=(−4b)(10)

Step 1: Flip the equation.

−40b=m

Step 2: Divide both sides by -40.

−40b

−40

=

m

−40

b=

−1

40

m

Answer:

b=

−1

40

m

Answer:

C

Step-by-step explanation:

negative four raised to the sixth power divided by negative four raised to the fourth power

because  negative four raised to the fourth power divided by negative four raised to the second power = negative four raised to the second power

negative four raised to the sixth power divided by negative four raised to the fourth power also = negative four raised to the second power

The answer is A: negative four raised to the second power divided by negative four raised to the fourth power. This is obtained by applying the rules of exponents, specifically, when dividing with the same base, subtract the exponents.

This question pertains to exponents division rules. According to the rule of Power of a Power in exponents, when you divide expressions with the same base, you subtract the exponents. So if you have negative four raised to the fourth power (-4⁴) and you want to divide it by negative four raised to the second power (-4²), you subtract 2 from 4 to get an exponent of 2. This results in a negative four raised to the second power (-4²). So, the correct option from the given choices in your question is A: negative four raised to the second power divided by negative four raised to the fourth power.

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Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

To calculate the future value of a three-year uneven cash flow given below, using an 11% discount rate, we need to use the formula;

Future value of uneven cash flow = cash flow at year 1/(1+discount rate)¹ + cash flow at year 2/(1+discount rate)² + cash flow at year 3/(1+discount rate)³ + cash flow at year 4/(1+discount rate)⁴

Given the cash flows;

Year 0: $0

Year 1: $600

Year 2: $500

Year 3: $400

Then the Future value of uneven cash flow

= $600/(1+0.11)¹ + $500/(1+0.11)² + $400/(1+0.11)³

= $600/1.11 + $500/1.23 + $400/1.36

=$540.54 + $405.28 + $293.00

=$1,238.82

Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

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The approximate surface area of the figure is 1254 square meters

Given that

The composite figure comprises of a right triangle and a circle cut out of the right triangle with the following dimensions

right triangle: Height = 56 meters and Base = 56 meters

Circle: Diameter = 20 meters

The surface area of the figure is calculated as

Surface area = Triangle -  Circle

Substitute the known values in the above equation, so, we have the following representation

Surface area = 0.5 * 56 * 56 - 3.14 * (20/2)^2

Evaluate

Surface area = 1254

Hence, the surface area is 1254

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The probability that a randomly selected Christian living in the United States would identify as Catholic can be calculated by dividing the number of Catholics in the US by the total number of Christians in the US.

To do this calculation, we need to know the accurate data on the number of Catholics and the total number of Christians in the US. Let's assume that there are X Catholics and Y total Christians in the US.

The probability of a randomly selected Christian being Catholic would be:

P(Catholic) = X/Y

Without the accurate data on the number of Catholics and total Christians in the US, it is not possible to calculate the exact probability. However, if we assume that the data provided is accurate and stable, we can use the formula above to calculate the probability.

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There are approximately over 60 million shipping containers in the world. Containers are stacked and arranged in these ports, creating an impressive sight and highlighting the scale of global trade.

Shipping containers are standardized metal boxes used for transporting goods by sea, rail, or road. They come in various sizes, including 20-foot and 40-foot lengths. These containers have revolutionized global trade, allowing for efficient and secure transportation of goods across long distances. While exact numbers are challenging to determine due to factors such as container movement and usage, estimates suggest that there are over 60 million shipping containers worldwide. This vast quantity of containers enables the global economy to function smoothly by facilitating the movement of goods between countries and continents.

The extensive use of shipping containers has led to the establishment of container ports and specialized container ships that can accommodate large numbers of containers.Moreover, repurposing shipping containers for alternative uses, such as modular homes or pop-up shops, has gained popularity in recent years, demonstrating the versatility and durability of these units.

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Answer: 7 hr

Step-by-step explanation:

Given

Distance between Emily and Kylie is \(140\ \text{miles}\)

Speed of Emily \(v_e=12\ mph\)

Speed of Kylie \(v_k=8\ mph\)

Distance traveled by Emily \(\Rightarrow d_e=12t\)

Distance traveled by Kylie \(\Rightarrow d_k=8t\)

\(\Rightarrow 12t+8t=140\\\Rightarrow 20t=140\\\Rightarrow t=7\ hr\)

They will meet after 7 hour.

The value of sin^2(x) + cos^2(x) for x = 75 degrees is approximately 1.001.

To determine the value of the given expression, we can use the trigonometric identity:

sin^2(x) + cos^2(x) = 1

x = 75 degrees

Using the identity, we can substitute sin^2(x) + cos^2(x) with 1:

sin^2(x) + cos^2(x) = 1

Substituting x = 75 degrees:

sin^2(75) + cos^2(75) = 1

Now, we need to evaluate the trigonometric functions for 75 degrees:

sin(75) ≈ 0.9659

cos(75) ≈ 0.2588

Substituting these values back into the expression:

sin^2(75) + cos^2(75) ≈ (0.9659)^2 + (0.2588)^2 ≈ 0.9339 + 0.0671 ≈ 1.001

Therefore, the value of sin^2(x) + cos^2(x) for x = 75 degrees is approximately 1.001.

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Answer:

hhuh eud e uue dui7d iiit

Answer:

400

Step-by-step explanation:

5x4=20,

20^2=400.

Answer:

100% probability or 1/1

Step-by-step explanation:

This is because since the basketball NEVER misses, there is no chance the the ball will not go inside the basket, leaving room for only the ball to GO inside the basket. Hope this helps!! :D

The graph has y-intercept (0,5) and increases with a constant ratio of 3.

A function in mathematics is a connection between a set of inputs (sometimes referred to as the domain) and a set of outputs (also referred to as the range). Each input value is given a different output value.

The y-intercept lies at (0, 5) because the value of the function at x=0 is 530 = 5. The 'constant ratio' is 3, meaning that any increment of 1 in x causes the function value to grow by a factor of 3. (That serves as the exponential term's foundation.)

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Missing parts;

Which of the following statements is true for a function with equation f(x) = 5(3)*?

The graph has y-intercept (0,5) and increases with a constant ratio of 3.

The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.

The graph has y-intercept (0, 3) and increases with a constant ratio of 5.

The graph has y-intercept (0,5) and decreases with a constant ratio of 3.

The area of the third side of the triangle is either 20 square unit or 12 square units.

Triangle:

in math, triangle refers a simple closed curve made of three line segments and it has three vertices, three sides and three angles.

Given,

Two sides of a right triangle measure 2 units and 4  units.

And we need to find the area of the square that shares a side with the third side of the triangle  ​

Let us consider is  Two sides of a right triangle measure 2 units and 4  units.

Here if sides are perpendicular sides, then by using Pythagorean theorem

=> third side² = 2² + 4²

When we simplify this one, then we get,

=> third side² = 4 + 16

So, the  third side² = 20

Then the area of the square that shares a side with the third side of the triangle =  third side² = 20 sq units

Similarly, if 4  units is hypotenuse side, then by using Pythagorean theorem, the third side is calculated as,

=> third side² = 4² - 2²

And when we simplify this one, then we get,

=> third side² = 16 - 4

Therefore, the third side² = 12

And the area of the square that shares a side with the third side of the triangle =  third side² = 12 sq units

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Answer: A monomial representation is a way to express a polynomial as a product of powers of its variables, where each power is a non-negative integer. For example, the polynomial 2x^3 + 4x^2 - 6x + 8 can be represented as a monomial representation of (2x^3)(x^2)(-6x)(8).

Symmetric polynomials are polynomials that are invariant under permutation of their variables. A symmetric presentation is a way of expressing a symmetric polynomial as a sum of elementary symmetric polynomials, which are defined as the sum of all possible products of variables taken i at a time, where i ranges from 1 to the number of variables. For example, the symmetric polynomial x^3 + y^3 + z^3 can be expressed as a symmetric presentation of x + y + z.

Step-by-step explanation:

After 4530 training sessions, Nia's salary for both options will be equal using the concept of equations.

A statement stating the equality of two expressions containing variables or numbers. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

Given Data

Nia has two offers.

a) would compensate her for each training session with $24750 + $20 in fillers.

b) For each training session, Option B would pay her $21,000 plus a $25 roller.

We will now examine the scenario in which the salary alternatives would be identical.

Under option A, Nia would pay

P = 20n + 24750

where n is training sessions

Under option B, Nia would pay

P = 25n + 2100

where n is training sessions

Both salary options are equal

20n + 24750 = 25n + 2100

5n = 22650

n = 4530

After 4530 training sessions, Nia's salary will be equal.

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Let us take the 2nd equation.

x + 2z = 4

x = 4 - 2z

Let us substitute this value of x in equation 1.

5x + 2y + z = 4

5(4-2z) + 2y + z = 4

20 - 10z + 2y + z = 4

2y - 9z + 20 = 4

2y = 9z - 16

y = (9z - 16)/2

Let us substitute this value of y, as well as that of x that we used earlier, in the third equation.

2x + y - z = -1

2(4-2z) + (9z-16)/2 + z = -1

8 - 4z + (9z/2) - 8 + z = -1

Let us multiply both sides of this equation by 2.

16 - 8z + 9z - 16 + 2z = -2

3z = -2

z = \(\frac{-2}{3}\)

x = 4 - 2z

  = 4 + \(\frac{4}{3}\)

  = \(\frac{16}{3}\)

y = (9z-16)/2

  = (\(\frac{-18}{3}\) - 16)/2

  = ( \(\frac{-66}{3}\))/2

  = -22/2

  = -11

Therefore, x = \(\frac{16}{3}\), y = -11, and z = \(\frac{-2}{3}\).

Answer:

they are star's and they are in straight line and all of them have more than one star

Step-by-step explanation:

because the figurers have same star