Choose the angle which is vertical to ∠ in the following figure.

Answer:

total angles in triangle = 180

180 = 44+56+ y

y = 180-44-56

y = 80°

now to find z and x

we know the 2 straight lines are parallel (indicated by arrows)

x = 56°

z = 44°

how?

alternate angles theorem

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape: There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

Answer:

The answer is B. i.e. 6.6units.

Answer: 25 sixth graders

Step-by-step explanation:

Sixth-graders are in a ratio with fifth graders in the band at 5:4 and there are 20 fifth-grade students in the band.

To find the number of 6th graders, use direct proportion and assume the sixth grader number is x:

5                   :            4

x                    :            20

4x = 100

x = 100 / 4

x = 25 sixth graders

Answer:

$50.99.

Step-by-step explanation:

Answer:$44.99

Step-by-step explanation:

1

Hey there,

The squeeze theorem shows if \(f(x)\leq g(x)\leq h(x)\) for all real numbers \((-\infty,~\infty)\) then f(x) = h(x) but g(x) has to equal that as well.

Let's say we have [ \(\lim_{n \to \infty} (\frac{cos~x}{x})\) ]

~Apply the theorem

Note that [ \(-1 \leq cos~x \leq 1\) ] and [ \(\lim_{n \to \infty} (-\frac{1}{x})\leq \lim_{n \to \infty} (\frac{cos~x}{x})\leq \lim_{n \to \infty} (\frac{1}{x})\) ]

~Apply the infinity property to every side but the middle

\(\lim_{n \to \infty} (-\frac{1}{x}) = 0\)

\(\lim_{n \to \infty} (\frac{1}{x}) = 0\)

So... \(\lim_{n \to \infty} (\frac{cos~x}{x})=0\)

Best of Luck!

That a full cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat.

carat weight is determined by a combination of a diamond's size and density. A diamond's size is measured by its diameter, which is the distance across the widest part of the diamond, known as the girdle. Therefore, a diamond with a larger girdle diameter will generally weigh more than a diamond with a smaller diameter, assuming all other factors are equal.

the weight of a diamond can be estimated based on its girdle diameter, and a full-cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat. However, it's important to note that other factors, such as depth, cut, and clarity, can also affect a diamond's weight and value.

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Answer:

P = 72 ft

Step-by-step explanation:

the perimeter P is the sum of the 3 sides.

Tangents to a circle from an external point are congruent , then

side 24 = 15 + 9

side 21 = 9 + 12

Third side = 12 + 15 = 27 ft

P = 24 + 21 + 27 = 72 ft

Answer:

46

Step-by-step explanation:

first you need to write out your question

then you need to multiply the following numbers (5.75*8)

and that gives you 46.

I hope this is the answer I just get every thing right and I think it is. hofuly it's helping!!

Answer: 26 46

Step-by-step explanation:

Answer:

26, 46, 23......

Step-by-step explanation:

Each number is divided by 2 then added by 20.

Answer:

2 students are in both clubs

Step-by-step explanation:

x = 1 student (this number may be more than the total because one student can be in 2 clubs)

Club a = 13

Club b = 20

13 + 20 = 27x

Total members of clubs - total number of students = 27x - 25 = 2

2 students are in both clubs

Hope this was useful to you!

Answer:

use 4 times as much pasta as the recipe called for

Step-by-step explanation:

14 people times 4= 56 people

Answer:

use 4 times as much pasta as the recipe called for

Step-by-step explanation:

14 people times 4= 56 people

The solution to the inequality ∣3x + 6∣ - 15∣ = 5 is x = -8, x = -4, and x = 4.

To solve the inequality, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: (3x + 6) - 15 = 5

Simplifying the equation:

3x + 6 - 15 = 5

3x - 9 = 5

3x = 14

x = 14/3

Case 2: -(3x + 6) - 15 = 5

Simplifying the equation:

-3x - 6 - 15 = 5

-3x - 21 = 5

-3x = 26

x = -26/3

Therefore, the solutions for the inequality ∣3x + 6∣ - 15∣ = 5 are x = 14/3 and x = -26/3.

However, we need to check these solutions to ensure they satisfy the original inequality.

For x = 14/3:

∣3(14/3) + 6∣ - 15∣ = 5

∣14 + 6∣ - 15∣ = 5

∣20∣ - 15∣ = 5

20 - 15 = 5

5 = 5

For x = -26/3:

∣3(-26/3) + 6∣ - 15∣ = 5

∣-26 + 6∣ - 15∣ = 5

∣-20∣ - 15∣ = 5

20 - 15 = 5

5 = 5

Both solutions satisfy the inequality, so x = 14/3 and x = -26/3 are valid solutions.

In addition to these solutions, we also need to consider the values of x that make the expression inside the absolute value equal to zero:

3x + 6 = 15

3x = 9

x = 3

However, we need to exclude this solution because it would result in dividing by zero in the original inequality.

Therefore, the final solutions to the inequality are x = 14/3 and x = -26/3.

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In the attached diagram the perimeter of the hall way is

The perimeter of the hall way is calculated by adding all the sides of the hallway

The perimeter of the hall way  = 2x - 7 + x + 1 + 4x - 9 + x - 2 + x + 2 + 3x - 11 + x - 2 + 3x - 11 + x + 4

adding like terms results to

The perimeter of the hall way  =  17x + (-34)

Finally, the simplified expression is:

17x - 34

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Answer:

$$0.8^4=0.4096$$ Explanation: The introduction to logarithms and definition of it is explained in the first link. 0.8 is the base of both logarithm and exponent

Step-by-step explanation:

The ladder can reach 21.17 feet high up of Denise's house.

Given,

The length of ladder Denise used to clean the outside of her second story windows = 24 feet

The distance between the base of the ladder and house = 13 feet

We have to find the height of the house which the ladder can reach:

For that we can use Pythagorean Theorem.

That is,

Hypotenuse² = Altitude² + Base²

Here,

Hypotenuse is the length of the ladder = 24 feet

Altitude is the height of the house ladder can reach = x

Base is the distance between base of the ladder and house = 13 feet

Therefore,

24² = x² + 13²

576 = x² + 169

x² = 576 - 169

x² = 407

x = \(\sqrt{407}\)

x = 21.17

That is, the ladder can reach 21.17 feet high up of Denise's house

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The elevator's rate of travel in meters per second is 2m/s and 1/2 s/m is in seconds per meter.

A division is a process of splitting a specific amount into equal parts.

Given,

An elevator in the Seattle Space Needle can rise 100 meters in 50 seconds,

We need to find the elevator's rate of travel in meters per second and in seconds per meter

To find in meter per second we just need to divide 100 by 50 seconds

100/50=2 m/s

To find in seconds per meter we just need to divide 50 by 100

50/100=1/2s/m

Hence, the elevator's rate of travel in meters per second is 2m/s and 1/2 s/m is in seconds per meter.

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Answer:

8.19 units.

Step-by-step explanation:

I didn't use desmos, i completed the question with all steps and working and didn't require desmos. Hope this Helps. Question was solved using trignometric ratios.

Step 1

Simplify the expression.

Step 2

Find a trigonometric identity that can be used to simplify the expression in step 1

Step 3

Get the final answer after substitution.

Hence the right answer is option B

Answer: 5 pounds

Step-by-step explanation:

80 / 16 = 5

Answer:

5 pounds

Step-by-step explanation:

Hope this helps!

Steps to solve:

3x - 5y = 20

~Subtract 3x to both sides

-5y = 20 - 3x

~Divide everything by -5

y = -4 + 3/5x

Best of Luck!

The equivalent value of the expression is y = ( 3x - 20 ) / 5

Given data ,

Let the equation be represented as A

Now , the value of A is

3x - 5y = 20

On simplifying the equation , we get

3x - 5y = 20

So , the left hand side of the equation is equated to the right hand side by the value of 20

Adding 5y on both sides , we get

3x = 20 + 5y

Subtracting 20 on both sides , we get

5y = 3x - 20

Divide by 5 on both sides , we get

y = ( 3x - 20 ) / 5

Therefore , the value of y = ( 3x - 20 ) / 5

Hence , the expression is y = ( 3x - 20 ) / 5

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We know that y varies directly with x.

First we need to find the constant of variation

7=14k

k= 7/14

k=1/2

the equation that relates x and y is

Answer:

first you subtract 2 from both sides

-6x>18

then you divide

-6 by 18 which is -3 and since you divided with a decimal that flips your sign so your answer is X<-3

Answer:

x<-3

Step-by-step explanation:

First, write the equation and subtract 2 on both sides.

-6x+2>20

     -2  -2

-6x>18

Divide both sides by -6.

-6x>18

/-6  /-6

x<-3

(Remember, we have to flip the sign when multiplying or diving by a negative.)

Hope this helps! Have an amazing day C:

Angle M is 33.5 degrees

Side l  is 10.4

Sid k is 14.7

The sine law and cosine law are two trigonometric formulas used to solve triangles and determine the relationships between their sides and angles.

We know that;

10.5/Sin M = 18.2/Sin 73

Sin M = 10.5 * Sin 73/18.2

M = Sin-1(10.5 * Sin 73/18.2)

M = 33.5 degrees

2. We know that;

M = 180 - (88 + 31)

= 88 degrees

l/Sin 88 = 5.4/Sin 31

l = 5.4 * Sin 88/Sin 31

l = 5.39/0.52

l = 10.4

3.

\(k ^2=m^2 + l^2 - 2mlCosK\\k^2 = (11)^2 + (17)^2 - (2 * 11 * 17)Cos 59\\k^2 = 121 + 289 - 374Cos59\)

k = 14.7

Thus these are the required angles and sides.

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Answer: The probability that a millet seed will fall next can be found by dividing the number of millet seeds by the total number of remaining seeds.

Total number of remaining seeds = 40 + 65 + 60 + 35 = 200

Probability that a millet seed will fall next = Number of millet seeds / Total number of remaining seeds

= 65 / 200

= 0.325 or 32.5% (rounded to one decimal place)

Therefore, the probability that a millet seed will fall next is 0.325 or 32.5%.

Step-by-step explanation:

The correct sequence of project phases is Definition - Planning  - Performance. The correct answer is B.

This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.

Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.

Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.

Therefore the sequence of project phase is  Definition - Planning  - Performance The correct answer is B.

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The distance between the points (-3, -6) and (5, 0) is 10 units.

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

To determine the distance between two points in a coordinate plane, you can use the distance formula, which is derived from the Pythagorean theorem.

The distance formula for two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is:

Distance = √{(x₂ - x₁)² + (y₂ - y₁)²}

Given the two points (-3, -6) and (5, 0), we can plug in the values into the distance formula as follows:

x₁ = -3, y₁ = -6 (coordinates of the first point)

x₂ = 5, y₂ = 0 (coordinates of the second point)

Distance = √{(x₂ - x₁)² + (y₂ - y₁)²}

= √{(8)² + (6)²}

= √{(64) + (36)

= √100

= 10

Hence, the distance between the points (-3, -6) and (5, 0) is 10 units.

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The funding received by schools in a certain state is dependent on the number of students that attend the school. For funding purposes, one school day is picked at random and the number of students in attendance is determined. High School A is among the schools that receive funds, and its funding is based on the number of students that attend the school daily.

The daily number of absences at High School A in the state is approximately normally distributed with a mean of 120 students and a standard deviation of 10.5 students.According to the central limit theorem, if a sufficiently large sample size is chosen, the distribution of sample means approximates a normal distribution. In this situation, if several school days are randomly selected and the average number of students who attended each day is calculated, the distribution of sample means approximates a normal distribution.Therefore, if the school day is chosen at random, the probability that fewer than 100 students attended is:P(X < 100) = P(Z < (100 - 120) / 10.5)= P(Z < -1.90)= 0.0287, where Z is the standard normal variable.Since 2.87 percent of the school days have less than 100 students, there is a low chance that the school funding will be affected by the attendance of students in this range.

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A. Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

B. The recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

(a) If Manager B always truthfully reports the state of the economy (s = 0.7), Manager A would send a recommendation that minimizes their disutility Ua. In this case, Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

(b) In a Nash equilibrium, both managers strategically make their recommendations based on their own utility. Manager A wants to minimize their disutility Ua, which increases as the decision deviates from 0.4. Manager B wants to minimize their disutility UB, which increases as the decision deviates from 0.7.

To find the Nash equilibrium, we need to consider the recommendations made by both managers simultaneously. Let's denote the recommendations as rA (from Manager A) and rB (from Manager B). The principal's decision, d, would be the average of the recommendations, so d = (rA + rB) / 2.

Given that both managers strategically choose their recommendations, they will aim to minimize their disutility. In this case, Manager A would recommend a decision of 0.4 (as it minimizes Ua), and Manager B would recommend a decision of 0.7 (as it minimizes UB). Therefore, the recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

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