Create a real-word mathematical problem as an equation that can be solved using all three properties

We use the arctangent function to find the angle [tex]theta[/tex]

[tex]\theta= 2(3 \sqrt{2},-3 \sqrt{2}) \approx 225.000^{\circ}[/tex]

Inverse tangent (notation: arctan or tan-1) is the inverse of the tangent. That is: Arctangent and tangent are inverse functions, so their composition is an identity. 

To find [tex]z_{-} 1+z_{-} 2[/tex], we add the complex numbers in rectangular form:

[tex]$$z_1+z_2=6\left(\cos 55^{\circ}+i \sin 55^{\circ}\right)+6\left(\cos 135^{\circ}+i \sin 135^{\circ}\right)$$[/tex]

Simplifying, we get:

[tex]$$z_1+z_2=6\left(\cos 55^{\circ}+\cos 135^{\circ}+i \sin 55^{\circ}+\sin 135^{\circ}\right)$$[/tex]

Using the trigonometric identities [tex]\backslash \cos (\backslash p i-\backslash$ theta) =- $\backslash \cos \backslash$ theta\$ and $\$ \backslash \sin (\backslash p i-$ $\backslash$ theta) $=\backslash \sin \backslash$ theta[/tex], we can simplify this to:

[tex]$$z_1+z_2=6\left(-\frac{\sqrt{2}}{2}+i \frac{\sqrt{2}}{2}\right)=-3 \sqrt{2}+3 i \sqrt{2}$$[/tex]

Therefore, [tex]z_{-} 1+z_{-} 2=-3 \backslash s q r t\{2\}+3 i \backslash s q r t\{2\}[/tex]

To find [tex]r[/tex] and [tex]theta[/tex] such that [tex]z_{-} 1+z_{-} 2=$ rlangle $\backslash$ theta[/tex], we first calculate [tex]r[/tex] as the magnitude of [tex]z_{-} 1+z_{-} 2[/tex] :

[tex]$$|r+s i|=\left|z_1+z_2\right|=\sqrt{(-3 \sqrt{2})^2+(3 \sqrt{2})^2}=3 \sqrt{2} .$$[/tex]

Next, we use the arctangent function to find the angle [tex]theta[/tex]

[tex]\theta= 2(3 \sqrt{2},-3 \sqrt{2}) \approx 225.000^{\circ}[/tex]

Hence, we can say the values of both the z_{-} 1+z_{-} 2 and r is [tex]z_{-} 1+z_{-} 2=-3 \backslash s q r t\{2\}+3 i \backslash s q r t\{2\}[/tex] and [tex]\theta= 2(3 \sqrt{2},-3 \sqrt{2}) \approx 225.000^{\circ}[/tex] respectively.

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The value of tangent (90°) is 1, so the rise in distance for the submarine to pass over the sunken ship is 1500 m.

Value is the worth of something as measured by its usefulness, importance, or desirability. It is something that is sought after and appreciated by individuals and society. Value is subjective and can vary among people and cultures, but can be broadly defined as the quality of something that makes it worth having or doing.

To calculate the distance the submarine must rise to pass over the sunken ship, we must use the tangent function. The tangent of an angle is equal to the opposite side (in this case, the rise in distance for the submarine) divided by the adjacent side (in this case, the 1500 m distance to the sunken ship).

Therefore, the formula to calculate the rise in distance for the submarine is:
Tangent (90°) = Rise / 1500 m

Solving for the rise, we get:
Rise = 1500 m x Tangent (90°)

Using a calculator, the value of tangent (90°) is 1, so the rise in distance for the submarine to pass over the sunken ship is 1500 m.

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Because the tangent (90°) value is 1, the distance travelled by the submarine to cross over the sunken ship is increased by 1500 m.

Trigonometric angles are the angles in a right-angled triangle that can be used to illustrate various trigonometric functions. Standard angles in geometry include 0°, 30°, 45°, 60°, and 90°. The trigonometric functions are real functions that link the angle of a right-angled triangle to side length ratios. The sine, cosine, and tangent angles are the main classification of trigonometric functions. The primary functions can be used to determine the three functions cotangent, secant, and cosecant.

According to the question draw the graph we should solve the length of BC

tan A = BC/AC

tan90° = BC/1500

BC = 1500 tan90°

  = 516.5 (m)

The value of BC is 516.5 m

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The     circumference   of    the circle who radius  is  14  centimeters   is approximately 87.92 centimeters.

What is circumference?

Circumference is distance around the edge of a circle. It can be thought as the perimeter of the circle. It is a measure of the total length of the circle, and is determined by the size of the circle's radius or diameter. The formula of circumference of  circle is C = 2πr

What is  radius ?

Radius is a term used in geometry to refer to the distance between the center of a circle or sphere and any point on its circumference     or surface, respectively. It is typically denoted by the letter "r"

In the given question,

The circumference of  circle is given by the formula:

C = 2πr

where r is the radius of  circle and π (pi) is  mathematical constant which is  approximately equal to 3.14.

Substituting the given value of  radius, we get:

C = 2 x 3.14 x 14

= 87.92 centimeters (rounded to two decimal places)

Therefore, the circumference of the circle is 87.92 centimeters.

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Answer:

27/70

Step-by-step explanation:

To find an area you have to multiply [tex]length*width[/tex] In this problem, the length of the striped rectangle is 3/7  and the width is 9/10. So you would multiply them together. After multiplying you get the answer of 27/70, most likely Khan Academy will ask for a simple answer so the answer is 27/70 (it is already in its simplest form)

Answer:

183.3

Step-by-step explanation:

Since there were 1 angle and 2 sides, I used law of cosines

Answer:

30.7

Step-by-step explanation:

sin(71) = 29/x

x = 29/sin71

≈ 30.7

a. The probability of rolling a number greater than 10 is 1/6.

b. The probability of rolling a number less than 5 is 1/3.

c. The expected number of times a 4, 6, or 9 will be rolled in 200 rolls is 50

a. The probability of rolling a number greater than 10 is equal to the number of faces with numbers greater than 10 (i.e., 11 and 12) divided by the total number of faces. Thus, P(number greater than 10) = 2/12 = 1/6.

b. The probability of rolling a number less than 5 is equal to the number of faces with numbers less than 5 (i.e., 1, 2, 3, and 4) divided by the total number of faces. Thus, P(number less than 5) = 4/12 = 1/3.

c. The probability of rolling a 4, 6, or 9 is equal to the number of faces with those numbers (i.e., 1 each) divided by the total number of faces. Thus, the probability of rolling a 4, 6, or 9 is 3/12 = 1/4.

Therefore, the expected number of times a 4, 6, or 9 will be rolled in 200 rolls is:

(expected number of times) = (probability of rolling a 4, 6, or 9) x (total number of rolls)

= (1/4) x (200)

= 50

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The tοtal price οf the game including tax is $29.96.

Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.

Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:

0.07 x $28 = $1.96 in taxes

As a result, the purchase tax is $1.96.

Tο calculate the tοtal price, add the purchase price and the tax:

Purchase price + Tax = Tοtal Price

Tοtal cοst: $28 + $1.96 = $29.96

As a result, the tοtal cοst οf the game, including tax, is $29.96.

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Answer:

44 students

Step-by-step explanation:

1200 for the first year

a third of that is 400

400 for the second year

a third of that is 133.4

133.4 for the third year

a third of that is 44

The true statement about the parallelogram is (c) Yes, because adjacent sides are congruent.

Given that

Figure ABCD is a parallelogram

Such that

Side lengths = 5 cm

This means that

The figure is a square

As a general rule

All squares can be classified as rhombus

This is because a rhombus is a quadrilateral with all four sides of equal length and square is a type of rhombus in which all four sides are equal in length

Hence, the true statement is (c)

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Answer:

The answer would be 14 miles!

Answer:

b=30

Step-by-step explanation:

The sum of the three angles of a triangle add to 180.

75+75+b = 180

150+b=180

Subtract 150 from each side.

b = 180-150

b=30

Answer:

b=30

Step-by-step explanation:

The sum of all the angles of a triangle add up to 180°

∠b = 75° + 75° = 150°

Now, we need to subtract 150° from 180° to see how much does angle b measure.

∠b = 150° - 180° = 30°

30° = ∠b

The angles of the triangle would be:

75°, 75°, and 30°

To prove this, we will sum all the angles again:

75° + 75° + 30° = 180°

75° + 75° = 150°

150° + 30° = 180°

Hence, the answer is ∠b = 30°

The area of this composite shape is 273 m².

What is an area?

An area is a measure of the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters, square feet, or square inches. The area of a shape or region is determined by multiplying the length of one side by the length of another side, such as the length and width of a rectangle or the radius of a circle. The concept of area is used in many areas of mathematics and science, including geometry, trigonometry, calculus, and physics.

first, refer figure that attached below:

The are a of "a"= area of ΔABC

AB = 20-14 = 6 m

BF = 18-11 = 7 m

Then, area of region  "a"  = 1/2*AB*BF  = 1/2*6*7 = 21 m².

Now, area of  region"b" = area of rectangle ABCD = ED*CD = 252 m².

Total area of this composite shape = a + b =21+252 = 273 m².

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Complete question is: The area of this composite shape is 273 m².

The given distribution is normal with mean μ = 7 and standard deviation σ = 2. So,The probability that a given garden has between 1 and 11 rows is approximately 0.9772 or 97.72%.

Probability is a mathematical concept that is used to measure the likelihood of a particular event occurring. It is a way to quantify uncertainty, and it is expressed as a number between 0 and 1.

We need to find the probability that a given garden has between 1 and 11 rows.

First, we standardize the values using the formula z = (x - μ) / σ, where x is the number of rows.

For x = 1, z = (1 - 7) / 2 = -3. For x = 11, z = (11 - 7) / 2 = 2.

Using the 68 - 95 - 99.7 rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Thus, the probability of a garden having between 1 and 11 rows can be calculated as:

P(1 ≤ x ≤ 11) = P(-3 ≤ z ≤ 2)

From the z-table, we can find that the probability of a standard normal distribution having a z-score between -3 and 2 is approximately 0.9772.

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Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

Answer: We can simplify the expression step by step:

3/4 − x(1/2 − 5/8) + (−3/8)x

3/4 − x(-1/8) + (−3/8)x

3/4 + x/8 − 3/8x

Multiplying everything by 8 to get rid of the fractions:

6 − x + (−3x)

6 − 4x

Therefore, the equivalent expression is D) 34 - 14x / (4/3).

Step-by-step explanation:

To break even, the company should charge a price that covers their expected loss. Therefore, the price that they should charge for the 2 year extended warranty is $9

What is expected value?

Expected value is a concept in probability theory that represents the average value of a random variable over a large number of trials. It is calculated by multiplying each possible outcome by its probability and adding up the products

Let x be the price that the company charges for the extended warranty. Then, the expected value of the extended warranty is:

E(x) = 0.98(0) + 0.02(-450) = -9

The negative expected value means that the company is expected to lose money on the extended warranty.

To break even, the company should charge a price that covers their expected loss. Therefore, the price that they should charge for the 2 year extended warranty is:

x = -$(-9) = $9

Therefore, the company should charge $9 for the 2 year extended warranty so that they break even.

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6. The ratio of the birth weight to the adult weight of a male black bear is 3:1000.

7. The measure of the angles in the triangle are 36°, 15 x 36° = 540°, and 19 x 36° = 684°.

An angle is an abstract concept in geometry which is formed by two lines or rays that meet at a common point. An angle is measured in degrees and can be classified by its size as acute, right, obtuse, or reflex. An angle can also be formed by three points or two intersecting planes.

6. The average birth weight is 12 ounces. The average adult weight is 12 x 1000 = 12000 ounces. Since there are 16 ounces in 1 pound, the average adult weight of the male black bear is 12000/16 = 750 pounds.

7. The measures of the angles in a triangle are in the extended ratio 2:15:19.To find the measure of each angle, we can set up an equation using the extended ratio. Let x be the measure of the first angle, then 15x and 19x will be the measures of the other two angles. This can be written as: 2x + 15x + 19x = 360°. Solving this equation, we get x = 36°. Therefore, the measure of the angles in the triangle are 36°, 15 x 36° = 540°, and 19 x 36° = 684°.

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Answer:

3x² -2xy + 4y² at x = -1, y = -2  = 15

Step-by-step explanation:

Given function is

f(x, y) = 3x² -2xy + 4y²

To find At x = - 1 and y - 2 just plug these values for x and y into f(x, y)

f(-1, -2) = 3(-1)² - 2(-1)(-2) + 4(-2)²

(-1)² = 1 ==>   3x²  = 3(-1)² = 3 x 1 = 3

(-1) (-2) = 2   ==>   2xy = 2(-1)(-2) = 2 x 2 = 4

(-2)² = 4  ==> 4y² = 4 (-2)² = 4 x 4 = 16

f(-1 1, - 2) = 3x² -2xy + 4y²
= 3 - 4 + 16

= 15

Answer: x=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

104.4 divided by 4 = 26.1

Approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.

What Is a Normal Distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

First, we standardize the value of 2.6 as follows:

z = (x - μ) / σ

where x is the value of 2.6, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:

z = (2.6 - 3.7) / 0.6 ≈ -1.83

z = (x - μ) / σ

where x is the value of 3.9, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:

z = (3.9 - 3.7) / 0.6 ≈ 0.33

We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we can find the area as follows:

P(-1.83 < Z < 0.33) ≈ 0.6068

Therefore, approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.

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Approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

First, we standardize the value of 2.6 as follows:

z = (x - μ) / σ

where x is the value of 2.6, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:

z = (2.6 - 3.7) / 0.6 ≈ -1.83

z = (x - μ) / σ

where x is the value of 3.9, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:

z = (3.9 - 3.7) / 0.6 ≈ 0.33

We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we can find the area as follows:

P(-1.83 < Z < 0.33) ≈ 0.6068

Therefore, approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.

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Answer:

Step-by-step explanation:

[tex]x+y=34\\x-y=8\\2x=42\\x=21\\y=34-21\\y=13\\13(21)=273[/tex]

The Converse of the Pythagorean Theorem is proved below.

What is Pythagoras Theorem ?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The converse of the Pythagorean theorem states that if a triangle has sides of length a, b, and c, where c is the longest side, and a² + b² = c², then the triangle is a right triangle.

To prove the converse of the Pythagorean theorem, we can use the fact that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. That is, if a triangle has sides of length a, b, and c, where c is the longest side and c² = a² + b², then the triangle is a right triangle.

Proof:

Suppose we have a triangle ABC, with sides of length a, b, and c, where c is the longest side. Assume that a² + b² = c². We want to show that triangle ABC is a right triangle.

We will use the Law of Cosines to show that angle C is a right angle. The Law of Cosines states that for any triangle ABC with sides of length a, b, and c opposite angles A, B, and C, respectively:

c² = a² + b² - 2ab cos(C)

Substituting a² + b² = c² into this equation, we get:

c² = c² - 2ab cos(C)

2ab cos(C) = 0

cos(C) = 0

Since 0 is the cosine of 90 degrees, this implies that angle C is a right angle. Therefore, triangle ABC is a right triangle.

Thus, this completes the proof of the converse of the Pythagorean theorem.

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Up to 180 degrees

Your Welcome

Answer:

The percent decrease in population can be calculated by dividing the difference between the two populations by the original population and then multiplying by 100. In this case, the percent decrease is ((137000-117820)/137000)*100 = 14%.

Step-by-step explanation:

Answer: yes correct i love math

Step-by-step explanation: