Given PU-UR, and the radius of the circle is 55, find x and UT.
10. x.
11. UT.

Show work

The lengths of the sides and angles of the triangles, obtained using Pythagorean Theorem and trigonometric ratios are;

D. 19.2

C. 5.3

F. 2·√5

G. √3

H. 8·√3

K. 18.9

O. 15.5

N. 14.5

M. 41.4°

I. 74.1°

The Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the triangle.

D. x = √(15² + 12²) ≈ 19.2

C. x = √(10² - 8.5²) ≈ 5.3

F. x = 2·√(5) (Special triangles)

G. tan (60°) = 30/x = √3

x = 30/√3 = 10·√3

H. x/16 = (√3)/2

x = 16 × (√3)/2 = 8·√3

x = 8·√3

K. tan(34°) = x/28

x = 28 × tan(34°) ≈ 18.9

O. cos(55°) = x/27

x = 27 × cos(55) ≈ 15.5

N. sin(16°) = 4/x

x = 4/(sin(16°) ≈ 14.5

M. x = arccos(9/12) ≈ 41.4°

I. x = arcsin(25/26) ≈ 74.1°

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The expression that represents a purely imaginary number is:

[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]

Option D is the correct answer.

We have,

A pure imaginary number is a number that does not have a real part and can be written in the form of bi, where b is a real number and i is the imaginary unit (√(-1)).

We have,

[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]

In this expression, we can simplify and rewrite it as:

[tex]3i^5 + i(2 - 4i^3) + 6 - 2i[/tex]

Now, let's evaluate the powers of i:

[tex]i^5 = i^{4 + 1} = i^4 \times i = 1 \times i = i\\i^3 = i^{2 + 1} = i^2 \times i = (-1) \times i = -i[/tex]

Substituting these values back into the expression:

[tex]3i^5 + i(2 - 4i^3) + 6 - 2i = 3i + i(2 - 4(-i)) + 6 - 2i[/tex]

= 3i + i(2 + 4i) + 6 - 2i

= 3i + 2i + 4i² + 6 - 2i

= 3i + 2i + 4(-1) + 6 - 2i

= 5i - 4 + 6 - 2i

= 5i - 2i - 4 + 6

= 3i + 2

The expression 3i + 2 represents a pure imaginary number, as it has no real part (the constant term is 2 and does not involve the imaginary unit i).

Thus,

The expression that represents a purely imaginary number is:

[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]

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Answer:

  All statements above are false

Step-by-step explanation:

You want to know which of the statements saying translation, rotation, and reflection change the measures of line segments or angles is true.

Translation, rotation, and reflection are referred to as "rigid motion." That means all parts of the transformed figure keep their measures and positions relative to other parts of the figure. No lengths or angle measures are changed.

  All of the (above) listed statements are false.

<95141404393>

Answer:

Because equations is not counting, and multiply is not addition.  

Step-by-step explanation:

Addition is: a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum. It is one of the essential mathematical functions we use in our everyday activities. There are many situations in which we add numbers.

Like lets say you have 1 apple, and your friend gives 2 more, then you have 3. If you have 4 apples, and your friend gives 5 more, then you have 9 apples.

Its always better to start with the bigger number, it makes it easier, like 2 + 1 = 3, or 5 + 4 = 9.

Now multiplication is harder. Multiplication is: the basic explanation of multiplication is adding a number, with respect to another number, repeatedly. For example, if we are multiplying 2 by 3, that means 3 is added to itself two times, i.e. 3 + 3 = 6. This is a simple technique for kids to multiply numbers.  

(Answer) 2 x 2 would equal 4. (Explanation) Add a 2, with respect to 2, repeatedly, would equal 4.

(Answer) 4 x 4 would equal 16. (Explanation) Add a 4, with respect to 4, repeatedly, would equal 16.

Answer: Step-by-step explanation:

because 1 + 2  does equal 3 but 4 + 5 does not equal to 6 because it equals to 9.

and 2 x 2  does equal to 4 but 4 x 4 does not equal to 8 because it equals to 16.

Answer:

Step-by-step explanation:

You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.

Newton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...

  T = 36 -26·(22/26)^(t/2)

At times of t=4 and t=9, the temperature readings will be ...

__

Additional comment

The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.

<95141404393>

The coffee club's assertion that the percentage of bags containing collectible cards is less than 0.2 is unsupported by sufficient data.

To test whether the coffee club's belief that the proportion of bags with collectable cards is less than 0.2 is supported by the sample, conduct a hypothesis test.

Null Hypothesis: The proportion of bags with collectable cards is equal to or greater than 0.2.

Alternative Hypothesis: The proportion of bags with collectable cards is less than 0.2.

Let p be the true proportion of bags with collectable cards in all Joe Coffee bags. Use a one-sample proportion test to test this hypothesis.

The test statistic is calculated as follows:

z = (p - p₀) / √(p₀(1-p₀)/n)

where p = sample proportion (11/65), p₀ = hypothesized proportion (0.2), and n = sample size (65).

Using a significance level of 0.05, the critical z-value for a one-tailed test is -1.645.

Calculating the test statistic:

z = ((11/65) - 0.2) / √(0.2(1-0.2)/65) = -1.469

Since -1.469 is not less than -1.645, we fail to reject the null hypothesis. There is not enough evidence to support the coffee club's belief that the proportion of bags with collectable cards is less than 0.2.

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The statement that justifies that ΔBAE ≅ Δ DAE is Side-Side-Angle Postulate. The best option from the statements given is "Classify A triangle". That is definition of a triangle.

The Side Side Angle Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Between both triangles, here are the congruent sides and angles:

AB ≅ AD  - Given

AE  = EA - Reflexive Property. Note that AE is shared by both triangles so we have Two congruent sides.

AC ⊥ BD - that means ∠AEB = ∠AED = ∠BEC = ∠CED = 90°

(perpendicular bisector theorem)

A perpendicular bisector is a line segment that cuts another line segment at 90 degrees. A perpendicular bisector, in other terms, meets another line segment at 90° and splits it into two equal halves.

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Para resolver este problema, podemos utilizar el Teorema de los Cosenos para calcular los ángulos interiores del triángulo.

Sea A, B y C los vértices del triángulo correspondientes a los centros de los engranajes. Sea a, b y c las longitudes de los lados opuestos a los ángulos A, B y C respectivamente.

Dado que los radios de los engranajes miden 15 cm, 16 cm y 17 cm, podemos considerar que los lados del triángulo son a = 15 cm, b = 16 cm y c = 17 cm.

El Teorema de los Cosenos establece que en un triángulo con lados a, b y c, y ángulos opuestos A, B y C respectivamente, se cumple la siguiente fórmula:

c^2 = a^2 + b^2 - 2ab * cos(C)

Podemos aplicar esta fórmula para cada uno de los ángulos del triángulo.

Para el ángulo A, tenemos:

c^2 = b^2 + a^2 - 2ab * cos(A)

17^2 = 16^2 + 15^2 - 2 * 16 * 15 * cos(A)

Resolviendo la ecuación, encontramos que cos(A) = -1/8. Tomando el coseno inverso (arcocoseno), encontramos que el ángulo A es aproximadamente 135.2 grados en el sistema de medición radial.

Para el ángulo B, tenemos:

a^2 = c^2 + b^2 - 2cb * cos(B)

15^2 = 17^2 + 16^2 - 2 * 17 * 16 * cos(B)

Resolviendo la ecuación, encontramos que cos(B) = -7/17. Tomando el coseno inverso, encontramos que el ángulo B es aproximadamente 120.6 grados en el sistema de medición radial.

Para el ángulo C, tenemos:

b^2 = a^2 + c^2 - 2ac * cos(C)

16^2 = 15^2 + 17^2 - 2 * 15 * 17 * cos(C)

Resolviendo la ecuación, encontramos que cos(C) = -1/2. Tomando el coseno inverso, encontramos que el ángulo C es aproximadamente 120 grados en el sistema de medición radial.

Entonces, los ángulos interiores del triángulo son:

A ≈ 135.2 grados

B ≈ 120.6 grados

C ≈ 120 grados

Estos valores están expresados en el sistema de medición radial.

The four-door model is sold at 15% discount.

Discount is the difference between list price and selling price.

List price is the original price of the product set by the seller.

Selling price is the price at which the product is actually sold.

We know that percentage of discount is:

Discount % = (Discount/ List price) * 100

where Discount= List price- Selling price

       ⇒ List price= Discount + Selling Price

       ⇒ List price = 9000 + 51000 = Birr 60,000

Calculating the discount percentage based on above mentioned results:

Discount % = (Discount/ list price)*100

⇒ (9,000/60,000)*100 = 15%

Therefore the percentage of discount for the four-door model sold at discounted price of Birr 51,000 with discount of Birr 9,000 is 15%.

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All the first five terms of sequence are,

A) -11, - 11/2 - 11/4 - 11/8 - 11/16

We have to given that;

Rule for sequence is,

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

Now, WE can find first five terms of sequence as;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

Put n = 1;

⇒ a (1) = - 11 × (1/2)¹⁻¹

⇒ a (1) = - 11

Put n = 2;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (2) = - 11 × (1/2)²⁻¹

⇒ a (2) = - 11 × (1/2)¹

⇒ a (2) = - 11 / 2

Put n = 3;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (3) = - 11 × (1/2)³⁻¹

⇒ a (3) = - 11 × (1/4)

⇒ a (3) = - 11 / 4

Put n = 4;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (4) = - 11 × (1/2)⁴⁻¹

⇒ a (4) = - 11 × (1/2)³

⇒ a (4) = - 11 / 8

Put n = 5;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (5) = - 11 × (1/2)⁵⁻¹

⇒ a (5) = - 11 × (1/2)⁴

⇒ a (5) = - 11 / 16

Thus, All the first five terms of sequence are,

A) -11, - 11/2 - 11/4 - 11/8 - 11/16

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Answer:

Step-by-step explanation:

The converse of the conditional statement "If a polygon has three sides, then it is a triangle" is:

D. If a polygon is a triangle, then it has three sides.

In the original conditional statement, the "if" part is "a polygon has three sides," and the "then" part is "it is a triangle." The converse switches the positions of the "if" and "then" parts, resulting in the statement "If a polygon is a triangle, then it has three sides."

Answer:

(i) Attached below.  You can copy what I drew

(ii) (a) 35, (b) 60, (c) 5

Step-by-step explanation:

(a) Thus, 35 students study French only.

(c) Thus, 5 students' study neither Arabic nor French

the number of students who study French only + the number of students who study both French and Arabic + the number of students who study Arabic only + the number of students who study neither Arabic nor French equals 75:

35 + 10 + 25 + 5 = 75

45 + 30 = 75

75 = 75

Thus, our numbers are correct.

(b) Also, the number of students who study only subject is 60, as 35 (number of students studying French only) + 25 (number of students studying Arabic only) = 60

Answer:

the answer is C

Step-by-step explanation:

any negative power is the reciprocal

so m^(-2) = 1/m^2

and so on

1/n^(-3) = n^(3)

The average rate of change for this problem is given as follows:

2.4 inches per hour.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The change in the output is given as follows:

8.1 - 3.3 = 4.8.

The change in the input is given as follows:

2 - 0 = 2.

Hence the average rate of change is given as follows:

4.8/2 = 2.4 inches per hour.

The table is given by the image presented at the end of the answer.

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Answer:

5

Step-by-step explanation:

Just do as the problem says:

xy-y = (2)(5)-(5) = 10-5 = 5

Answer: 5

Step-by-step explanation: All you have to do is substitute x & y for their respective numbers. In this case, change x for 2 & y for 5, So xy-y becomes 2(5)-5, which equals 10-5, which is 5.

Answer:

The two numbers are -10 and 4

Step-by-step explanation:

[tex]x+y=-6\\y=14+x\\\\x+(14+x)=-6\\2x+14=-6\\2x=-20\\x=-10\\\\x+y=-6\\-10+y=-6\\y=4[/tex]

150 degrees is the measure of the angle x from the figure

The given diagram is a circle and the angle x and 30 degrees can be seen to be on a straight line.

The sum of the measure of angle on a straight line is 180 degrees, hence:

x + 130 = 180

Subtract 130 degrees from both sides to have:

x + 30 - 30 = 180 - 30
x = 180 - 30
x = 150 degrees

Hence the measure of the angle x from the given equation is 150 degrees

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Step-by-step explanation:

x and y are directly proportional means that

y = kx

y grows with the same factor k applied to x.

the area of a circle (the cross section of a cylindrical pipe) is

pi × r²

r being the radius (which is half of the diameter).

so, the area in terms of the diameter is

pi × (d/2)² = pi × d²/4

so, we know

36 correlates to pi × (d small)²/4

60 correlates to pi × (d large)²/4

therefore (directly proportional),

d small² = 36×4/pi

d small = 12/sqrt(pi)

d large² = 60×4/pi

d large = sqrt(4×15×4/pi) = 4×sqrt(15/pi)

the difference between large and small diameter (increase from small to large) is then

4×sqrt(15/pi) - 12/sqrt(pi)

d small = 100%

1% = 100%/100 = 12/sqrt(pi) / 100 = 12/(100sqrt(pi))

the % of the diameter increase is then

increase/1% =

(4×sqrt(15/pi) - 12/sqrt(pi)) / 12/(100sqrt(pi)) =

= (400sqrt(pi)×sqrt(15/pi) - 1200sqrt(pi)/sqrt(pi)) / 12 =

= (400×sqrt(15) - 1200) / 12 = 100×sqrt(15)/3 - 100 =

= 100×(sqrt(15)/3 - 1) = 29.09944487...% ≈ 29.1%

the diameter has to increase by about 29.1%, so that the pipe can carry 60 liters per second.

please consider : only the area of the cross section and the carrying capacity are directly proportional.

the diameter of the cross section and the area of the cross section are NOT directly proportional.

they have the pi×(d/2)² relationship.

and so, while the capacity and the cycle area both increase by the same factor, the impact on the diameter (or radius) is different.

so, for capacity and area we have

60 = k×36

k = 60/36 = 5/3 = 1.66666666...

and therefore both increase by 66.66666...%.

but because of the square relation between diameter and cross section area, the diameter only increases by 29.1%.

The quadrilateral given on the image can be said to be a parallelogram because the diagonals bisect each other.

An effective way to check if a four-sided figure is a parallelogram is through the diagonal test, which involves inspecting its diagonals. According to the examination, if the two diagonals of a four-sided shape intersect at their midpoint, the shape is classified as a parallelogram.

The two diagonals in a parallelogram intersect at their midpoint, although they may not have the same length. This implies that the intersection point of every diagonal bisects the diagonal into two identical parts. Despite the unequal length of its diagonals, the parallelogram is still considered as such due to the bisecting property.

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The result of the transformation of the parent function y = x² are;

13. y =  (x - 2)²

14. y = x² + 5

15. y = (x + 3)² - 4

16. y = (x - 7)² + 4

17. y = -(x²) - 3

18. y = -(x - 5)² - 2

19. y = (1/2)x²

20.  y = (3x²) + 8

The transformations on the parent function y = x² can be described as;

13. Translated 2 units right:

The equation will be y = (x - 2)²

14. Translated 5 units up:

The equation will be y = x² + 5

15. Translated 3 units left and 4 units down:

The equation will be y = (x + 3)² - 4

16. Translated 7 units right and 4 units up:

The equation will be y = (x - 7)² + 4

17. Reflected over the x-axis, then translated 3 units down:

The equation will be y = -(x²) - 3

18. Reflected over the x-axis, then translated 5 units right and 2 units down:

The equation will be y = -(x - 5)² - 2

19. Vertically compressed by a factor of 2:

The equation will be y = (1/2)x²

20. Vertically stretched by a factor of 1/3, then translated 8 units up:

The equation will be y = (3x²) + 8

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Answer:

1. x = 13.75

2. 17 degrees

3. a = 4, b = 2√2

Step-by-step explanation:

1. cos(37) = 11/x

since cos(37) = 4/5

4/5 = 11/x

4x = 55

x = 13.75

2. tan(0) = opp/adj

tan(0) = 4/13 = 0.30769

=> (0) = 17.1 degrees or 17 degrees

3. since the triangle is right triangle with 2 angles of 45 degress

=> isosceles right triangle

then b = 2√2

a^2 = (2√2)^2 + (2√2)^2

a^2 = = 8 + 8 = 16

a = √16= 4

Rounding to the nearest tenth, the mean lifespan for Kamila's sample is 11.9 years.

To find the mean (average) for Kamila's sample, you need to sum up all the lifespans and then divide by the total number of breeds in the sample.

Sum of lifespans = 13 + 11 + 12 + 14 + 12 + 10 + 11 + 12 = 95

Total number of breeds = 8

Mean = Sum of lifespans / Total number of breeds

= 95 / 8 = 11.875

Rounding to the nearest tenth, the mean lifespan for Kamila's sample is 11.9 years.

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(a) Probability of getting a flush is 0.000546.

(b) Probability of getting three of a kind is 0.00451.

(c) Probability of getting two pairs is 0.0150.

We have,

(a)

To calculate the probability of getting a flush, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of balls = 11 (red) + 11 (yellow) + 11 (green) + 11 (black) = 44 balls

The number of ways to choose 4 balls (without replacement)

= 44C4 = 44! / (4! x (44 - 4)!) = 44! / (4! x 40!)

= 44 x 43 x 42 x 41 / (4 x 3 x 2 x 1)

= 7315

The number of favorable outcomes:

There are 4 different colors of balls, so we have 4 possible flushes (all red, all yellow, all green, all black).

Probability of getting a flush = Number of favorable outcomes / Total number of outcomes = 4 / 7315 ≈ 0.000546

(b)

To calculate the probability of getting three of a kind, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of ways to choose 4 balls = 44C4 = 7315 (as calculated in part (a)).

Number of ways to choose 3 balls of the same denomination: We have 11 denominations, so we can choose 3 balls of the same denomination in 11C1 = 11 ways.

Number of ways to choose the fourth ball of a different denomination: After choosing 3 balls of the same denomination, we have 3 denominations left from which we can choose the fourth ball. So, the number of ways to choose the fourth ball = 3.

Number of favorable outcomes = Number of ways to choose 3 balls of the same denomination x Number of ways to choose the fourth ball of a different denomination

= 11 x 3

= 33

Probability of getting three of a kind = Number of favorable outcomes / Total number of outcomes = 33 / 7315 ≈ 0.00451

(c)

To calculate the probability of getting two pairs, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of ways to choose 4 balls = 44C4 = 7315 (as calculated in part (a)).

Number of ways to choose the first pair: We have 11 denominations, so we can choose the first pair in 11C1 = 11 ways.

Number of ways to choose the second pair: After choosing the first pair, we have 10 denominations left from which we can choose the second pair. So, the number of ways to choose the second pair = 10.

Number of favorable outcomes

= Number of ways to choose the first pair x Number of ways to choose the second pair

= 11 x 10

= 110

Probability of getting two pairs = Number of favorable outcomes / Total number of outcomes = 110 / 7315 ≈ 0.0150

Thus,

(a) Probability of getting a flush = 4/7315 ≈ 0.000546

(b) Probability of getting three of a kind = 33/7315 ≈ 0.00451

(c) Probability of getting two pairs = 110/7315 ≈ 0.0150

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Answer:

60°

Step-by-step explanation:

In similar triangles, the corresponding angles are congruent.

          ∠O = R

          O = 70°

In ΔOMN,

      ∠O + ∠M + ∠N = 180     {Angle sum property of triangle}

       70 + 50 + Ф    = 180

               120 + Ф  = 180

Subtract 120 from both sides,

                        Ф  = 180 - 120

                         Ф = 60°  

Using the intersecting chord theorem, we can calculate the value of x as: 12

The intersecting chord theorem states that If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.

Applying the intersecting chord theorem to the two chords of the circle, we can say that:

3x = (9 * 4)

3x = 36

x = 36/3

x = 12

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Answer:

weel you have to start by addition of tose numbers and after you're done with the addition if the numbers you do 2n-1 which is equal to n so you use this formula to solve it hope this helps

The reference angle of 13π/8 is 3π/8 and the sketch of the angle is attached

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

Angle = 13π/8

Rewrite as

θ = 13π/8

The above angle is in the fourth quadrant

So, we subtract it from 2π to calculate the reference angle

Using the above as a guide, we have the following:

Reference angle = 2π - 13π/8

Evaluate the difference

Reference angle = 3π/8

Hence, the reference angle is 3π/8 and the sketch of the angle is added as an attachment

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The solution to the function h(x) = 2x² - x - 1 is given by the graph attached which is a positive quadratic graph.

A quadratic graph represents a quadratic equation in the form:

   y = ax² + bx + c,

where a, b, and c are constants.

The graph of a quadratic equation is a curve called a parabola.

The general shape of a quadratic graph depends on the value of the coefficient "a." If "a" is positive, the graph opens upward, and if "a" is negative, the graph opens downward.

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The probability of picking a blue marble and then a green marble without replacing the blue one is 2/15.

From the figure we can write

Number of Blue marbles = 2

Number of Green marbles = 6

Number of Purple marbles = 2

Total number of marbles = 2 + 6 + 2 = 10

Now, Probability of picking a blue marble

= Number of Blue marbles / Total number of marbles

= 2 / 10

= 1/5

After removing the blue marble, the total number of marbles becomes 9

Probability of picking a green marble

= 6 / 9

= 2/3

So, the probability of picking a blue marble and then a green marble

Probability = (1/5) x (2/3) = 2/15.

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The domain and the range of the graph seen in the figure are X = {- 5, - 4, - 1, 3} (or x ∈ [- 5, 3]) and Y = {- 2, 0, 2, 4} (or y ∈ [- 2, 4]).

Herein we find a graph generated by four points of the form (x, y) set on Cartesian plane. The domain of the graph consists in the set of all x-coordinates of the graph, whereas range is for the set of all y-coordinates.

Domain

X = {- 5, - 4, - 1, 3}

(Interval notation)

x ∈ [- 5, 3]

Range

Y = {- 2, 0, 2, 4}

(Interval notation)

y ∈ [- 2, 4]

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