Express the following in the form; a+jb
1. Cos(e^j)
2.exp(e^j)
3.(sqrt(j))^sqrt(j)​

The coordinates of point C in the given right triangle ABC is (2, 2√3-2)

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Given that, triangle ABC is a 30°-60°-90° triangle, where two vertices are A(-4, -2) and B(4, -2).

Now, AB=4-(-4)=8

AC=AB×sin60°= 8×√3/4√3

In right triangle ACD

AD=AC×cos30°

= 4√3×√3/2

= 6

Xc=6-4=2

Yc=AC×sin30°-2

= 4×3×1/2-2

= 2√3-2

The coordinates of point C(2, 2√3-2)

Therefore, coordinates of C(2, 2√3-2).

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It would take Caro-line 3 hours to sketch 9 cartoon str-ips.

What is a ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

We are given that, Caro-line can sketch 6 car-toon str-ips in two hours.

And we are asked that how much time it would require for Caro-line to sketch 9 str-ips

Now let the time required be x

Hence, the ratio becomes

6/2=9/x

x= (9*2)/6

x= 3

Hence, It would take Caroline 3 hours to sketch 9 cartoon str-ips

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Step-by-step explanation:

The average rate of change of a function on an interval [x, x + h] is given by the formula:

(F(x + h) - F(x)) / h

For the function F(x) = 6x^2 + 5, the average rate of change on the interval [x, x + h] is:

(F(x + h) - F(x)) / h = (6(x + h)^2 + 5 - (6x^2 + 5)) / h = (6(x^2 + 2xh + h^2) - 6x^2 + 5) / h = (6(2xh + h^2)) / h = (12xh + 6h^2) / h

So the average rate of change of the function on the interval [x, x + h] is (12xh + 6h^2) / h for a real number h.

Answer:

2489

Step-by-step explanation:

it would be 30+ 1,000+29+30+400+1,000+ 2489

I really hope this helps

Proverbs 4:6-7

Do not forsake wisdom, and she will protect you; love her, and she will watch over you. The beginning of wisdom is this: Get wisdom. Though it cost all you have, get understanding. Cherish her, and she will exalt you; embrace her, and she will honor you. (just a little encouragement to keep studying hard!)

Answer:

2489

Step-by-step explanation:

On solving the provided question, we can say that in the equation,Often, there is only one variable, which also serves as the symbol. An illustration would be , [tex]D = 4(82-D)+2[/tex]

The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.

For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.The two sentences on either side of a letter are connected by a mathematical formula.

Each equation has a formula. Not every equation has a formula. Equations are created with the intention of being solved for a variable. If an equation meets the requirements for a function, it is a function. But not every equation is a function.

M+D = 82 marbles

[tex]M= 82- D[/tex]

[tex]D= 4M+2[/tex]

[tex]D= 4(82-D) +2[/tex]

[tex]D= 328 - 4D+2[/tex]

[tex]5D = 330[/tex]

[tex]D= 66[/tex]

Therefore, Don has 66 and Mark has 82-66 = 16

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No, it is impossible to construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm as the dimensions defy the triangle inequality theorem.

It follows from the triangle inequality theorem that the sum of any two side lengths of a triangle must be greater than the third side length and also, the difference of two side lengths of a triangle must be less than the third side lengths.

However, in this case, since QR + PR = PQ, it can be inferred that the two side lengths cannot possibly be used to construct a triangle.

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Answer: A = 15 units²

Step-by-step explanation:

The figure has 1 pair of parallel sides and is therefore a trapezium.

The area (A) of a trapezium is calculated as

A =  h (b₁ + b₂ )

where h is the perpendicular height between bases and b₁, b₂ are bases

here h = 3, b₁ = 3 , b₂ = 7 , then

A =  × 3 × (3 + 7) = 1.5 × 10 = 15 units²

The measure of the side AE would be 70 units.

We know that the triangle midpoint theorem says that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

In the given triangle B, D, F are the midpoints of the triangle.

AC=50, CE=60,

BD=35

Then, in the given triangle if BD is connecting the midpoints of AC and CE then it must be parallel to AE and equal to FE ( half of AE).

⇒ BD ≅ FE= 1/2 AE

AE = 70 units

Then, the length of line segment AE = 70 units

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The evaluation of the cubic function represented by the graph can be presented as follows;

a. The equation of the function, S = a·t³ + b·t² + c·t + d, indicates that the equation is a cubic equation

b. i. d = -5

ii. The three equations are;

a + b + c = 8...(1)

8·a + 4·b + 2·c = 4...(2)

27·a + 9·b + 3·c = 0...(3)

iii. a = 2, b = -12, and c = 18

c. The student is expected to be in debt for 2 years, 4 months and 3 days

A cubic function is a degree three polynomial that can be expressed in the form; f(x) = a·x³ + b·x² + c·x + d.

The specified function can be presented as follows;

S = a·t³ + b·t² + c·t + d

a. A feature of the graph that indicates that a cubic equation is the appropriate model, is the largest power of the input time variable t in the function is 3, which is the same as the power of a cubic function.

b. i. The value of d can be found by plugging in t = 0, in the function; S = a·t³ + b·t² + c·t + d

From the table in the question, we get;

At t = 0, S = -5

Therefore;

S = a×0³ + b×0² + c×0 + d = -5

d = -5

The value of d = -5

b. ii. The simultaneous equations can be obtained by plugging in the values of t from the table into the function for S as follows;

S = a·t³ + b·t² + c·t + d

S = a·t³ + b·t² + c·t - 5

When t = 1, we get;

S = a·1³ + b·1² + c·1 - 5 = 3

a + b + c - 5 = 3

a + b + c = 3 + 5 = 8

When t = 2, we get;

S = a·2³ + b·2² + c·2 - 5 = 3

8·a + 4·b + 2·c - 5 = -1

8·a + 4·b + 2·c = -1 + 5 = 4

When t = 3, we get;

S = a·3³ + b·3² + c·3 - 5 = 3

27·a + 9·b + 3·c - 5 = -5

27·a + 9·b + 3·c = -5 + 5 = 0

iii. Solving the system of equations using a graphing calculator, indicates that we get;

c. Plugging in the values into the specified equation, we get;

S = 2·t³ - 12·t² + 18·t - 5

The solution of the above equation can be found as follows;

2·t³ - 12·t² + 18·t - 5 = 0

Based on an online tool, the Newton Raphson method indicates that a solution of the equation is; t ≈ 0.35821, which indicates that a factor of the equation, 2·t³ - 12·t² + 18·t - 5 = 0 is; (x - 0.35821)

(2·t³ - 12·t² + 18·t - 5) ÷ (x - 0.35821) ≈ 2·t² - 11.28356·t + 13.95804

The other solutions are therefore;

t ≈ 1.83, and t ≈ 3.81

The student is expected to be in debt at time t = 0, and from the graph, cross the x-axis out of depth first at time, t ≈ 0.35821 of a year

The student will be in dept again between t ≈ 1.83 and t ≈ 3.81

The total time the student is expected to be in debt is therefore;

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The radius, diameter, area and circumference of circle 1, 2, 3 and 4 are; (2, 4, 4π, 4π), (4, 8, 16π, 8π), (1, 2, 1π, 2π) and ( 8, 16, 64π, 16π) respectively.

The diameter of a circle is 2 times the radius of the circle.

The area of a circle is expressed as: A = πr²

The circumference of a circle is expressed as: 2πr

For question 1)

Radius r = 2

Diameter = 2 × radius = 2 × 2 = 4

Area = πr² = π( 2 )² = 4π

Circumference = 2πr = 2 × π × 2 = 4π

For question 2)

Radius r = 4

Diameter = 2 × radius = 2 × 4 = 8

Area = πr² = π( 4 )² = 16π

Circumference = 2πr = 2 × π × 4 = 8π

For question 3)

Diameter d = 2

Radius = diameter / 2 = 2/2 = 1

Area = πr² = π( 1 )² = 1π

Circumference = 2πr = 2 × π × 1 = 2π

For question 4)

Diameter d = 16

Radius = diameter / 2 = 16/2 = 8

Area = πr² = π( 8 )² = 64π

Circumference = 2πr = 2 × π × 8 = 16π

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The measure of angle A is given as follows:

<A = 60º.

The three trigonometric ratios are defined as follows:

For the angle A, we have that:

Applying the sine ratio, the angle measure is given as follows:

sin(A) = 13/15

A = arcsin(13/15)

A = 60º.

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Answer:

5/6

Step-by-step explanation:

The magnitude of the vector is 25.5 metres.

The magnitude of a vector is the length of the vector. Therefore, the magnitude of a vector can be found using Pythagoras's theorem as follows:

Hence,

c² = a² + b²

where

Therefore,

| N | = √22.2² + 12.6²

| N | =  √492.84 + 158.76

| N | =  √651.6

| N | = 25.5264568634

| N | = 25.5 metres

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Answer:

Step-by-step explanation:

The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, we can use points A(4, 5) and B(9, 7):

slope = (7 - 5) / (9 - 4) = 2 / 5

So, the slope of line AB is 2/5.

The difference between the median rating for each company is approximately 0.3 times the interquartile range.

Generally speaking, the median for 20 observations is the average of the 10th and 11th number:

Median rating of Company A = (4 + 4)/2

Median rating of Company A = 8/2

Median rating of Company A = 4.

Median rating of Company B = (3 + 3)/2

Median rating of Company B = 6/2

Median rating of Company B = 3.

Difference in median = 4 - 3

Difference in median = 1

For the required expression that models the difference between the median rating for each company and the interquartile range, we have the following:

1 = 3x

x = 1/3.

x = 0.3

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Answer:

Note that 0.01 is the decimal form of 1%, so 0.01 multiplied by 7 yields 7%. So, if we were to find 1% of 250, which is 2.5, we can multiply the value by 7, which is 17.5.

Therefore, 7% of 250 is 17.5

Answer:

51°

Step-by-step explanation:

180°-129°=51°

I hope it helps you

Answer:

...here is the answer...

Answer:

Step-by-step explanation:

The cost of renting a car for "d" days can be represented by the following function:

c(d) = 75d + 30

where "c" is the total cost of the car rental and "d" is the number of days the car is rented for. The first term, 75d, represents the daily rental fee of $75 per day. The second term, 30, represents the flat fee for the full tank of gas that can be returned either full or close to empty.

The value of y from x= 0 to x = 3 is: y = 5(2)⁰ = 5, y = 5(2)¹ = 10, y = 5(2)² = 20, y = 5(2)³ = 40. The most rapid rate of change is: y = 7ˣ. The constant 1.20 is greater than 1 thus, the function is exponential growth.

The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

The given function is:

y = 5(2)ˣ

The value of y from x= 0 to x = 3 is:

y = 5(2)⁰ = 5

y = 5(2)¹ = 10

y = 5(2)² = 20

y = 5(2)³ = 40

The most rapid rate of change as x increases beyond 0 is:

y = 7ˣ

This is observed as the graph increases rapidly with change in value of x.

3. y = (1.20)ˣ

The constant 1.20 is greater than 1 thus, the function is exponential growth.

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Answer:

∠ a = 30° , ∠ b = 90°

Step-by-step explanation:

∠ a and 150° are a linear pair and sum to 180° , that is

∠ a + 150° = 180° ( subtract 150° from both sides )

∠ a = 30°

------------------

the sum of the 3 angles in a triangle = 180° , that is

∠ b + ∠ a + 60° = 180°

∠ b + 30° + 60° = 180°

∠ b + 90° = 180° ( subtract 90° from both sides )

∠ b = 90°

The probability that a randomly chosen college student exercises in the morning or afternoon is B. 0. 39.

The probability that a college student chosen at random will either exercise in the morning or afternoon can be found by the formula :

= Probability that student exercises in the morning + Probability that student exercises in the afternoon

Probability that student exercises in the morning = 0. 25

Probability that student exercises in the afternoon = 0. 14

The probability would therefore be:

= 0. 25 + 0. 14

= 0. 39

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Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the reflections:

Point R is located at (1, 1) on the coordinate plane.

Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).

Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).

So the final location of R'' is at the ordered pair (-1, -1).

The expression represents a quintic polynomial with 4 terms. The constant term is -6, the leading term is x⁵/2, and the leading coefficient is 1/2.

A polynomial expression is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.

From the polynomial expression given:

[tex]\dfrac{1}{2}x^5 - 6 - x^4 -5x^2[/tex]

The degree of a polynomial is the highest degree of its terms which helps us to determine the type of polynomial (quintic polynomial). The constant term is -6.

The leading term in a polynomial is the term with the highest degree = x⁵/2. The leading coefficient of a polynomial is the coefficient of the leading term is 1/2.

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Answer:

quadrinomial, 4, -6, 1/2x^5, 1/2

Step-by-step explanation:

quadrinomials are polynomials with 4 terms

constant is the number with no variable

leading term is the term at the beginning

leading coefficient is the number at the beginning

Answer:

The answer is 100, see Step-by-step explanation:

Step-by-step explanation:

If anyone looks at the verified answer, its wrong and so are the comments under it. In the answer above it says "Sci-fi = 100-24-22-20-14=20" that is correct but the answer is not. 20 percent of 500 is 100 not 72 or 20, I don't know how anyone got those answers.

The  total manufacturing costs for each factory are to be the same is M = 3318.52.

Let's denote the number of pairs of jeans produced at the Medney factory as M, and the number of pairs of jeans produced at the Selbourne factory as S.

Total cost of production at the Medney factory = Total cost of production at the Selbourne factory

28000 + 30M = 35200 + 24S

Total number of pairs of jeans produced = 6000

M + S = 6000

We can solve for M and S by using substitution or elimination. Here, we will use substitution:

M + S = 6000 (from equation 2)

M = 6000 - S (subtracting S from both sides)

28000 + 30M = 35200 + 24S (from equation 1)

Substituting M = 6000 - S:

28000 + 30(6000 - S) = 35200 + 24S

180000 - 30S = 35200 + 24S

180000 = 54S + 35200

54S = 144800

S = 2681.48

So the number of pairs of jeans produced at the Selbourne factory is approximately 2681.48. To find the number of pairs of jeans produced at the Medney factory, we can substitute this value of S back into equation 2:

M + S = 6000

M + 2681.48 = 6000

M = 3318.52

So the number of pairs of jeans produced at the Medney factory is approximately 3318.52.

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Answer:yes

Step-by-step explanation:

The degree of the polynomial is; 6.

The leading coefficient of the polynomial is; 1.

The maximum number of real zeroes is; 6.

As evident in the task content; the given polynomial is;

f (x) = 2x⁵ - x³ + x⁶ - 4.

By observation, the term with the highest power of x is; x⁶.

Therefore, the degree is; 6.

The leading coefficient is the coefficient of x⁶ which is; 1.

The maximum number of real zeroes possible is dependent on the degree of the polynomial and is; 6.

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