Find the sum of the three expressions and choose the correct answer. -8a^3b + 3a^2b^2 - 5 2 + 5a^2b^2 3a^3b + 7 - 9a^2b^2 A -5 a3b - a2b2 + 2 B -5 a3b - a2b2 + 4 C -5 a3b + 8 a2b2 + 4

Answer:

-3/4

Step-by-step explanation:

y2-y1/x2-x1

-17+2 divided by 24-4

-15/20

-3/4

Answer:

-3/4

Step-by-step explanation:

The slope of a line is given by

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

   = (-17- -2)/(24-4)

   = (-17+2)/(20)

    = -15/20

   =-3/4

Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i

The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.

Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),

r = |z|  magnitude of z

it becomes

r = √((5)² + (5√3)²) = 10

θ = arg(z) is the argument of z.

θ = atan2(b, a) = atan2(5√3, 5) = π/3

(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)

De Moivre's theorem to raise the complex number to the 7th power

(5 + 5√3i)⁷

= 10⁷× (cos 7π/3 + i sin 7π/3)

= 10⁷ × (cos 2π/3 + i sin 2π/3)

Convert this back to rectangular form:

Real part = r cos θ = 10⁷× cos (2π/3) = -5000000

Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i

∴  (5 + 5√3i)⁷ = -5000000 + 8660254.03i

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Answer:10^7 (1/2 - √3/2 i)

Step-by-step explanation:

To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:

Magnitude:

|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10

Argument:

arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3

So the number can be written in polar form as:

5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))

Now we can use DeMoivre's theorem:

(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))

To simplify, we need to find the cosine and sine of 7π/3:

cos(7π/3) = cos(π/3) = 1/2

sin(7π/3) = -sin(π/3) = -√3/2

Explanation:

So the final answer in rectangular form is:

10^7 (1/2 - √3/2 i)

Answer:

answer attached

Step-by-step explanation:

use Excel to easily find MANY ordered pairs for the solution to the equation

The percentage rate of change per day is approximately 0.1932%.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To represent the number of users on the website after t years, we can use the exponential growth formula:

\(N_t = N_0 \times e^{rt}\)

where \(N_0\) is the initial number of users, r is the growth rate, and t is the time in years.

Given that \(N_0\) = 6300 and the growth rate is 73%, or 0.73, per year,

The function is:

\(N_t = 6300 \times e^{0.73t}\)

To find the percentage rate of change per day, we can use the formula:

\(r = (e^{0.73/365} - 1) \times 100%\)

where 0.73/365 is the daily growth rate.

Solving for r, we get:

\(r = (e^{0.73/365} - 1)\) x 100%

r ≈ 0.1932%

Therefore,

The percentage rate of change per day is approximately 0.1932%.

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Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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Answer:

proportional

Step-by-step explanation:

test = 100%

Answer: The correct answer is that it is proportional?

Answer:

\(3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }\)

Step-by-step explanation:

Just to make it easier to see, \(\sqrt{x} = x^{\frac{1}{2} }\) and \(\sqrt[5]{x} = x^{\frac{1}{5} }\)  This way we could more easily use the power rule of derivatives.

So if f(x) = \(x^{2} +x^{\frac{1}{2} } +x^{\frac{1}{5} }\) then f'(x) will be as follows.

f'(x) = \(x^{1} +\frac{1}{2} x^{-\frac{1}{2} } +\frac{1}{5} x^{-\frac{4}{5} } = x +\frac{1}{2x^{\frac{1}{2} }} +\frac{1}{ 5x^{\frac{4}{5} }} = x +\frac{1}{2\sqrt{x}} +\frac{1}{ 5\sqrt[5]{x^4} }\)

to find f'(3) just plug 3 into f'(x) so \(3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }\)

Answer:

it ccccccccccccccccccccc

Step-by-step explanation:

Answer:

(1,2) and (x-2)-3 should be on the graph

Step-by-step explanation:

Answer:

your answer is 117

Step-by-step explanation:

2460÷12=117

i hope this helps

have a nice day/night

mark brainliest please :)

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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The low Q₁ is 13 and the median Q₃ is 16.5, the high is 18 and the interquartile range is 3.5

The interquartile range is a measure of dispersion that tells us how spread out the middle 50% of a dataset is. To calculate the IQR, we first need to find the quartiles of the dataset. Quartiles divide a dataset into four equal parts, with the first quartile (Q₁) representing the 25th percentile, the second quartile (Q₂) representing the 50th percentile (also known as the median), and the third quartile (Q₃) representing the 75th percentile.

To find the quartiles of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18}, we first need to order the data in ascending order:

10, 13, 13, 14, 15, 15, 16, 17, 18

The low is the smallest value in the dataset, which is 10.

To find Q₁, we need to find the value that is 25% of the way through the dataset. Since we have 9 values in our dataset, 25% of 9 is 2.25. This means that Q₁ lies between the 2nd and 3rd values in the dataset, which are both 13. To find the exact value of Q₁, we can take the average of these two values:

Q₁ = (13 + 13) / 2 = 13

The median is the middle value in the dataset, which is 15.

To find Q₃, we need to find the value that is 75% of the way through the dataset. 75% of 9 is 6.75, which means that Q₃ lies between the 6th and 7th values in the dataset, which are 16 and 17, respectively. To find the exact value of Q₃, we can take the average of these two values:

Q3 = (16 + 17) / 2 = 16.5

The high is the largest value in the dataset, which is 18.

Now that we have found the quartiles, we can calculate the IQR by subtracting Q1 from Q₃:

IQR = Q₃ - Q₁ = 16.5 - 13 = 3.5

Therefore, the interquartile range of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18} is 3.5. This tells us that the middle 50% of the dataset is relatively tightly clustered around the median, with values ranging from 13 to 16.5.

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Based on the given responses, the student who factored 20x^6 = (2x)(10x^5) correctly is Andrei. Therefore, the correct answer is (Choice A) Andrei.

Among the given responses, the student who factored 20x^6 = 20, x to the power of 6 correctly is Andrei. Andrei's factorization is (2x)(10x^5), which correctly represents the original term 20x^6. Therefore, the correct answer is (Choice A) Andrei.

Amit's factorization is (4x^3)(5x^3), which is incorrect because it breaks down the term into two factors with the same exponent, while the original term has an exponent of 6.

Andrew's factorization is (20x^2)(x^3), which is also incorrect as it does not accurately represent the original term 20x^6.

Hence, the only student who correctly factored 20x^6 = 20, x to the power of 6 is Andrei.

The right answer is A. Andrei who factored 20x^6 = (2x)(10x^5) correctly.

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Answer:

it is a -3/-2

Step-by-step explanation:

The sum of the given series is 20/3. Option ii is the correct answer.

A geometric series is a group of terms where each phrase is produced by multiplying the one before it by a fixed quantity known as the common ratio. Many branches of mathematics and science, such as computer science, physics, and finance, use geometric series. The following formula can be used to get the sum of an infinite geometric series:

S = a/(1-r) (1-r)

assuming that |r| 1.

The sum of the infinite series is given by the formula:

S = a/(1-r)

For the given series we have:

first term is for n = 1:

-4(5/8) = -5/2,

and the common ratio is 5/8

Substituting the values:

S =-5/2/(1 - 5/8) =-5/2(8/3) = 20/3

Hence, the sum of the given series is 20/3.

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As the given equation is (36)ˣ⁺²  = 6 , then the solution for the given equation is x ≈ -1.54.

The given equation in the question is (36)ˣ⁺²  = 6

according to the given equation , the goal is to solve the equation for x.

For solving this equation ,

we'll have to use logarithmic operations which is as follows:  

log36(6) = x+2.

We will be further using a calculator to determine the logarithmic value: log36(6) ≈ 0.4607.

Now, By subtracting 2 from both sides, we will get the value of x as:

x ≈ -1.54.

When we round off this value to the nearest 100th, we will get  -1.54.

Thus , the solution for the given equation is x ≈ -1.54.

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Answer: D

according to scientific notation,

The statement which is true about the quadrilateral is D. Some rhombuses have four right angles.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

Rectangles, squares, trapezium, parallelogram, rhombus are all quadrilaterals.

A. All squares are rectangles but all rectangles are not squares, since for squares, all sides need to be equal.

But for a rectangle, opposite sides only need to be equal.

B. A rhombus has all the sides equal and opposite sides are parallel.

So there are 2 pairs of parallel sides.

C. A trapezoid can have only one pair of sides parallel.

D. Some rhombuses have four right angles.

This is true since square is a rhombus and it has 4 right angles.

Hence the true option is D.

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Answer: No, she cannot

Step-by-step explanation:

this is because 194 divided by 6 = 32.333333333, which is an uneven number. hope this helps!

Answer:

sorry no idea

Step-by-step explanation:

Answer:

252 Cake Cones

Step-by-step explanation:

You have to make your own formula with the numbers in the problem. Here's how I set it up:

w= number of waffle cones

c=number of cake cones

We know that the number of waffle cones is the number of cake cones plus 50, so we write that out here: w=c+50

And we know that the sales total was $1422.50. That is, the number of waffle cones times the cost per cone plus the number of cake cone times their cost per cone, and we can write that out here: (3.25× w) + (1.75×c) =1,422.50.

Now, we can substitute our first formula into the second formula to solve for  C. The new equation reads: 3.25(c+50) + 1.75c=1,422.50

Distribute 3.25 to c and 50: 3.25c +162.50+1.75c=1,422.50

Combine like terms: 5c +162.50=1422.50

Subtract 162.50 from both sides: 5c=1260

Divide both sides by 5: C=252

TO CHECK YOUR WORK

Now that you have solved for C, plug that figure back into the first equation to solve for w: (252)+50=w, W=302

Now plug both numbers into your equation for the total cost:

3.25(302) + 1.75(252)=1,422.50

981.5+441= 1,422.50

You're done!

Answer:

(9,16)

Step-by-step explanation:

We Know

The equation y = 3x - 2

Find the y coordinate (9, ?)

We just simply put 9 in for x and solve for y

y = 3(9) - 2

y = 18 - 2

y = 16

So, the coordinate are (9,16)

Answer:

letter C.

Step-by-step explanation:

because the answer is 65

Answer:

y = x/2 + 4

Step-by-step explanation:

x = 2y + 4

divide 2 + 4 on both sides in order to isolate y by its self.

x/2 + 4 = 2y + 4/2 + 4

x/2 + 4 = y

y = x/2 + 4

a) The opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.

b) The sum of the given number and its opposite will be 7.928.

It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.

A rational number is a sort of real number that has the form p/q and does not equal zero.

The given number is as,

3, 7.5, and -2(2/3)

a)

The opposite number is obtained as 1 by dividing the given number,

⇒ 1 / 3 = 0.33

⇒ 1 / 7.5 = 0.133

⇒ 1 / -2(2/3) = -0.375

b)

The sum of the given number and its opposite is,

= 3+0.33 + 7.5 + 0.133+ (-2(2/3) ) + (-0.375)

= 7.928

Thus, the opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.and the sum of the given number and its opposite will be 7.928.

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Team Tackle's score was 28 points. And team Sack's score was 9 points.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

During the 2005 football season, Team Tackle beat Team Sack by 19 points. If their combined scores totaled 37.

Let 'x' be the Tackle's score and 'y' be the Sack's score. Then the equations are given as,

x + y = 37        ...1

x = y + 19        ...2

From equations 1 and 2, then we have

y + 19 + y = 37

2y = 18

y = 9

Then the value of 'x' is given as,

x = 9 + 19

x = 28

Team Tackle's score was 28 points. And team Sack's score was 9 points.

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