Find the quotient of (9-6i)/(5+3i)

Answer:

1024x^15

Step-by-step explanation:

First, we'll do 4 to the 5th power which results in 1024

Next, we'll multiply the exponents following the laws of exponents, so 3 times 5=15

This results in 1024x^15

Hope I helped :)

Answer:

\(1024 {x}^{15} \)

Step-by-step explanation:

\((4 {x}^{3} ) ^{5} \\ {4}^{5} \times {x}^{3 \times 5} \\ 1024 {x}^{15} \)

hope this helps you.

Have a nice day!

Answer:

see below and attachment

Step-by-step explanation:

a=30°

because, the marked angle of 30° is an alternate interior angle to angle a.  Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.

b=50°

because the marked angle of 50° is a vertical angle to angle b.  Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.

c=50°

because the marked angle of 50° is a corresponding angle (same side angle) to angle c.  These corresponding angles are congruent because the 2 horizontal lines are parallel.

d=100°

because the 3 interior angles of a triangle must add up to 180°.  We have 30°, 50°, so the last angle must be 100°.  We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°.  We have angle a as 30°, angle c as 50°, so angle d must be 100°.

Hope this helps!  See attachment for visual.

Answer:

2.13kg

Step-by-step explanation:

fnet=ma

17=m(8)

17÷8 =m

2.13=m

Answer:

The mass is 2¹/₈, or 2.125, kg

Step-by-step explanation:

We know that force is equal to mass times acceleration, so given a force of 17 newtons and an acceleration of 8m/s², we can say:

\(f = ma\\m = f/a\\m = \frac{17\ N}{8\ m/s^2}\\m = \frac{17\ kg\times m/s^2}{8\ m/s^2}\\m = 17/8\ kg\\m = 2.125 kg\)

giving us a mass of 2¹/₈, or 2.125 kg.

The five in 35.76 is 100 times bigger than the five in 26.95.

Here we want to compare the values of the 5's in two different numbers, which are 35.76 and 26.95.

To compare them we need to compare the place value in which each five is.

To compare them, just write the numbers but replacing all the other values by zeros:

35.76 = 05.00 = 5

26.95 = 00.05 = 0.05

Now take the quotient of these two, we will get:

5/0.05 = 100

Thus, the 5 in 35.76 is 100 times bigger than the 5 in 26.95.

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a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Answer: C) (1, -1)

Step-by-step explanation:

\(\boldsymbol{\sf{\underline{\diamond System \ of \ equations \ by \ the \ reduction \ method:} }}\)

   \(\boldsymbol{\sf{We\:have\:the\:system\:of\:equations \ --\to \ \left \{ {{x+2y=1 \ } \atop {2x-3y=5 }} \right. }}\)

Multiply the first equation by 2, and the second equation by -1, then both equations must be added.

             \(\boldsymbol{\sf{\star \ 2(x+2y=-1) }}\\ \boldsymbol{\sf{\star -1(2x-3y=5) }}\)

We add these equations to eliminate x.

             \(\boldsymbol{\sf{\star \ 7y=-7 }}\)

Then we solve 7y=-7 for y (divide by 7).

               \(\boldsymbol{\sf{\star \ \dfrac{7y}{7}=\dfrac{-7}{7} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ y=-1}}}\)

We place the found value of y, in one of the original equations y to solve for x.

                  \(\boldsymbol{\sf{\star \ x+2y=-1}} \\ \\ \boldsymbol{\sf{\star \ x+2(-1)=-1}}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}\)

Simplify (We add x to both sides.)

                  \(\boldsymbol{\sf{\star \ 0+(x)=-x+1+(x) }}\\ \\ \boldsymbol{\sf{\star \ x=1}}\\ \\ \boldsymbol{\sf{\star -2=-1-x}}\)

Add (2) to both sides.

                   \(\boldsymbol{\sf{\star \ -2+(2)=-x-1+(2) }}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}\)

We divide by 1.

                      \(\boldsymbol{\sf{\star \ \dfrac{x}{1}=\dfrac{1}{1} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ x=1}}}\)

                                     \(\underline{\bf{ \ \ x,y \ answer\ \ \ \ }}\\\boxed{\boldsymbol{\sf{x=1,y=-1 }}}\)

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Answer:

r = 5.0

Step-by-step explanation:

                   4

The ratio ------- is equal to the sine of 53.1 degrees, or to 0.78.  

                    r

Solving this for r, we get

r = 4/0.78, or r = 5.0

Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = \(Pe^(^r^t^)\)

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = \(Pe^(^0^.^0^3^5^*^9^)\)

640 = Pe^0.315

P =\(640/e^0^.^3^1^5\)

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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The numbers could be:

6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

The place value of a number is given as:

Example:

1234.567

1 = thousand place value

2 = hundred place value

3 = tens place value

4 = ones place value

5 = tenths place value

6 = hundredths place value

7 = thousandths place value

We have,

Shawn rounded a number to the nearest tenth and got 6.5.

When he rounded it to the nearest whole number, he got 6.

Now,

The number = 6.45

Rounded to the nearest tenth = 6.5

Rounded to the nearest whole number = 6

The numbers can be 6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

Thus,

The possible numbers are:

6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

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Answer:

c

Step-by-step explanation:

The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

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Answer:

im not sure but I think is c

The number 2000 is 10 times as much as the number 200.

The number 0.5 is 1/10 as much as the number 5.

Answer:

a) 1/24 do total

Step-by-step explanation:

We have that:

The total is 1.

The first friend gets 1/4 of the total.

The second friend gets 1/3 of the total

The third friend gets 3/8 of the total.

The remaining is x.

So

\(\frac{1}{4} + \frac{1}{3} + \frac{3}{8} + x = 1\)

The least common multiple between 4, 3 and 8 is 24. So

\(\frac{6 + 8 + 3*3 + 24x}{24} = 1\)

\(23 + 24x = 24\)

\(24x = 1\)

\(x = \frac{1}{24}\)

So the correct answer is:

a) 1/24 do total

The surface area in the image is 416 cm^2

Surface area is the measurement of the total area that the surface of a three-dimensional object occupies. It is typically measured in square units, such as square meters, square centimeters, or square feet. The surface area of an object can be calculated by finding the sum of the areas of all its faces or surfaces.

surface area = (2*0.5*12*8) + (2*10*10) + (12*10)

= 96 + 200 + 120

= 416 cm^2

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The simplified form of the univariate monomial expression as requested in the task content is; 1.6 y⁴.

It follows from the task content that the simplified form of the univariate monomial expression is to be determined.

Since the given expression is;

32 y⁶ / 20 y²

The expression can be simplified as follows;

( 32 / 20 ) • y⁶ / y²

= 8/5 • y⁴

= 1.6 y⁴.

On this note, it can be inferred that the simplified form of the expression is; 1.6 y⁴.

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The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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1 year insurance policy covering its equipment was purchased for 6,144. The date purchased was June 14 but it doesn't go into effect until June 16th, the amount paid for the month of June is approximately $252.75, and the amount paid for the entire year is approximately $6,144.

To calculate the amount paid for the month and the year, we need to consider the number of days covered by the insurance policy. Let's break it down step by step:

Step 1: Determine the number of days covered in June.

Since the policy doesn't go into effect until June 16th, there are 15 days remaining in June that will be covered by the insurance policy.

Step 2: Calculate the daily rate.

To find the daily rate, we divide the total cost of the insurance policy by the number of days in a year:

Daily rate = 6,144 / 365

Step 3: Calculate the amount paid for June.

The amount paid for June can be found by multiplying the daily rate by the number of days covered:

Amount paid for June = Daily rate * Number of days covered in June

Step 4: Calculate the amount paid for the year.

To calculate the amount paid for the year, we simply multiply the daily rate by 365 (the total number of days in a year):

Amount paid for the year = Daily rate * 365

Now let's perform the calculations:

Step 2: Daily rate

Daily rate = 6,144 / 365 ≈ 16.85 (rounded to two decimal places)

Step 3: Amount paid for June

Amount paid for June = 16.85 * 15 ≈ 252.75 (rounded to two decimal places)

Step 4: Amount paid for the year

Amount paid for the year = 16.85 * 365 ≈ 6,144 (rounded to two decimal places)

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Answer:

88.00 and subtract 28 and the 3 shirts were

Step-by-step explanation:

answer 60

Answer:

I didn't got the ans but u can ask it to google assistant she is smarter than me

Answer:

640 dm

Step-by-step explanation:

200+40+400=640dm

The signature of the Principal Investigator on the final proposal does not imply responsibility for the availability of funding or the financial aspects of the project.

The complete question should be What does the signature of the Principal Investigator on the final proposal NOT imply responsibility for?

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Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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You are not dumb. No one is dumb. Einstein failed math in high school.

Anna is x years old.

Jane is y years younger.

This means the Jane is x - y years old.

In three years, Anna will be x + 3 years old.

In three years, Jane will be (x - y) + 3 years old.

Let S = the sum of their ages in 3 years.

S = x + 3 + (x - y) + 3

S = 2x + 6 - y

Got it?

Answer:

58.45

Step-by-step explanation:

Use BIDMAS

14.5 X 3.1 = 44.95

44.95 + 13.5 = 58.45

Answer:

58.45

Step-by-step explanation:

Answer:

8 cubic feet

Step-by-step explanation:

First find the volume of the sand box

2 x 2 x 3 = 12

then multiply the total volume by 2/3

12 x 2/3 = 8

That leaves you with the total cubic feet of sand he would need.

Answer:

2/3 and 9

Step-by-step explanation:

Answer:

- - 12 / 5

Step-by-step explanation: