Evaluate (10 – 4i) ÷ (5 + i).

A) Fifty-four twelfths minus fifteen twelfths i
B) Twenty-three twelfths minus fifteen twelfths i
C) Fifty-four thirteenths minus fifteen thirteenths i
D) Twenty-three thirteenths minus fifteen thirteenths i

Answer:

The equation would be a quadratic trinomial

Step-by-step explanation:

Step 1: Expand the equation to remove the brackets

0 = 8x² + 3x - 12x² + 1

Step 2: Collect like terms

0 = -4x² + 3x + 1

Step 3: Count number of terms

0 = -4x² + 3x + 1

1 2 3

Therefore there are 3 terms and this is a quadratic equation making the answer B, a quadratic trinomial

Answer:

1. 7%

2. 55%

3. 15%

Step-by-step explanation:

That's the answer

Answer:

2

Step-by-step explanation:

Lisa paints 1/3 of the room in an hour

Therefore the number of rooms she will paint in 6 hours can be calculated as follows

1 hour= 1/3

6 hours= x

Cross multiply

x= 1/3 ×6

= 2

Hence 2 rooms can be painted in 6 hours

The area of the composite figure is 89.065 ft^2

We can divide the figure into 3 simpler ones, these are:

A rectangle of 5ft by 2 ft

A rectangle of 8ft by 9 ft

A fourth of a circle of radius R = 3ft

Remember that the area of a circle of radius R is:

A = 3.14*R^2

Then the area of the fourth a circle of radius R = 3ft is:

a = (1/4)*3.14*(3ft)^2 = 7.065 ft^2

And the areas of the rectangles are equal to the product between the dimensions, so the areas are:

a' = 5ft*2ft = 10ft^2

a'' = 8ft*9ft = 72 ft^2

The total area is the sum of these:

7.065 ft^2 + 10ft^2 +72ft^2 = 89.065 ft^2

Learn more about area at:

https://brainly.com/question/24487155

#SPJ1

Answer:

the second one, third one

Step-by-step explanation:

you can expand using the distributive property

The true statement is (C) the biased coin has about a 33% probability of displaying tails.

To find the true statement:

Therefore, the true statement is (C) the biased coin has about a 33% probability of displaying tails.

Know more about probability here:

https://brainly.com/question/24756209

#SPJ4

The correct question is given below:
A coin is biased such that it results in 2 heads out of every 3 coin flips, on average. Which statement is true?

A.)The theoretical probability of getting heads from an unbiased coin is about 66%.

B.)The sequence HTHTTHTTT is valid for the biased coin.

C.)The biased coin has about a 33% probability of displaying tails.

D.)The sequence HTTHTHTHT is valid for the biased coin.

Answer:

43 remainder of 6.

Step-by-step explanation:

Answer:

Step-by-step explanation:

?

The deflection angle of light by the white dwarf star is approximately \(\(0.00108 \times 206,265 = 223.03\)\)arcseconds (rounded to two decimal places).

To calculate the deflection angle of light by a white dwarf star, we can use the formula derived from Einstein's theory of general relativity:

\(\[\theta = \frac{4GM}{c^2R}\]\)

where:

\(\(\theta\)\) is the deflection angle of light,

G is the gravitational constant \((\(6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}\)),\)

M is the mass of the white dwarf star,

c is the speed of light in a vacuum \((\(299,792,458 \, \text{m/s}\)),\) and

(R) is the radius of the white dwarf star.

Let's calculate the deflection angle using the given values:

Mass of the white dwarf star, \(\(M = 1.2 \times \text{solar mass}\)\)

Radius of the white dwarf star, \(\(R = 0.0088 \times \text{solar radius}\)\)

We need to convert the solar mass and solar radius to their respective SI units:

\(\(1 \, \text{solar mass} = 1.989 \times 10^{30} \, \text{kg}\)\(1 \, \text{solar radius} = 6.957 \times 10^8 \, \text{m}\)\)

Substituting the values into the formula, we get:

\(\[\theta = \frac{4 \times 6.67430 \times 10^{-11} \times 1.2 \times 1.989 \times 10^{30}}{(299,792,458)^2 \times 0.0088 \times 6.957 \times 10^8}\]\)

Evaluating the above expression, the deflection angle \(\(\theta\)\) is approximately equal to 0.00108 radians.

To convert radians to arcseconds, we use the conversion factor: 1 radian = 206,265 arcseconds.

Therefore, the deflection angle of light by the white dwarf star is approximately \(\(0.00108 \times 206,265 = 223.03\)\)arcseconds (rounded to two decimal places).

Hence, the deflection angle is approximately 223.03 arcseconds.

Learn more about radius here:

https://brainly.com/question/14963435

#SPJ11

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b. This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

To find the equation for the tangent plane to the graph of the function f(x, y) = 2e^x - y at a given point (x0, y0), we need to calculate the partial derivatives of f with respect to x and y at that point.

The partial derivative of f with respect to x, denoted as ∂f/∂x or fₓ, represents the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y or fᵧ, represents the rate of change of f with respect to y while keeping x constant.

Let's calculate these partial derivatives:

fₓ = d/dx(2e^x - y) = 2e^x

fᵧ = d/dy(2e^x - y) = -1

Now, we have the partial derivatives evaluated at the point (x0, y0). Let's assume our point of interest is (a, b), where a = x0 and b = y0.

At the point (a, b), the equation for the tangent plane is given by:

z - f(a, b) = fₓ(a, b)(x - a) + fᵧ(a, b)(y - b)

Substituting fₓ(a, b) = 2e^a and fᵧ(a, b) = -1, we have:

z - f(a, b) = 2e^a(x - a) - (y - b)

Now, let's substitute f(a, b) = 2e^a - b:

z - (2e^a - b) = 2e^a(x - a) - (y - b)

Rearranging and simplifying:

z = 2e^a(x - a) - (y - b) + 2e^a - b

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b.

This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

Learn more about tangent here:

https://brainly.com/question/10053881

#SPJ11

Answer:

-3

Step-by-step explanation:

divide both side by 6 to find t

Answer:

-.175, 1.425, and 2

Step-by-step explanation:

easiest way, if you're allowed to use a graphing calculator, is to graph it and find the x-intercepts

Answer:

Step-by-step explanation:

9 + 4 = 13 Two minus' make a plus

14-9 = 5     this is just subtraction

-4 + 5 = 1   two minus's make a plus.

-7-9 = -16

Answer:

you will need 0.25 pound of sugar

Answer:

it's gonna be the 3rd one g(×)=1.07

Step-by-step explanation:

if im wrong im sorry tell me and ill correct it

A negative correlation coefficient indicates an inverse or indirect relationship between two variables. As one variable increases, the other tends to decrease or become smaller.

A correlation coefficient measures the strength and direction of the relationship between two variables. It can range from -1 to +1. A negative correlation coefficient indicates an inverse relationship between the variables.

In an inverse relationship, as one variable increases, the other variable tends to decrease or become smaller. Conversely, as one variable decreases, the other variable tends to increase or become larger. This means that the variables move in opposite directions.

For example, if we observe a negative correlation between the amount of studying done for an exam and the number of mistakes made, it means that as studying increases, the number of mistakes decreases, and vice versa.

On the other hand, a positive correlation coefficient indicates a direct relationship, where both variables tend to move in the same direction. In a positive correlation, as one variable increases, the other variable also increases, or as one variable decreases, the other variable decreases.

In conclusion, a negative correlation coefficient signifies an inverse relationship between two variables, where an increase in one variable is associated with a decrease in the other variable, and vice versa.

Learn more about coefficient here:

https://brainly.com/question/1594145

#SPJ11

Answer:

25 , 30

Step-by-step explanation:

x > 50 -28

x > 22

x is greater than 22.

Answer:

Step-by-step explanation:

D and E because x must be greater than 23

To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

To know more about a series solution:- https://brainly.com/question/31522450

#SPJ11

The linear speed of a point on the circumference is approximately 9895 feet per minute.

(a) To find the angular speed in radians per minute, we need to convert the given rotational speed from rpm (revolutions per minute) to radians per minute. Since there are 2π radians in one revolution, we can use the conversion factor:

Angular speed (in radians per minute) = Rotational speed (in rpm) * 2π

Given that the rotational speed is 2100 rpm, we can calculate the angular speed:

Angular speed = 2100 rpm * 2π ≈ 13194 radians per minute

Therefore, the angular speed of the wheel is approximately 13194 radians per minute.

(b) To find the linear speed of a point on the circumference in feet per minute, we can use the formula:

Linear speed = Angular speed * Radius

Given that the radius of the wheel is 9 inches, we need to convert it to feet:

Radius = 9 inches * (1 foot / 12 inches) = 0.75 feet

Now, we can calculate the linear speed:

Linear speed = 13194 radians per minute * 0.75 feet ≈ 9895 feet per minute

Therefore, the linear speed of a point on the circumference is approximately 9895 feet per minute.

to learn more about circumference click here:

brainly.com/question/23881522

#SPJ11

The domain is a set tht contains all possible x-values in a relataion or a function. In this problem, we just need to know what the x-coordinates are to be able to identify the domain.

Let us first list down the coordinates of the given points. We have:

The x-coordinates are: -3, -1, 1, 3, and 6.

So the domain is: {-3, -1, 1, 3, 6}. The answer is option C.

Answer:

Heres one

c = 5 + 1.5t

Step-by-step explanation:

Let t represent the number of toppings

and c represent the total cost of the pizza

Answer:

Step-by-step explanation:

B Cevap rica ederim

Answer:

y=4x+2 or f(x)=4x+2

Step-by-step explanation:

This is because the equation format for a line is y=mx+b, the slope is m and the y-intercept is b. So all you have to do is fill it out to get y=4x+2. Or the other way I listed the equation is right too. Hope this helps!

The probability that the paint on a sample of 65 test panels will have a mean life before corrosive failure of less than 144 hours is approximately 0.0005 or 0.05%.

To find the probability that the paint on a sample of 65 test panels will have a mean life before corrosive failure of less than 144 hours, we will use the Central Limit Theorem (CLT). The CLT states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population distribution.

Given:
- Mean life before corrosive failure (μ) = 155 hours
- Standard deviation (σ) = 27 hours
- Sample size (n) = 65 test panels
- Target mean life before corrosive failure (x) = 144 hours

First, we need to calculate the standard error (SE) of the sample mean:

SE = σ / √n = 27 / √65 ≈ 3.343

Next, we will calculate the z-score for the target mean life of 144 hours:

z = (x - μ) / SE = (144 - 155) / 3.343 ≈ -3.293

Now, we will use the standard normal distribution table or a calculator to find the probability that the sample mean life is less than 144 hours:

P(z < -3.293) ≈ 0.0005

Learn more about probability here: brainly.com/question/11234923

#SPJ11

The factors of the quadratic equation are found as the 7 and -3/2

For the given question, the quadratic equation is give as;

2x² - 11x - 21 = 0

Find the factors of -21×2 = 42 such that on subtraction it gives -11.

2x² - 14x + 3x - 21 = 0

Take 2x common from the first two terms and 3 from the last two terms.

2x(x - 7) + 3(x - 7) = 0

Take (x - 7) common from the terms.

(x - 7)(2x + 3) = 0

Then,

x - 7 = 0

x = 7

and, 2x + 3 = 0

x = -3/2

Thus, the factors of the quadratic equation are found as the 7 and -3/2.

To know more about factorization method, here

https://brainly.com/question/25829061

#SPJ10

The integral is evaluated and the value of the integral is found to be 3/2.

Given that,

The integral is ∫∫(5+10y) dy dx

To find : To evaluate the iterated integral,

= ∫(5y + 10y²/2) dx

= ∫ (5y + 5y²) dx

Substituting the limits x and x² in the variable y

= ∫ (5x + 5x² - (5x² + 5x⁴)) dx

= ∫(5x + 5x² - 5x² - 5x⁴) dx

= ∫(5x - 5x⁴) dx

= (5x²/2 - 5x⁵/5)

= (5/2 - 1)

= 3/2

Hence, The integral is evaluated and the value of the integral is found to be 3/2.

To know more about integral click here:

brainly.com/question/18125359

#SPJ4

Answer:

The answer is  a= \(\frac{8x^2+11x+1}{2}\)

Step-by-step explanation:

Combine like terms and we get,

\(24x^2+83x+3=6ax\)

\(\frac{24x^2+33x+3}{6x} =a\)             divide both sides of the equation by ax, and simplify further,

\(\frac{x(8x^2+11x+1)}{2}\)                          notice that we can reduce the 24 over 6 1/2,

\(\frac{8x^2+11x+1}{2} =a\)                 distribute and simplify further

And a=\(\frac{8x^2+11x+1}{2}\)

Answer:pink

Step-by-step explanation:

Answer:

\(\sqrt{5}\)

Step-by-step explanation:

Since we can see that \((5^{\frac{3}{4} } )^{\frac{2}{3} }\) has a parentheses, the exponents are being multiplied by each other.. To find their product, just multiply across..

3*2 = 6/4*3 = 12. So we have 6/12 which can be simplified to just 1/2.

So now we have \(5^{\frac{1}{2} }\) which is equal to \(\sqrt{5}\)..