Operations with Complex Numbers: Tutorial
Question
Select all the correct answers.
Which expressions are equivalent to √-27?
D3i√3
□9i√/3
□ √27i
□ i√27
3√9i³

The SI units for the quantities you mentioned are:

1. Length: The SI unit for length is the meter (m).

2. Mass: The SI unit for mass is the kilogram (kg).

3. Time: The SI unit for time is the second (s).

4. Electric current: The SI unit for electric current is the ampere (A).

5. Amount of substance: The SI unit for the amount of substance is the mole (mol).

6. Temperature: The SI unit for temperature is the kelvin (K).

7. Luminous intensity: The SI unit for luminous intensity is the candela (cd). An angstrom (symbol: Å) is a unit of length equal to 10^(-10) meters or 0.1 nanometers. It is often used to express the sizes of atoms and molecules.

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Answer:

1. x = -1.5y

2. 5 (2x-3)

3. p = 4

Step-by-step explanation:

1) Simplifying

7x + 2y + -3x + 4y = 0

Reorder the terms:

7x + -3x + 2y + 4y = 0

Combine like terms: 7x + -3x = 4x

4x + 2y + 4y = 0

Combine like terms: 2y + 4y = 6y

4x + 6y = 0

Solving

4x + 6y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6y' to each side of the equation.

4x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0

4x + 0 = 0 + -6y

4x = 0 + -6y

Remove the zero:

4x = -6y

Divide each side by '4'.

x = -1.5y

Simplifying

x = -1.5y

2)

Common factor

10x - 15

5 (2x-3)

3) Simplifying

5p = 3p + 8

Reorder the terms:

5p = 8 + 3p

Solving

5p = 8 + 3p

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-3p' to each side of the equation.

5p + -3p = 8 + 3p + -3p

Combine like terms: 5p + -3p = 2p

2p = 8 + 3p + -3p

Combine like terms: 3p + -3p = 0

2p = 8 + 0

2p = 8

Divide each side by '2'.

p = 4

Simplifying

p = 4

The resulting vertices after the translation are:

A' = [-6, 1, -1]

B' = [1, -1, -5]

C' = [0, 0, 0]

To find the resulting vertices after the translation of triangle ABC using matrix subtraction, we need to subtract the translation vector from each vertex of the triangle.

The translation vector is given as:

T = [3, 3, 3]

-1, -1, -1]

The original vertices of triangle ABC are:

A = [-3, 4, 2]

B = [4, 2, -2]

C = [3, 3, 3]

To translate the vertices, we subtract the translation vector from each coordinate of the corresponding vertex:

A' = A - T = [-3, 4, 2] - [3, 3, 3] = [-3 - 3, 4 - 3, 2 - 3] = [-6, 1, -1]

B' = B - T = [4, 2, -2] - [3, 3, 3] = [4 - 3, 2 - 3, -2 - 3] = [1, -1, -5]

C' = C - T = [3, 3, 3] - [3, 3, 3] = [3 - 3, 3 - 3, 3 - 3] = [0, 0, 0]

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It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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The width of the parking lot is 78 m

We have been given the perimeter of a rectangular parking lot which is equal to 350 m.

We know the perimeter of a rectangular plot is 2 X (width of the plot ) + 2 X (length of the parking lot ).

And the length of the parking lot is given as 97 m.

2 X (width of the plot ) +2 X (length of the parking lot ) =350 m

2 X (width of plot ) + 2 X 97 =350

2 X (width of the plot ) =156 m

width of the plot = 78 m

Hence the width of the plot is 78 meters.

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The width of this rectangular parking lot is equal to 78 meters.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following:

P = 2(L + W)

350 = 2(97 + W)

175 = 97 + W

Width, W = 175 - 97

Width, W = 78 meters.

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Answer:

901334 x 2368 = 2134358912 is the correct answer

Step-by-step explanation:

I hope this helps you :)

The probability of experiencing exactly k delays in n days is given by:

P(X = k) = (nCk) * p^k * (1 - p)^(n - k)

To calculate the probability that Sasha will experience a delay due to traffic on at least 3 of the next 21 days, we need to consider the probability of experiencing a delay on each individual day and then use the binomial distribution.

Let's assume that the probability of experiencing a delay on any given day is p. The probability of not experiencing a delay on a single day is 1 - p.

Using the binomial distribution formula,

In this case, we want to find the probability of experiencing at least 3 delays, which means we need to calculate the probabilities for k = 3, 4, 5, ..., 21 and sum them up.

P(at least 3 delays) = P(X = 3) + P(X = 4) + P(X = 5) + ... + P(X = 21)

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Answer:

Two hundred sixty and ninety-four hundredths

Step-by-step explanation:

hope this helps

Answer:

two hundred sixty and ninety-four hundredths

Step-by-step explanation:

Answer:

-17.7

Step-by-step explanation:

-9.1-14.6-(-6)

-9.1-14.6+6

-23.7+6

-17.7

Answer: B. Inequality: 6x+2 < ( less than or equal too ) 32

F. Inequality: 2x+6 < ( less than or equal too ) 32

Step-by-step explanation: he's left with 26$ after the overall meal

Answer:

increase percent=12%

hom much increase

500 of 12%

500×12/100=60

new value=500+60

new value=560

Answer:(n-5)(4n+5)

Step-by-step explanation:

If the velocity is 2 meters per second. Then the kinetic energy of the Shawn will be 96.2 Joules.

The energy an item has as a result of motion is known as kinetic energy in mechanics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its propulsion until its speed changes.

The kinetic energy is given as,

KE = (mv²)/2

Where m is the mass and v is the velocity.

Shawn and his bike have a total mass of 48.1 kg. Shawn rides his bike 1.5 km in 12.5 min at a constant velocity.

The velocity is given as,

v = 1.5/12.5

v = 0.12 km/min

v = 0.12 x 1000 / 60

v = 2 m/s

Then the kinetic energy of Shawn will be given as,

KE = (48.1 x 2²) / 2

KE = 48.1 x 2

KE = 96.2 J

If the velocity is 2 meters per second. Then the kinetic energy of the Shawn will be 96.2 Joules.

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The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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Answer:

Step-by-step explanation:

It will fit in the space but it won't cover the entire space. the area is 48m2, but the patio in question will cover 43.75 of the 48m2. Also, it stated that the rectangular space is 3 times as long, and the patio is 3.57x as long as the width. So yes, it will fit, but it will not be a picture perfect fit, there will be some obscenities.

Step-by-step explanation:

Let length of space be lm and width be wm.

l = 3w --(1)

lw = 48 --(2)

sub (1) into (2):

3w(w) = 48

3w^2 = 48

w^2 = 16

w = ± 4 (rej -4 since w > 0)

when w = 4, l = 3(4) = 12

Since dimensions of the patio is 3.5m by 12.5m, and the dimensions of the space is 4m by 12m it does not fit

This is a topic known as simultaneous equations. If you would like to find out more / know when and how to use it, you can check out my Instagram page (learntionary)

Answer:

\(m=-2\)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-1, 0)

Point (-3, 4)

Step 2: Find slope m

Answer: i see you got the answer already, but I was wondering if you could give me brainliest to help me level up. I would really appreciate it.

Step-by-step explanation:

The expression, representing the total amount he paid, is $1.3x

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, Nolan in a restaurant, had a bill of x dollars with a tax of 6%, and we want to leave a tip of 24%, We need to write an expression that represents the total amount he paid,

The bill = X

Tax = 6%

Tip = 24%

In total, he should have to pay = x+(6% of x)+(24% of x)

= x+0.06x+0.24x

= 1.3x

Hence, the expression representing the total amount he paid, is $1.3x

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The equation of the tangent line to the ellipse 3x^2 + xy + 3y^2 = 7 at the point (1,1) is y = (-7/37)x + 44/37.

To find the equation of the tangent line to the ellipse given by the equation 3x^2 + xy + 3y^2 = 7 at the point (1,1), we can use implicit differentiation.

Taking the derivative of both sides with respect to x, we get:

6x + y + x(dy/dx) + 6y(dy/dx) = 0

Simplifying and solving for dy/dx, we get:

dy/dx = -(6x + y) / (x + 6y)

At the point (1,1), we have x=1 and y=1, so:

dy/dx = -(6(1) + 1) / (1 + 6(1)) = -7/37

Thus, the slope of the tangent line to the ellipse at (1,1) is -7/37.

To find the equation of the tangent line, we can use the point-slope form:

y - y1 = m(x - x1)

where (x1,y1) is the point of tangency, in this case (1,1), and m is the slope we just found. Plugging in the values, we get:

y - 1 = (-7/37)(x - 1)

Simplifying, we can rewrite this equation in slope-intercept form:

y = (-7/37)x + 44/37

Therefore, the equation of the tangent line to the ellipse 3x^2 + xy + 3y^2 = 7 at the point (1,1) is y = (-7/37)x + 44/37.

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Answer:

\( \rightarrow \sf \: −31\)

Step-by-step explanation:

\( \rightarrow \sf \frac{1}{4} (4)-5(6)-2\)

\( \rightarrow \sf \: \frac{1}{4} \times \frac{4}{1} - 30 - 2\)

\( \rightarrow \sf \: 1 - 30 - 2\)

\( \rightarrow \sf \: - 31\)

Answer:

I thik it is B

Step-by-step explanation:

Answer:

the correct answer would be d.

Step-by-step explanation:

These lines should be straight line, since they have no slope.

Answer:

D.

Step-by-step explanation:

Since we see that any x-value for the piecewise function will either be always y-value 4 or 2, we know that we are looking for a graph with all horizontal lines. Therefore, our answer is D.

Answer: 3353

Let's solve this equation:

[(3)(3)+(4)(4)]2+[(8)(3)+(7)(4)]2+(2)(3)(4)

=(9+(4)(4))2+((8)(3)+(7)(4))2+(2)(3)(4)

=(9+16)2+((8)(3)+(7)(4))2+(2)(3)(4)

=252+((8)(3)+(7)(4))2+(2)(3)(4)

=625+((8)(3)+(7)(4))2+(2)(3)(4)

=625+(24+(7)(4))2+(2)(3)(4)

=625+(24+28)2+(2)(3)(4)

=625+522+(2)(3)(4)

=625+2704+(2)(3)(4)

=3329+(2)(3)(4)

=3329+(6)(4)

=3329+24

=3353

Hope this helps!!

An equation is formed of two equal expressions. The correct option is x+y=557 and Three-fifths(x)+five-sixths(y)=407.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the total number of pages in the shorter book be represented by x, and the total number of pages in the longer book be represented by y.

Given the total number of pages of the shorter book and the longer book is  557. Therefore, the equation can be written as,

x+y =557

Also, Scott reads Three-fifths of the shorter book and StartFraction 5 Over 6 EndFraction of the longer book, which is equal to 407 pages. Therefore,

(3/5)x + (5/6)y = 407

Hence, the correct option is x+y=557 and Three-fifths(x)+five-sixths(y)=407.

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Answer:

y=3x (squared) -30x+79 and y-intercept is 79

Step-by-step explanation:

It will take Sofia 3 hours to travel 13.5 miles at the same rate.

A rate is a ratio which compares two different quantities with different units.

For rate, the quantity at the denominator is usually expressed as a single unit to ascertain the extent of change of the other quantity

Sofia travelled 9miles for 2 hours so that her rate is 4.5 miles per hour

If she travels with the same speed and covered 13.5 miles,

Then the time she took to cover 13.5 miles is  = 13.5/4.5 = 3

In conclusion, It took Sofia 3 hours to cover 13.5 miles at the rate of 4.5 miles per hour.

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Using the definition of slope, the points (-2 , 6), (0 , 2), and (1 , 0) are collinear.

Three or more points are said to be collinear if they lie on a single straight line.

To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.

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

Getting the slope of each pair of points:

(-2 , 6) and (0 , 2)

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

m = (2 - 6)/(0 - -2)

m = -4/2

m = -2

(0 , 2), and (1 , 0)

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

m = (0 - 2)/(1 - 0)

m = -2/1

m = -2

(-2 , 6) and (1 , 0)

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

m = (0 - 6)/(1 - -2)

m = -6/3

m = -2

Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is equal with each other, then they are collinear.

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When s = 0, it will take 20 units of time for the account to double to 2X.

(a) When s = 0, it means the deposit is made at time t = 0. We want to find the time it takes for the account to double to 2X.

To find this time, we need to solve the equation a(t) = 2, where a(t) is the accumulation function.

1 - 0.05t = 2

Simplifying the equation, we have:

-0.05t = 1

Dividing both sides by -0.05, we get:

t = -1 / (-0.05)

t = 20

Therefore, when s = 0, it will take 20 units of time for the account to double to 2X.

(b) When s = 5, it means the deposit is made at time t = 5. We want to find the time it takes for the account to double to 2X.

Using the same equation a(t) = 2 and substituting t = 5, we have:

1 - 0.05(5) = 2

1 - 0.25 = 2

0.75 = 2

This equation is not satisfied, which means the account will not double to 2X when the deposit is made at time t = 5.

(c) The answer in (a) is greater than the answer in (b) because when the deposit is made at time t = 0, the account has more time to accumulate interest and grow compared to when the deposit is made at time t = 5. As time progresses, the effect of compounding becomes more significant, and starting earlier allows for more growth and a shorter time to double the account.

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Answer:

\(y=5-2x\)

Step-by-step explanation:

You have to give the equation in the form \(y=mx+c\), where m is the gradient and c is the y-intercept (where the line crosses the y-axis).

From the graph, we can see the line crossed the y-axis at (0,5), so the y-intercept is (0,5), which means c is 5.

We can work out the gradient with the two points (2,1) and (1,3) by doing:

\(\frac{change in y}{change in x} =\frac{1-3}{2-1}=-2\)
So the gradient of the line, m, is -2.

Thus the equation of the line is \(y=5-2x\).

Answer: x=12

This solution is not extraneous

Step-by-step explanation:

\(\frac{-4\sqrt{x-3}}{-4}=\frac{-12}{-4}\)  Divide both sides by -4

\(\sqrt{x-3}=3\) Simplify

\(\left(\sqrt{x-3}\right)^2=3^2\) Square both sides

\(3^2=9\)

\(x-3=9\)

add 3 on both sides

\(9+3=12\)

\(x=12\)

Answer:

x=12

Step-by-step explanation:

The data in the question will be represented by a geometric sequence given by 3 (2) ⁿ⁻¹.

A geometric sequence is defined as the sequence in which the ratio between the consecutive terms of the sequence remains constant. The ratio is known as common ratio. The nth term of geometric sequence is written as a (r)ⁿ⁻¹ where a is the first term, r is the common ratio and n is the number of terms. We know from the question that the time in minutes Aurora takes to complete the task forms a sequence as 3, 6, 12, 24.....

The common ratio of this sequence is given by 6/3 = 2. The first term being equal to 3. Now, for the nth term the sequence will be represented as

a (r)ⁿ⁻¹

=> 3 (2)ⁿ⁻¹

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