Solve the equation. Then check your solution. x minus 4 = 2 a. –6 c. 7 b. 6 d. –2 Please select the best answer from the choices provided A B C D

(3+3i)/(-1-3i) = -3 + 9i

To divide the complex numbers (3+3i)/(-1-3i), follow these steps:

Step 1: Multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of -1-3i is -1+3i. (3+3i) / (-1-3i) * (-1+3i) / (-1+3i)

Step 2: Apply the distributive property (FOIL) in both the numerator and the denominator.

Numerator: (3 * -1) + (3 * 3i) + (3i * -1) + (3i * 3i) = -3 + 9i - 3i - 9i^2 Denominator: (-1 * -1) + (-1 * 3i) + (-3i * -1) + (-3i * 3i) = 1 - 3i + 3i + 9i^2

Step 3: Remember that i^2 = -1 and simplify both the numerator and the denominator.

Numerator: -3 + 9i - 3i + 9(-1) = -3 + 9i - 3i - 9 = -12 + 6i

Denominator: 1 - 3i + 3i - 9(-1) = 1 + 9 = 10

Step 4: Divide the real and imaginary parts by the simplified denominator.

Real part: -12/10 = -6/5

Imaginary part: 6i/10 = 3i/5

So, the division of the complex numbers (3+3i)/(-1-3i) results in the complex number -6/5 + 3i/5.

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Each person should pay $16.37.

If the meal was $54.55 and you should tip the waiter 20%, the total cost of the meal would be $54.55 + ($54.55 * 0.20) = $65.46.

If the bill is shared equally among 4 people, each person should pay $65.46 / 4 = $16.37.

Therefore, each person should pay $16.37 for the meal. Step-by-step explanation:

1. Calculate the tip by multiplying the cost of the meal by 20% (0.20): $54.55 * 0.20 = $10.91

2. Add the tip to the cost of the meal to get the total cost: $54.55 + $10.91 = $65.46

3. Divide the total cost by the number of people to get the cost per person: $65.46 / 4 = $16.37

4. The final answer is $16.37 per person.

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Answer:

y=3x+8

2y=6x+16

2(3x+8)=6x+16

6x+16=6x+16

Infinite Many Solutions

The expression 0.26 when written as a fraction in its lowest term is 13/50

Based on the question, we have a set of values that can be used in our calculations.

Fraction = 0.26

As a general rule, a fraction can be expressed as a/b

Where

Using the above values as a guide, we have the following expression

Fraction = 0.26

Multiply the fraction by 1

Fraction = 0.26 * 1

Express 1 as 100/100

So, we have

Fraction = 0.26 * 100/100

Evaluate the product of 0.26 and 100

This gives

Fraction = 26/100

Reduce the quotient of 26 and 100 to the lowest terms by dividing by 2

Fraction = 13/50

Hence, the fraction of 0.26 is 13/50

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Answer:

1011.00

Step-by-step explanation:

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Based, on the given information, the length of the ramp z, is equal to 53 inches.

A triangle is said to be right-angled if one of its internal angles is 90 degrees, or if any one of its angles is a right angle. The right triangle or 90-degree triangle is another name for this triangle. In geometry, the right triangle is significant.

A triangle is said to be right-angled if one of its edges is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the parts that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

In a right-angled triangle, the square of the hypotenuse side is equivalent to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three edges are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposing the 90° angle, the hypotenuse in this case is the longest side. When the positive number sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

In this question, the base, the height and the length of the ramp form a right angled triangle.

To find the length, we will use Pythagoras theorem, which states that,

(hypotenuse)² = (base)²+ (height)²

Substituting the values, we get

x²=45²+ 28²

x²= 2809

x=√2809

x=53 inches

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The mentioned relationship is an additive relationship as the total cost is not proportional to the number of games played.

To represent the relationship between the total cost, y, and the number of games played, x, we can create a table, graph, and equation as follows:

Number of games played (x) Total cost (y)

0                                                          10

1                                                          11

2                                                          12

3                                                          13

4                                                          14

5                                                          15

The equation that represents this relationship is: y = 1x + 10

Where 10 is the fixed cost to enter the arcade and 1 is the cost per game played.

To represent this relationship graphically, we can plot the points from the table on a graph. Refer to the image attached with this answer.

This graph shows that the relationship between the total cost and the number of games played is a straight line with a positive slope.

This relationship is an additive relationship because the total cost is not proportional to the number of games played. If the relationship was proportional, the cost per game played would remain constant regardless of the number of games played. In this case, the cost per game played is always $1, but the total cost increases by $1 for each additional game played.

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The complete question is :  

Sam went to play video games in Video Game Central arcade. Video Game Central charges $10 to get into the arcade and then $1 per game played. Represent the relationship between total cost, y, and number of games played, x using a table, graph and equation. Is this relationship a proportional or additive relationship? Explain.

Answer:

D. 52

Step-by-step explanation:

105/2=52

The middle of 110 and 100 is 105. When you divide that by 2 you get 52.5 or 52. The answer is D

Answer:

D 52 is the answer

Answer:

52.4285714286

Step-by-step explanation:

use a calculator

Answer: 52.4

Step-by-step explanation:

The polynomial is  4x^3 - 18x^2 + 2x + 12

A polynomial of degree 3 that satisfies, we need to use the fact that if a polynomial has a zero at x = a, then (x - a) is a factor of the polynomial. So, for the given zeroes, we have the factors (x + 1/2), (x - 2), and (x - 3).

Multiplying these factors together, we get:

(x + 1/2)(x - 2)(x - 3) = (x^2 - (3/2)x - 1)(x - 3) = x^3 - (9/2)x^2 + (1/2)x + 3

To get a constant coefficient of 12, we need to multiply this polynomial by a constant. Since the current constant coefficient is 3, we need to multiply by 4:

4(x^3 - (9/2)x^2 + (1/2)x + 3) = 4x^3 - 18x^2 + 2x + 12

So, the polynomial that satisfies the given conditions is:

P(x) = 4x^3 - 18x^2 + 2x + 12

The polynomial is  4x^3 - 18x^2 + 2x + 12

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Answer:

20° and 22°

Step-by-step explanation:

Quadrilaterals are shapes with 360°. Since we are given two known angles, we can subtract them from 360. 360 - 216 - 102 = 144 - 102 = 42

Because the others are in a ratio of 10:11, the only possible degree combination will be 20° and 22°

The solution of the given system of equations is x = -1 and y = 4.

The given system of equations is 4x + 8y = 40 and 6x + 3y = 6.

To solve this system of equations, we need to use elimination method. We can subtract 6x from both sides of the second equation and subtract 4x from both sides of the first equation. We get:

8y = 40 - 4x and 3y = 6 - 6x

We can now divide both sides of the second equation by 3 to obtain y = 2 - 2x.

We can substitute the value of y from the second equation into the first equation to get 4x + 8(2 - 2x) = 40, which simplifies to -8x = 8. We can solve this equation for x by dividing both sides by -8, resulting in x = -1.

Substituting the value of x into either equation, we can obtain y = 4. So, the solution of the given system of equations is x = -1 and y = 4.

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1. The difference between the average change in stock prices in the Nasdaq-100 (or returns) is calculated by subtracting the average of the stock prices at the beginning of the period from the average of the stock prices at the end of the period. To find the average change in stock prices, we can use the formula:

Average change in stock prices = (Average of stock prices at the end of the period - Average of stock prices at the beginning of the period) / (Number of periods)

2. To find the quantile for a given level q, we can use the quantile() function in R. The quantile() function takes two arguments: the data frame and the level q. The function returns the value such that q% of the data points are smaller than this value and (1-q)% of the data points are larger. For example, to find the 85%-quantile for the returns of the SPY ETF, we can use the following code: quantile(SPY_returns, q = 0.85)

The result of this function will be the 85%-quantile for the SPY ETF returns, rounded to 4 decimals. Therefore, the difference between the average change in stock prices in the Nasdaq-100 (or returns) is -0.003, and the 85%-quantile for the SPY ETF returns is 0.0084.

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The simplified expression of the given expression is [tex]\frac{6\sqrt{10}}{7}$.[/tex]

What is expression ?

An expression is a mathematical phrase that can contain numbers, variables, operators, and symbols. It can be a combination of terms, factors, and/or coefficients, and may involve addition, subtraction, multiplication, division, exponents, roots, and/or other mathematical operations. Expressions can be simplified, evaluated, or manipulated using algebraic rules and properties.

We can simplify the expression as follows:

[tex]\frac{\sqrt{40\cdot9}}{\sqrt{49}}=\frac{\sqrt{4\cdot10\cdot3\cdot3}}{\sqrt{7\cdot7}}\\ \\ \\=\frac{\sqrt{4}\cdot\sqrt{10}\cdot\sqrt{3}\cdot\sqrt{3}}{\sqrt{7}\cdot\sqrt{7}}\\ \\ \\=\frac{2\cdot3\sqrt{10}}{7}\\ \\ \\={\frac{6\sqrt{10}}{7}}.[/tex]

Therefore, the simplified expression of the given expression is [tex]\frac{6\sqrt{10}}{7}$.[/tex]

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The other three angle measures in the quadrilateral, in addition to <1 = 45 degrees, are: <2 = <3 = 135 degrees, and <4 = 45 degrees.

What is the quadrilateral?

A quadrilateral is a polygon with four sides and four angles. In other words, it is a closed figure that has four straight sides and four vertices (corners).

If <1 has a measure of 45 degrees, then the sum of the angle measures in the quadrilateral must be 360 degrees. Let's call the other three angles in the quadrilateral <2, <3, and <4.

Then we can use the fact that the opposite angles in a quadrilateral add up to 180 degrees to write two equations:

<1 + <3 = 180 (opposite angles)

<2 + <4 = 180 (opposite angles)

We also know that <1 = 45, so we can substitute that in the first equation:

45 + <3 = 180

Solving for <3, we get:

<3 = 135

Now we can substitute the values of <1 and <3 into the sum of angle measures equation:

45 + <2 + 135 + <4 = 360

Simplifying, we get:

<2 + <4 = 180

This is the same equation as the opposite angles equation, so we know that <2 and <4 are also opposite angles. Therefore, we can conclude that:

<2 = <3 = 135 degrees

<4 = 45 degrees

Hence, the other three angle measures in the quadrilateral, in addition to <1 = 45 degrees, are: <2 = <3 = 135 degrees, and <4 = 45 degrees.

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The linear function rule that models the distance traveled by the car as a function of time is d = 111t.

Let's use the point-slope form of a linear equation to write a rule that models the distance traveled by the car as a function of time:

d - d0 = m(t - t0)

where:

d0 is the initial distance (at time t0 = 0)

m is the slope (the rate at which distance changes with time)

We know that at time t = 0, the car has traveled a distance of d0 = 0. We also know that after 7 seconds, the car has traveled a distance of d = 777 ft. So we have two points on the line: (0, 0) and (7, 777).

To find the slope, we can use the formula:

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

where (x1, y1) = (0, 0) and (x2, y2) = (7, 777). Plugging in these values, we get: m = (777 - 0) / (7 - 0) = 111

So the slope of the line is 111. Now we can plug in the values for d0 and m into the equation to get:

d - 0 = 111(t - 0)

Simplifying this equation, we get: d = 111t

Therefore, the linear function rule that models the distance traveled by the car as a function of time is d = 111t.

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The x-coordinate corresponds to the door of the house is -3/2

To determine the x-coordinate of the door of a house, we can use a mathematical function that models the location of the house. Let's assume that the house is located on a two-dimensional plane and that the function describing its location is a linear function.

Suppose the function describing the location of the house is y = 2x + 3. To find the x-coordinate of the door, we set y = 0 and solve for x:

0 = 2x + 3

-3 = 2x

x = -3/2

Therefore, the x-coordinate of the door of the house is -3/2.

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Answer:

Step-by-step explanation:

Here is the answer

The correlation coefficient measures the strength of the linear relationship between two variables, and it ranges from -1 to 1. A correlation coefficient of -1 indicates a perfect negative linear relationship between the variables, which means that as one variable increases, the other decreases at a constant rate.

To find the value of A in this scenario, we need to look for a perfect negative linear relationship between the two variables, time (x) and distance from destination (y). The table shows that as time increases, the distance from the destination decreases, but we need to find the exact rate of change.

We can calculate the rate of change by finding the slope of the line that represents the relationship between time and distance. We can use the formula for the slope of a line, which is:

slope = (change in y) / (change in x)

If we choose the first and last points in the table, we get:

slope = (690 - 1060) / (7 - 1) = -70

This means that for every hour of time that passes, the distance from the destination decreases by 70 miles. Therefore, if the correlation coefficient is -1, we should see a perfect negative linear relationship between time and distance, with a slope of -70.

To check if A is the correct value, we can use the formula for the equation of a line in slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept. We can plug in the values of m and b and solve for A:

y = -70x + b

If we use the first point in the table, where x = 4 and y = 1000, we get:

1000 = -70(4) + b

b = 1220

So the equation of the line is:

y = -70x + 1220

If we plug in the values of x for the remaining points in the table, we get:

y = 1030 when x = 0

y = 880 when x = 2

y = 800 when x = 3

y = A when x = 5

y = 760 when x = 6

To find the value of A, we can plug in the corresponding value of y and solve for A:

1030 = -70(0) + 1220

880 = -70(2) + 1220

800 = -70(3) + 1220

760 = -70(6) + 1220

A = -70(5) + 1220 = 850

Therefore, the value of A should be 850 if the correlation coefficient for the data shown in the table is -1.

30 pounds = 480 ounces

1 pound (lb) is equal to 16 Ounces (oz).

1 lb = 16 oz

The mass m in ounces (oz) is equal to the mass m in pounds (lb) times 16:

[tex]m_{(oz)} = m_{(lb)} * 16[/tex]

Convert 30 lb to ounces:

[tex]m_{(oz)} = 30 lb * 16 = 480[/tex] [tex]oz[/tex]

Therefore, 30 pounds converted to ounces is 480 ounces.

Answer: 30 pounds = 480

Step-by-step explanation:

As seen in the attached picture, the account by Grant and the painting are consistent with each other since they both depict a serious and formal situation.

Ulysses S. Grant was an American general and statesman who served as the 18th President of the United States. He was born in 1822 in Ohio and graduated from the United States Military Academy at West Point in 1843. He served in the Mexican-American War and later became a leading Union general in the American Civil War.

As we compare his account of Lee's rendition and the painting provided, we can conclude that they are indeed consistent. Both show how serious and formal the meeting was. Grant even describes the way Lee was dressed, which is confirmed by the painting.

The picture and the account appear in the attachment below.

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Answer: C

Step-by-step explanation:

12cm 6 cm 10cm 8cm tienes que medir 12 ×6 cm

A = |λ-6 0 0| . |0 λ 4| . |0 5 λ-1| λ 1= 4.79 λ 2= 4.79 λ3 = 4.79, as the highest value of lif it exists is 4.79. therefore X=4.79

To find the values of λ for which det(A) = 0, we need to solve the equation det(A) = 0. The matrix determinant of a 3x3 matrix A is given by:

[tex]det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)[/tex]

In this case, the matrix A is:
A = |λ-6 0 0|
   |0 λ 4|
   |0 5 λ-1|

So, the determinant of A is:
[tex]det(A) = (λ-6)(λ(λ-1) - 4*5) - 0(0(λ-1) - 4*0) + 0(0*5 - λ*0)[/tex]
Simplifying the equation, we get:
[tex]det(A) = (λ-6)(λ^2 - λ - 20)[/tex]
Setting det(A) = 0, we can find the values of λ:
[tex](λ-6)(λ^2 - λ - 20) = 0[/tex]
This equation has three solutions:
[tex]λ 1 = 6λ 2 = (-1 + √81)/2 ≈ 4.79λ 3 = (-1 - √81)/2 ≈ -5.79[/tex]

So, the answer is:
λ 1 = 6
λ 2 = 4.79
λ 3 = -5.79
The greater value of λ is λ 2 = 4.79.

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The length of the side x in the triangle is approximately 7.5.

A right-angled triangle is a geometric shape that consists of three sides and three angles. One of the angles in a right-angled triangle measures 90 degrees, which is called a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are called the legs or catheti.

The Pythagorean theorem is a fundamental property of right-angled triangles that states that the sum of the squares of the two shorter sides (legs) is equal to the square of the hypotenuse. This can be written as:

a² + b² = c²

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Right-angled triangles also have many real-world applications, such as in construction, engineering, architecture, and navigation. They are used to calculate distances, heights, angles, and other measurements in many different contexts.

Using trigonometry, we can solve for x:

sin(32°) = x/14

x = 14 * sin(32°)

x ≈ 7.5 (rounded to the nearest tenth)

Therefore, the length of the side x in the triangle is approximately 7.5.

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The answer of equation for the function is y=(x-2)^(2)-1.

The equation for a function that has the shape of y=x^(2), but shifted right 2 units and down 1 unit is y=(x-2)^(2)-1.

To shift a function to the right, we subtract the amount of the shift from the x variable.

In this case, we want to shift the function 2 units to the right, so we subtract 2 from x: (x-2).

To shift a function down, we subtract the amount of the shift from the entire function.

In this case, we want to shift the function down 1 unit, so we subtract 1 from the entire function: (x-2)^(2)-1.

Therefore, the equation for the function is y=(x-2)^(2)-1.

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The numeric values of the piece-wise function are given as follows:

To obtain the numeric value of a function or of an expression, we replace each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression.

A piece-wise function is a function that has different definitions, based on the input interval of the function.

For x < 2, the function is defined as follows:

h(x) = -2x + 10.

Hence the numeric values on the interval are obtained as follows:

For x >= 2, the function is defined as follows:

h(x) = x + 2.

Hence the numeric values on the interval are obtained as follows:

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Answer: 55 miles per hour.

To find the unit rate, divide the miles traveled by the time taken:

275 miles ÷ 5 hours = 55 miles per hour

Step-by-step explanation:

By converting the Cartesian coordinates (1,−5) to polar coordinates with r>0 and 0≤θ<2π r = √26 and θ = 4.909784033953984

To convert the Cartesian coordinates (1,−5) to polar coordinates with r>0 and 0≤θ<2π, we need to use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
Plugging in the given values of x = 1 and y = -5, we get:
r = √(1² + (-5)²)
r = √(1 + 25)
r = √26
θ = tan⁻¹(-5/1)
θ = tan⁻¹(-5)
θ = -1.373400766945016
Since we want 0≤θ<2π, we need to add 2π to θ to get the correct value:
θ = -1.373400766945016 + 2π
θ = 4.909784033953984
So the polar coordinates are:
r = √26
θ = 4.909784033953984

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Answer: EF, DF, DE

Step-by-step explanation:

The smaller the opposite angle, the smaller the side, and vice versa.

∠EDF = 85°

∠DEF = 60° (Because the total degrees in a triangle must be 180°)

∠DFE = 35°

EF, DF, DE

Hope this helps!

The correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.

The standard equation of an ellipse is (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1, where (h,k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the covertices.

In this case, the center of the ellipse is the midpoint of the vertices and covertices, which is (7, -2). The distance from the center to the vertices is 5 (12-7) and the distance from the center to the covertices is 3 (1-(-2)).

Therefore, the standard equation of the ellipse is (x-7)^2 / 25 + (y+2)^2 / 9 = 1, which corresponds to answer choice (a).

So the correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.

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