Answer:
complex and imaginary.
Answer:
Imaginary/Complex. While the i means negative, it can also mean an imaginary integer. Often times, i is described as the square root of negative one, or simply an undefinable/negative integer. Since 80i can be considered both complex and imaginary, imaginary is more fitting due to the fact that i cannot be defined fully by mathematical means other than it meaning "imaginary" or "complex". In conclusion, you should pick both imaginary and complex.
Hope this helps!
X^2+4x-2=0
Solve with explaining and show steps
The solution of the given quadratic equation is -2 ± √6.
What are Quadratic Equations?Quadratic expressions are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Solution of a quadratic equation ax² + b x + c = 0 can be found by,
x = [-b ± [tex]\sqrt{b^2-4ac}[/tex]] / 2a, where [tex]b^2-4ac[/tex] is called discriminant.
Given quadratic equation is x² + 4x - 2 = 0.
Discriminant = 4² - (4 × 1 × -2) = 16 + 8 = 24
x = [-4 ± √24] / 2
= [-4 ± 2√6] / 2
= -2 ± √6
Hence the solution of the given quadratic equation is -2 ± √6.
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An arrow is shot vertically upward at a rate of 180ft/s. Use the projectile formula h=−16t2+v0t to determine at what time(s), in seconds, the arrow is at a height of 420ft. Round your answer(s) to the nearest tenth of a second.
The number of seconds when the height is 420 ft will be 7.95 seconds and 3.3 seconds.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
An arrow is shot vertically upward at a rate of 180ft/s.
Then the equation is given as,
h = −16t² + 180t
The number of seconds when the height is 420 ft will be given as,
420 = −16t² + 180t
16t² - 180t + 420 = 0
4t² - 45t + 105 = 0
t = [-(-45) ± √{(-45)² - 4 × 4 × 105}] / (2 × 4)
t = (45 ± 18.57) / 8
t = 7.95, 3.3 seconds
The number of seconds when the height is 420 ft will be 7.95 seconds and 3.3 seconds.
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Danielle put $1,000 into a savings account that earns 4% in interest. How much interest will she have after 6 months?
Answer:2
Step-by-step explanation:
Use factors and a spreadsheet to determine the interest rate per period from the following equation:
0 = -27,000 + 8,000(P/A,i∗,5) + 8,000(P/F,i∗,8)0 = -27,000 + 8,000P/A,i*,5 + 8,000P/F,i*,8
The interest rate per period is %....
The sum of the present values is equal to -27,000, which confirms that our answer is correct.
To solve for the interest rate per period, we can set up a spreadsheet to help us. In the spreadsheet, we will enter the known values and the formula 0 = -27,000 + 8,000P/A,i*,5 + 8,000P/F,i*,8. We will then solve for the interest rate, i.
To solve for i, we can start by rearranging the formula to isolate the i term. We can do this by subtracting 27,000 from both sides of the equation and then dividing both sides by 16,000. This results in the equation
i = (27,000 - 0) / 16,000.
We then enter the known values into the spreadsheet and solve for the interest rate. When we do this, we find that the interest rate per period is 1.6875%.
To check our answer, we can calculate the present value of the payments at the given interest rate. We can do this by calculating the present value of the annuity payment (P/A,i*,5) and the present value of the future payment (P/F,i*,8). When we do this, we find that the sum of the present values is equal to -27,000, which confirms that our answer is correct.
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Given that both p and p + 1 are prime, what is the smallest composite whole number
that is not divisible by p or p + 1?
Answer:
39
Step-by-step explanation:
The vertices of a figure are A(2,-2), B(4,-1),C(4,-3),and D(2,-4).
Rotate the figure 90° counterclockwise about the origin. Find the coordinates of the image.
Check the picture below.
Keith bought a package with 2 9/16 pounds of ground meat to make hamburgers. He has 2/5 pound of ground meat left. About how many pounds of ground meat did he use for the hamburgers? Question due tomorrow please answer !
The number of pounds of ground meat used is 2(13/80).
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
The number of pounds of ground meat bought = 2(9/16).
The number of pounds of ground meat left = 2/5.
Now,
The number of pounds of ground meat used.
= 2(9/16) - 2/5
= 41/16 - 2/5
= (205 - 32) / 80
= 173/80
= 2(13/80)
Thus,
2(13/80) pounds of ground meat were used.
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For the following exercise, consider this scenario: The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten year span, (number of units sold, profit) for specific recorded years: (46, 250), (48, 305), (50, 350), (52, 390), (54, 410). Use linear regression to determine a function y, where the profit in thousands of dollars depends on the number of units sold in hundreds.
The linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.
The linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.
To calculate the equation, we first need to calculate the slope and the y-intercept. Since we have 5 points, we can calculate the slope using the formula m=(y2-y1)/(x2-x1). For this problem, we'll use (46,250) and (54,410). Plugging the values into the formula, we get m = (410-250)/(54-46) = 4.5.
Next, we need to find the y-intercept, which is 200. The formula for this is b = y-mx. For our problem, we'll use (46,250). Plugging in the values, we get 200 = 250 - 4.5(46), so b = 200.
Therefore, the linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.
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Nikhil and Mae work at the same company. Nikhil has been at the company 6 times as long as Mae. Nikhil's time at the company is 8 more than 4 times Mae's. The following system of equations models the scenario:
x = 6y
x = 8 + 4y
How many years has each person been employed by the company?
Nikhil has been with the company for 36 years, while Mae has been there for 6 years.
Nikhil has been with the company for 30 years, while Mae has been there for 5 years.
Nikhil has been with the company for 24 years, while Mae has been there for 4 years.
Nikhil has been with the company for 18 years, while Mae has been there for 3 years.
The number of years that each person would have been employed would be that Nikhil has been with the company for 24 years, while Mae has been there for 4 years. That is option C.
How to calculate the number of years each person has been employed?Nikhil has been at the company 6 times as long as Mae.
That is,
x = 6y-----> equation 1
where X= Nikhil
y = Mae
Nikhil's time at the company is 8 more than 4 times Mae's.
That is,
x = 8 + 4y----> equation 2
To solve for each years, substitute for X into equation 2;
6y = 8+4y
8 = 6y-4y
8 = 2y
y = 8/2 = 4
Substitute y into equation 1;
X= 6×4
X= 24
Therefore, Nikhil has been with the company for 24 years, while Mae has been there for 4 years.
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Answer: Option C. Nikhil has been with the company for 24 years, while Mae has been there for 4 years.
Step-by-step explanation:
Define units for the time that Marshall has the beans and the amount of coffee beans that Marshall has left.
After 4 weeks the amount of coffee that Marshall will have left would be = 20 ounces.
How to calculate the amount of coffee left?The amount of ground coffee that Marshall bought for his office machine = 40 ounces
The quantity of coffee he uses per week in his office = 5 ounces.
Therefore for 4 weeks would be= ?
But, 1 week = 5 ounces
4 weeks = X
make X the subject of formula;
X = 5×4 = 20 ounces
The amount of ground coffee that will remain = 40-20 = 20 ounces.
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Use the Pythagorean Theorem to find the length of the leg in the triangle shown below. The figure shows a right triangle with one leg marked 3. The hypotenuse is marked 5.
The length of the leg in the triangle is 4 units
How to find the length of the leg in the triangleFrom the question, we have the following parameters that can be used in our computation:
The figure shows a right triangle with one leg marked 3. The hypotenuse is marked 5.The length of the other leg using Pythagorean Theorem is
Other Leg = √(Hypotenuse² - One Leg²)
So, we have
Orher Leg = √(5² - 3²)
Evaluate
Other leg = 4
Hence, the other leg is 4 units
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find the following probabilities for the standard normal distribution in r or using the standard normal table. note i always recommend drawing the distribution. (round your answers to four decimal places.)
The probabilities for the standard normal distribution in r or using the standard normal table are
a) P(X<2.18) = 0.9854
b)P(X>2.18)= 0.0146
c) P(<-2.49) = 0.0064
The standard normal table is a mathematical table that allows us to know the percentage of values below the z-score (left) of the standard normal distribution. This is the "bell-shaped" curve of the standard normal distribution. It is a normal distribution with mean 0 and standard deviation 1. Using the Z-table:
Go to the row representing the ones place and the first decimal place (10's place) of the Z-score.Go to the column that represents the second decimal place (100ᵗʰ) of the z-score.Cross the rows and columns from steps 1 and 2. This result represents the probability that the random variable Z is less than the value Z, that is p(Z < z).Now, we have to determine the probability value for (a) , (b) and (c) .
a) P(X < 2.18) = P( Z< 2.18) = intersection point of row value 2.1 and column 0.08 = 0.9854
b) P(X >2.18) = P( Z> 2.18) = 1 - P( Z< 2.18)
= 1 - 0.9854 = 0.0146
c) P(X < -2.49) = P(Z < -2.49) = intersection point of row value -2.4 and column 0.09 = 0.0064.
Hence, we got all the required probability values.
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Complete question:
Find the following probabilities for the standard normal distribution in R or using the standard normal table. NoteI always recommend drawing the distribution. (Round your answers to four decimal places.) ### Example R code mu = 0; sigma = 1; x = x; # Note you will have to change the value of x. pnorm(x,mu,sigma)
(a) P(X < 2.18)
b) P(X >2.18)
(c) P(X < -2.49)
26-14 divided by 2+5x7=
Please show me how to do it.
Answer: 0.32432432432
Step-by-step explanation:
5x7=35
35+2=37
26-14=12
12/37= 0.32432432432
Which segment of this graph shows a decreasing velocity?
Answer:
7
Step-by-step explanation: just do it
At noon, the temperature in Hampstead, Virginia was 50℉
. By midnight, the temperature had fallen to 10℉
. What was the change in temperature over the 12-hour period?
The change in temperature over the 12-hour period was 50℉ - 10℉ = 40℉.
Please help!!! I suck at algebra and this is middle school stuff:((
Answer:
77
Step-by-step explanation:
1. solve the first part by plugging in 7 for y.
14(7)+37/5
98+37/5
135/5
27
2. then solve the second part by plugging in 7 for y.
8(2(7)-1)
8(14-1)
104
3. then subtract 27 from 104
104-27=77
the material for the base costs 29 cents/ft2, the material for the top costs 24 cents/ft2, and the material for the sides costs 10 cents/ft2. if x denotes the length of one side of the base (in feet), find a function in the variable x giving the total cost of materials used in constructing the box in cents. total cost, as a function of x
The total cost of materials used in constructing the box in cents can be given by the function [tex]C(x) = 29x^2 + 24x^2 + 10(4x) = 63x^2 + 40x[/tex].
This formula can be derived by multiplying the cost per square foot of the base, top, and sides with their respective areas. The area of the base and top can both be expressed as [tex]x^2[/tex], while the area of the four sides can be expressed as 4x. Thus, multiplying the cost per square foot of each material with its respective area, we obtain the total cost of materials used in constructing the box in terms of x, which is given by the expression [tex]C(x) = 63x^2 + 40x[/tex].
For example, if x = 4, then the total cost of materials used in constructing the box in cents is [tex]C(4) = 63(4^2) + 40(4) = 1512 + 160 = 1672 cents[/tex].
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On the planet Gespil, there are 5 dogs to every 12 cats. If farmer Pisquet has 50 cats on her joogh farm, how many dogs are on the farm?
Number of dogs in the farm of Pisquet is approximately 21.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
If we have two ratio p : q and r : s and if these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
Given that,
On the planet Gespil, there are 5 dogs to every 12 cats.
Number of dogs for 12 cats = 5
Let Number of dogs for 50 cats = x
Using concept of proportion,
12 / 5 = 50 / x
Cross multiplying,
12x = 5 × 50
12x = 250
x = 20.83 ≈ 21
Hence there are approximately 21 dogs for 50 cats.
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Simplify the function f(x) = 7(3/54*). Then answer the
questions below.
The initial value for the function is
The simplified base for the function is
The domain of the function is
The range of the function is
√√/2.
<>
Se
fac
Answer:
The function f(x) = 7(3/54*) can be simplified as follows:
Simplified base: 7 * (3/54) * x = (3/54) * 7 * x = (3/54) * 7 * x = (3/54) * 7 * x = 7 * (3/54) * x
Initial value: None provided
Domain: The domain of a function refers to the set of all possible input values (x-values) for which the function produces a valid output (y-value). In this case, it would depend on the restrictions on x, but typically, real numbers are assumed as the domain unless otherwise stated.
Range: The range of a function refers to the set of all possible output values (y-values) that the function can produce. In this case, the range would be all real numbers since there are no restrictions on the output.
Note: There seems to be some errors or typos in the original function and the question, as the expression (3/54*) does not have a clear mathematical meaning. The information provided is based on the assumptions made from the given information
Complete the square to factorise x^2+4x-6
6 x 1/3 _ 6
please explain or give and answer I beg of u
The complete expression is 6 * 1/3 = 1/3 * 6
How to complete the expressionFrom the question, we have the following parameters that can be used in our computation:
6 x 1/3 _ 6
Express properly
So, we have the following representation
6 * 1/3 = _6
Represent the blank with x
6 * 1/3 = x * 6
So, we have
2 = 6x
Divide by 6
x =1/3
Hence, solution to the expression is 1/3
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a researcher selects a simple random sample of 1,200 women who are students at midwestern colleges in the united states to use for an observational study. which of the following describes the population to which it would be most reasonable to generalize the results?
The population to which it would be most reasonable to generalize the results of the observational study is women who are students at Midwestern colleges in the United States.
This population is well-defined and can be used to make generalizations about the results from the study.
This population can be calculated by taking the total number of college students in the United States and subtracting the number of college students in other regions, as well as the number of male students in the Midwestern region.
The total population of women college students in the Midwestern region of the United States can then be calculated by multiplying the total population by the percentage of female students in the region.
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circles of radii , and are mutually externally tangent, where and are relatively prime positive integers. find
The ratio of the areas of the two circles equals the square of the ratio of their radii: = 1/4
Let O1 be the center of the larger circle and O2 be the center of the smaller circle. T is the tangent point between the two circles.
The distance between their centers, O1O2, is equal to the sum of their radii, i.e., r1 + r2.
The Pythagorean theorem gives us:
(O1O2)^2 = r1^2 + r2^2
By substituting r1, r2, and O1O2 values, we obtain:
(r1 + r2)^2 = r1^2 + r2^2
By broadening and simplifying, we get:
2r1r2 = r2^2
When both sides are divided by r22, we get:
2r1/r2 = 1
So, r1/r2 = 1/2. r2 = 2r1.
The ratio of the areas of the two circles equals the square of the ratio of their radii:
A1/A2 = (r1/r2)^2 = 1/4
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Write a word phrases for the expression 16 ÷ (X + 4)
Answer:
16 divided by the total of x and 4
Step-by-step explanation:
16 / (x+4) can be rewritten as 16 divided by the total of x and 4
A phone receives signals from a transmitter that is 13 km west and 21 km south of it.
What is the bearing from the phone to the transmitter?
Give your answer to the nearest degree.
To find the bearing from the phone to the transmitter, we can use the arctangent function.
The formula to find the bearing is:
θ = atan2(dy, dx)
where dx = difference in x-coordinates and dy = difference in y-coordinates.
Here, dx = -13 km and dy = -21 km, since the transmitter is located to the west and south of the phone.
Therefore, the bearing is:
θ = atan2(-21, -13) = atan2(21, 13) = 63.434948822922° (to the nearest degree)
So the bearing from the phone to the transmitter is approximately 63.4°.
The perimeter of the front of an aquarium is 230m and its length is 85m. What is the width of the front of the aquarium?
The width of the front of the aquarium is 30m
How to determine the value of the widthThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2( l + w)
Given that the parameters are;
P is the perimeter of the rectanglel is the length of the rectanglew is the width of the rectangleFrom the information given, we have that the values are;
Perimeter = 230m
Length = 85m
Width = w
Substitute the values, we get
230 = 2(85) + 2w
expand the bracket
2w = 230 -170
subtract the values
2w = 60
Make 'w' the subject
w = 30m
Hence, the value is 30m
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Calculate each quotient.
2 divided by 1.176
Answer:
Step-by-step explanation:
The quotient of 2 divided by 1.176 can be calculated as follows:
2 ÷ 1.176 = 1.70860927152318
Therefore, 2 divided by 1.176 is equal to 1.70860927152318.
find the values of x and y
The value of x is 10 and y is -5.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Three parallel lines.
From the diagram,
we have system of equations
6x + 2y + 130 = 180
2x - 4y + 140 = 180
Simplifying both equations,
3x + y = 25....(1)
x - 2y = 20,....(2)
Now, substituting the value of x from the equation 2 to equation 1,
7y = 25 - 60
y = -5.
And x = 10.
Therefore, the value of x is 10 and y is -5.
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determine whether each transaction below would be included in gdp, and if so, indicate which category it would fall under. assume all goods and services are produced in the domestic country unless otherwise stated.
Let the Transaction be: John purchases a new car manufactured in Japan. And as part of Personal Consumption Expenditures (PCE), it will be included in GDP.
GDP measures the total value of all goods and services produced within a country's borders during a specific time period. When John purchases a new car manufactured in Japan, it would be included in the country's GDP as part of Personal Consumption Expenditures (PCE).
PCE includes all goods and services purchased by individuals for personal use, regardless of the origin of the product. Since John is a resident of the domestic country and is buying a car for his own use, this transaction would be included in the country's GDP as part of PCE.
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Complete Question:
determine whether each transaction below would be included in gdp, and if so, indicate which category it would fall under. assume all goods and services are produced in the domestic country unless otherwise stated.
Transaction: John purchases a new car manufactured in Japan.The graph shows two functions, f(x) and g(x).
If the functions are combined using addition, which
statements describe the resulting graph h(x)? Check
two options
O domain: x 2 -2
O domain: x 22
O The point (2, 2) is on h(x).
O The point (-2, 0) is on h(x).
O The point (0, -3) is on h(x).
The graph shows two functions, f(x) and g(x). So, the statements that describe the resulting graph h(x) is point (-2,2) is on h(x)
What is graph?A graph is described as the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
In the question above, we have two functions f(x)=x²-2 and g(x)=x²+2 by adding the function we will get the combined function.
The graph that the function is varying from the coordinates (-2,2) is seen on the attached graph.
Therefore, we can conclude that the graph shows two functions, f(x) and g(x). So point (-2,2) is on h(x)
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