The square root of -12, an imaginary number, can be simplified to 2i√3. This involves breaking -12 into -1 * 12 and taking the square root of both parts to get 'i' and 2i√3 respectively.
Explanation:The question asked is to simplify the imaginary number square root of -12. Imaginary numbers are those numbers whose square is less than or equal to zero. They are expressed in the form of 'i' where 'i' is the imaginary unit with the property i^2 = -1. When we take square root of a negative number, 'i' is involved in the solution.
To simplify the square root of -12, we can express -12 as -1 * 12. In this case, square root of -1 is 'i' and square root of 12 is 2 * square root of 3 (since 12= 4*3 and square root of 4 is 2).
Therefore, square root of -12 can be written as 'i' * 2 * square root of 3 or simply 2i√3.
Learn more about Imaginary Numbers here:https://brainly.com/question/6748860
#SPJ12
Carpet sells for $3 per square foot and will cost you $810 to recarpet your rectangular room. if your room is 18 feet long, how many feet wide is it?
1. Solve the equation. -4x = 0
X = -4
X = 4
X = 0
X = 1
2. decide whether the given number is a solution of the given equation. Is 8 a solution of y + 9 = 17 ?
Yes or no
3. simplify the expression by combining like terms. 10x - x - 2x - x
8x
x² + 8x
6x
-x2 + 8x
4. Name the property shown. 12x( y ) = 12(xy)
Given f(x) = 3x+4 . What is f(8)
one method of estimating is to
Given: ΔABC ≅ ΔFDE. . What is the length of segment DE rounded to the nearest tenth?. . 3.2. . 4.2. . 2.2. . 3.6. .
Answer:
The length of segment DE is 3.2 (A)
Step-by-step explanation:
The ordered pairs below represent a function
(-2,-17.5),(5,8.75),(0,-10),(-1,-13.75),(3,1.25)
What is the rate of change of the function?Round to the nearest hundreth if necessary. PLEASE HELP ASAP WILL AWARD BRAINLIEST!!!
Answer:
The answer is 3.75.
Step-by-step explanation:
I did this before
Mark has 36 drawings of horses and 4 drawings of spaceships. write and solve an equation to find how many times as many drawings of horses he has as spaceships.
Find the percent of increase from 4.5 inches to 13.5 inches.
Final answer:
To calculate the percent of increase from 4.5 inches to 13.5 inches, subtract the original value from the new value, divide by the original value, and then multiply by 100, resulting in a 200% increase.
Explanation:
To find the percent of increase from one number to another, you can use the formula: (New Value - Original Value) / Original Value × 100%. Applying this to the question, the original value is 4.5 inches, and the new value is 13.5 inches.
Calculate the increase: 13.5 - 4.5 = 9 inches.Divide the increase by the original number: 9 / 4.5 = 2.Convert this to a percentage by multiplying by 100: 2 × 100% = 200%.Therefore, the percent of increase from 4.5 inches to 13.5 inches is 200%.
what is the y- coordinate of the y- intercept of the line that passes through the points (-4,-4) and (4,8)
orginal price is 82$ the sales price is 65.60 what is the discount
Analyze the graph of the quadratic function that contains the points (0,-2), (1,0) and (3,10). Create the equation of the function given the three points.
123456780-646472.657
What is the domain of y = cos θ?
A. [-1, 1]
B. [0, infinity]
C. All real numbers
D. 2pi,
Answer:
Option C - All real numbers
Step-by-step explanation:
Given : Function [tex]y=\cos \theta[/tex]
To find : The domain of given function ?
Solution :
Domain is defined as the set of values for which function is defined.
We have given the function,
[tex]y=\cos \theta[/tex]
We know, for any value of [tex]\theta[/tex] the function [tex]y=\cos \theta[/tex] is defined.
Which means the set of all real numbers defined the given function i.e. [tex]x\in(-\infty,\infty)[/tex]
Therefore, Option C is correct.
The domain of [tex]y=\cos \theta[/tex] is all real numbers.
Javier bought a 20 oz smoothie that contains 450 total calories how many calories does a smoothie contain per ounce
In circle C, what is the value of X?
X=112 degrees
X=90 degrees
X=68 degrees
X=22 degrees
Answer:
x=22 degrees
Step-by-step explanation:
We are given a circle C
Centre is at C
A line passes through the centre makes angle x and 68 on either side
A triangle is formed with angles x, 68 and another angle at the circumference.
Since the line passing through the centre is diameter of the circle, we have
the third angle of the triangle = 90 degrees ( BY semi circle angle theorem)
In the triangle sum of three angles
=90+x+68 =180
x =22 degrees
Carolina is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus $6 for each hour of work. Her total fee for a 4-hour job, for instance, is $ 32.
Carolina's charges can be represented by the linear equation y = 8 + 6x, where x represents hours worked and y represents the total fee charged for the service.
Explanation:The subject this question pertains to is Mathematics, specifically linear equations. Carolina's job can be modelled by a linear equation, where the independent variable is the number of hours worked and the dependent variable is the total fee charged.
In this case, Carolina charges an initial flat fee plus $6 per hour worked. Her total charge for a 4-hour job is $32, which means her initial fee can be deduced by subtracting four times her per-hour fee from the total fee, that is $32 - 4*$6 = $32 - $24 = $8. Therefore, the linear equation that models Carolina's job is y = 8 + 6x, where x is the number of hours worked and y is the total fee charged.
This is similar to the linear equation that represents Svetlana's tutoring job in Example 12.4, where each tutoring session earns her a one-time fee of $25 plus $15 per hour of tutoring, modeled by the equation y = 25 + 15x.
Learn more about linear equations here:https://brainly.com/question/32634451
#SPJ12
Suppose you invest $500 at an annual interest rate of 8.2% compounded continuously. How much will you have in the account after 15 years? (1 point)
$1,671.74
$17,028.75
$1,710.61
$8,140.92
Use the quadratic formula to find both solutions to the quadratic equation given below 2x^2-3x+1=0
Answer:
[tex]x_1=1\\x_2=\frac{1}{2} =0.5[/tex]
Step-by-step explanation:
Given a equation of the form:
[tex]ax^2+bx+c=0[/tex]
The roots of this equation can be found using the quadratic formula which is given by:
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
In this case we have this equation:
[tex]2x^2-3x+1=0[/tex]
So:
[tex]a=2\\b=-3\\c=1[/tex]
Using the the quadratic equation :
[tex]x= \frac{-(-3)\pm\sqrt{(-3)^{2}-4(2)(1) } }{2(2)} = \frac{3\pm\sqrt{9-8 } }{4}=\frac{3\pm 1}{4}[/tex]
Therefore the two roots would be:
[tex]x_1=\frac{3+ 1}{4}=\frac{4}{4}= 1\\x_2=\frac{3- 1}{4}=\frac{2}{4}=\frac{1}{2}=0.5[/tex]
What exponential function is the best fit for the data in the table?
x f(x)
2 −3
3 0
4 12
f(x) = 4(4)x − 1 + 4
f(x) = 4(4)x − 1 − 4
f(x) = one fourth(4)x − 1 + 4
f(x) = one fourth(4)x − 1 − 4
A light bulb manufacturing machine produces 72 light bulbs per minute. How much time would it take to make 5400 light bulbs?
Match each correlation coefficient with the type of association it indicates between the variables x and y.
r = 0.9
r = -1.0
r = -0.6
r = 0.1
a perfect linear association in which y increases as x increases
a perfect linear association in which y decreases as x increases
a strong linear association in which y increases as x increases
a strong linear association in which y decreases as x increases
a moderate linear association in which y increases as x increases
r = 0.9 (a strong linear association in which y increases as x increases)
r = -1.0 (a perfect linear association in which y decreases as x increases)
r = -0.6 (a moderate linear association in which y decreases as x increases)
r = 0.1 (no linear association or a very weak association)
PLZ HELP ASAP WILL GIVE BRAINLIEST ANSWER!!!!!
What do you predict the current will be in the absence of sunlight?
The expanded form 700,000 + 10,000+9 represents the whole number. 701,309. 713,009. 710,309. 713,090.
Find an nth degree polynomial function with real coefficients satisfying the given conditions. calculator
To find an nth-degree polynomial function with real coefficients given certain conditions, we can write the polynomial as a product of its linear factors using the given roots.
Explanation:To find an nth-degree polynomial function with real coefficients, we need to use the given conditions. Let's say the conditions include the roots of the polynomial. If we have n distinct real roots, the polynomial will have n factors. So, if the roots are a, b, c, ..., we can write the polynomial as P(x) = (x - a)(x - b)(x - c)...
Example:To find a quadratic polynomial with roots 2 and -3, we can write the polynomial as P(x) = (x - 2)(x - (-3)) = (x - 2)(x + 3) = x² + x - 6.
Similarly, for higher-degree polynomials, we use the same approach. We write the polynomial as a product of its linear factors using the given roots.
Learn more about Polynomial Functions here:https://brainly.com/question/30474881
#SPJ12
Find a rational number that is between 9.5 and 9.7
Answer:
9.6
Step-by-step explanation:
It is a rational number as it has terminating decimal expansion
If tan x=a/4 and cos x=4/b what is the value of sin x?
The value of sin x is sqrt(b^2 - 16)/16.
Explanation:
To find the value of sin x, we can use the trigonometric identity: sin^2(x) + cos^2(x) = 1.
Given that tan x = a/4 and cos x = 4/b, we can use the Pythagorean identity (1 + tan^2(x) = sec^2(x)) to find the value of sin x:
1 + (a/4)^2 = (4/b)^2
Simplifying the equation, we get: 1 + a^2/16 = 16/b^2Multiplying both sides by 16, we get: 16 + a^2 = 256/b^2Substituting the value of cos x, we get: 16 + a^2 = 256/(16/b^2)Further simplifying, we get: 16 + a^2 = 16b^2/16Cross multiplying, we get: 16 + a^2 = b^2Substituting the value of tan x, we get: 16 + (4a)^2 = b^2Simplifying the equation, we get: 16 + 16a^2 = b^2Subtracting 16 from both sides, we get: 16a^2 = b^2 - 16Taking the square root of both sides, we get: 4a = sqrt(b^2 - 16)Dividing both sides by 4, we get: a = sqrt(b^2 - 16)/4Substituting the value of a in the equation sin x = a/4, we get: sin x = sqrt(b^2 - 16)/16
Learn more about Trigonometry here:https://brainly.com/question/31896723
#SPJ11
Which graph represents the function on the interval [−3, 3] ?
PLEASE HELP ME ON THIS
In the figure, line TU is tangent to the circle at point U. Use the figure to answer both of the questions. Show all of your work.
(a) Describe the relationship among the lengths of the segments formed by the secant, RT , and the tangent segment, TU. You may use words and/or an equation to describe.
(b) Suppose RT= 9 in. and ST = 4 in. Is it possible to find the length of TU ? If so, show how to find the length. If not, explain why not.
Answer:
(a) The relation is RT × ST = TU²
(b) TU = 6
Step-by-step explanation:
(a) There is a secant law for circles that says the following: "if two secants are drawn to a circle from one exterior point, then the product of the external segment and the total length of each secant are equal". Applying this for the mentioned question, we have that RT × ST = TU x TU = TU² (considering that for TU case, the tangent is also a secant).
Then RT × ST = TU²
(b) Let's apply the equation in (a). RT × ST = TU² means 9 × 4 = TU²
Solving that equation, we have TU = √36 = 6
Thus TU = 6
Among 320 randomly selected airline travelers, the mean number of hours spent travelling per year is 24 hours and the standard deviation is 2.9. What is the margin of error, assuming a 90% confidence level? Round your answer to the nearest tenth. 0.01
Answer:
The margin of error assuming a 90% confidence level is 0.3
Step-by-step explanation:
Size of the sample: n=320
Mean: m=24
Standard deviation: s=2.9
Confidence interval: 90%
100(1-α)=90
Solving for α: Dividing by 100 both sides of the equation above:
100(1-α)/100=90/100
1-α=0.9
Subtracting 1 both sides of the equation:
1-α-1=0.9-1
-α=-0.1
Multiplying the equation by -1:
(-1)(-α=-0.1)
α=0.1
n= [z(1-α/2) s / E]^2
where E is the margin of error
z(1-α/2)=z(1-0.1/2)=z(1-0.05)=z(0.95)=1.64 (Table standard normal distribution)
z(1-α/2)=1.64
Replacing the known values in the equation above:
320= [(1.64) (2.9) / E]^2
320= (4.756/ E)^2
Solving for E: Square root both sides of the equation:
sqrt(320)=sqrt[ (4.756/ E)^2]
17.88854382=4.756/E
Cross multiplication:
17.88854382 E = 4.756
Dividing both sides of the equation by 17.88854382:
17.88854382 E / 17.88854382 = 4.756 / 17.88854382
E=0.265868486
Rounding tho the nearest tenth:
E=0.3