Answer:
To simplify
√(-x) = √((x)(-1)) = √((x)(i^2))
√(-x) = √(i^2) × √x = i√x
For example;
Simplify √-9
√-9 = √(-1×9) = √-1 × √9
√-9 = √(i^2) × √9 = i × 3
√-9 = 3i
Step-by-step explanation:
Given a negative square root √(-x);
From our knowledge of complex numbers, we know that
i^2 = -1 and vise versa
To simplify
√(-x) = √((x)(-1)) = √((x)(i^2))
√(-x) = √(i^2) × √x = i√x
For example;
Simplify √-9
√-9 = √(-1×9) = √-1 × √9
√-9 = √(i^2) × √9 = i × 3
√-9 = 3i
Step-by-step explanation:
The square root of a number A, is a number B such that, when it is multiplied by itself, the result is A.
If A × A = B
Then √B = A.
Now the multiplication of two numbers gives a positive number if both numbers are positive, or both numbers are negative.
2 × 2 = -2 × -2 = 4
3 × 3 = -3 × - 3 = 9
And so on.
So, the square root of 4 = 2 or -2
The square root of 9 = 3 or -3
But if one of the numbers is positive while the other is negative, then the result is negative.
2 × -2 = -4
3 × -3 = -9
Clearly, √(-4) ≠ 2 ≠ -2
√(-9) ≠ 3 ≠ -3
It is impossible to find the square root of negative numbers on the real line. This gives rise to the introduction of Complex Number.
Let i² = -1, then we have that
√(-1) = i.
This is the idea of Complex number, and it helps solve the problem of the negative square roots, and every negative number can be written as the multiplication of -1 and the inverse of the number.
-A = -1 × A
So, √(-A) = √(-1 × A)
= √(-1) × √A
= i × √A
= i√A
Example, to simplify √(-16)
√(-16) = √(-1 × 16)
= √(-1) × √16
= i × ±4
= ±4i
The sum of two irrational numbers is _____ a rational number. Which word correctly fills in the blank to create a true statement?
A) always
B) never
C) sometimes
Answer:
C.) Sometimes
Step-by-step explanation:
The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational.
The word that correctly fills the blank is sometimes, the correct option is C.
What is a Rational Number ?Rational Numbers are numbers that can be written in the form of p/q, q≠0.
The sum of two irrational number is sometimes a rational number.
For example the summation of the irrational number with its additive inverse, the sum will be 0, which is a rational number and a whole number.
Therefore, the word that correctly fills the blank is sometimes, the correct option is C.
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Express the solution of the following initial value problem in terms of an integral.
dy/dx = 2 + x, y(2 ) = -6
Answer:
[tex]y = 2x + \frac{x^2}{2} - 6[/tex]
Step-by-step explanation:
Solution:-
- We are given the following initial value problem:
[tex]\frac{dy}{dx} = 2 + x , y ( 2 ) = -6[/tex]
- We will first isolate the variables:
[tex]dy = ( 2 + x ).dx[/tex]
- Perform integration for both sides of the equation:
[tex]\int {dy} = \int {( 2 + x )}.dx + c\\\\y = 2x + \frac{x^2}{2} + c\\[/tex]
Where,
c: The constant of integration
- We will solve for the constant of integration by using the initial value y ( 0 ) = -6 as follows:
[tex]-6 = 2(0) + \frac{0^2}{2} + c\\\\c = -6[/tex]
- The final solution can be expressed as follows:
[tex]y = 2x + \frac{x^2}{2} - 6[/tex]
Please answer this correctly
Answer:
22 1/8 mm.
Step-by-step explanation:
First add the whole numbers, then the fractions:
3 + 5 + 5 + 7 = 20
7/8 + 7/8 + 3/16 + 3/16 Change the 7/8's to 14/16:
= 14/16 + 14/16 + 3/16 + 3/16
= 28/16 + 6 /16
= 34 /16
= 2 2/16
= 2 1/8
So the final answer is 20 + 2 1/8
= 22 1/8 mm.
Step-by-step explanation:
the perimeter of this
3 7/8 + 5 3/16 + 5 3/16 + 7 7/8
= 31/8 + 83/16 + 83/16 + 63/8
= 62 + 83 + 83 + 126/ 16
= 354/16 ans
Brady can feed, water, and clean up after 24 cows in 120 minutes. McKenna takes 360 minutes to care for 24 cows. How long will it take Brady and McKenna working together to care for 24 cows?
Answer:
Minutes= 90
Step-by-step explanation:
Brady will take care of 24 cows in 120 minutes.
Rate of Brady = 24/120
Mc Kenna takes care of same 24 cows in 360 minutes.
Rate of Mc Kenna = 24/360
Sum of rates = 24/120 + 24/360
Sum of rates =( 72+24)/360
Sum of rates = 96/360
Sum of rates = 96/360
Let's determine how many minutes it will take them total to take of Same 24 cows
Minutes = 24/rate
Minutes = 24/(96/360)
Minutes =( 24*360)/96
Minutes= 90
What’s the correct answer for this? Select all the ones that apply
Answer:
C and E
Step-by-step explanation:
ANP = BNP = 90 WILL PROVE THAT CD IS PERPENDICULAR TO AB.
What is the sum of the fractions? Use the number line to help find the answer. 3/5 + ( - 7/5) Answers: Wh Three-fifths + (Negative StartFraction 7 over 5 EndFraction A number line going from negative 2 to positive 2 in increments of one-fifth. Negative 2 Negative four-fifths Four-fifths 2
Answer:
[tex]\frac{-4}{5}[/tex]
Step-by-step explanation:
[tex]\frac{3}{5} - \frac{7}{5} = \frac{3-7}{5} = \frac{-4}{5}[/tex]
The sum of the fractions is -4/5.
What is a number line?The real numbers arranged in order on a geometric line form a number line. The points on the geometric line represent real numbers.
On the number line, the addition of a positive number a to a number b moves the point at b to the right by a units.
The addition of a negative number -a to a number b moves the point at b by a units to the left.
The point H in the diagram is at the number 3/5, third stick to the right of 0.
Adding -7/5 to 3/5 means moving the point H to the left by 7 sticks. Doing so we find the point at -4/5 as shown in the figure.
The final position of the point after addition is -4/5.
The value of 3/5 - 7/5 is, thus, -4/5.
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find the distance from the origin to the graph of 6x+3y+2=0
Answer:
C. 0.3
Step-by-step explanation:
How many fluid ounces are there in 5 quarts?
Answer:
160
Step-by-step explanation:
So there are 32 ounces in a quart.
32 * 5 = 160
Answer:160 fluid ounces :)
Step-by-step explanation:
F(x)=4x>2+12x+9 Rewrite to function by completing the square F(x)=...(x+....)>2+...
Answer:
f(x) = 4( x + 3/2)^2
Step-by-step explanation:
F(x) =4 x^2 + 12x + 9
= 4 [ x^2 + 3x] + 9
Add (3/2)^2 - (3/2)^2 to the square bracket, we have:
4 [ x^2 + 3x+ (3/2)^2 - (3/2)^2] + 9
4[ (x + 3/2 )^2 - 9/4] + 9
4( x + 3/2)^2 - 9/4 ×4 + 9
4( x + 3/2)^2 - 9 + 9
4( x + 3/2)^2 +0
4( x + 3/2)^2
Note the (3/2)^2 - (3/2)^2 is decoded by dividing b by 2 and squaring it and then subtracting same. Look at the general equation of a circle given below
ax^2 + bx + c
To form a square expression we adopt (b/2)^2 - (b/2)^2 to the general equation provided a = 1;
To make a = 1; we had to factor out 4 from the coefficient of x; making perfect square is of concern when we have ax^2 + bx ; irrespective of 'c' or not.
This is usually referred to as method of completing the square in solving quadratic equation
ANYONE WHO ANSWERS THIS GETS BRAINIEST!! THANK YOU!!! :)
When adding 24.72 to a certain number, the sum is 28.42, as seen below. What number should go in the box to complete the addition problem? (The little box with the question mark is the missing number.)
THIS IS THE BOX:
24.72
+ [?].7
= 28.42
ANSWERS:
A: 2
B: 3
C: 11
D: 14
All answers are appreciated.
Answer:
B;3
Step-by-step explanation:
That is because to complete the box you need the sum to subtract from one of the addends to be able to find the other and
28.42-24.72=3.7
Hope this helps:)
The missing number is 3.
What are mathematical operatiors?In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows:
Operands: The numbers used in an operation are called operands. Depending on the type of operation, different terms are applied to the operands.
Operator: An operator is the sign used to represent a mathematical operation, such as + for addition, subtraction, multiplication, and division.
Given adding certain number to 24.72 gives 28.42
24.72 + [?].7 = 28.42
let the number be x + .7
equation is
24.72 + x +.7 = 28.42
x = 28.42 - 0.7 - 24.72
x = 3
Hence 3 is the missing digit.
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Use the mapping to determine which of the following are elements of the range.
Name
Amy
Carol
Devon
Harrison
Jackson
Labron
Mason
Natalie
Paul
Sylvester
Birthday
January 5
January 7
February 24
March 1
April 7
May 30
July 20
August 1
November 13
November 26
Answer:
The elements of the range are the birthdays.
Step-by-step explanation:
A function is a distinct sort of relation in which each element of the domain is combined with precisely one element in the range. A mapping displays how the elements are combined.
A mapping figure comprises of two parallel columns. The 1st column signifies the domain of a function, and the other column for its range.
Lines or arrows are drawn from domain to range, to signify the relation between any two elements.
A function denoted by the mapping, in which each element of the range is combined with accurately one element of the domain is called one-to-one mapping.
From the diagram provided it is clear that the function denoted by the mapping is an one-to-one mapping.
The elements of the range are:
Birthday : {January 5 , January 7 , February 24 , March 1 , April 7 , May 30 , July 20 , August 1 , November 13 , November 26 }
Thus, the elements of the range are the birthdays.
Answer:
Amy
Devon
Labron
Step-by-step explanation:
An animal shelter needs to find homes for 40 dogs and 60 cats. If 15% of the dogs are female, and 25% of the cats are female, what percent of the animals are female?
Someone please answer.... I really need this
I will give brainliest. PLEASE HELP!!!
Answer:
21% of the animals are female
Step-by-step explanation:
In total:
There are 40 + 60 = 100 animals.
Female animals.
40 dogs. Of those, 15% are female. So 0.15*40 = 6.
60 cats. Of those, 25% are female. So 0.25*60 = 15.
21 female animals.
21/100 = 0.21 = 21%
21% of the animals are female
Imagine the United States only had two postage stamps, a 3 cent stamp and a 7 cent stamp. If you can put any number of stamps on an envelope that you want, what amounts of postage can and cannot be paid for?
Answer:
not possible: 1, 2, 4, 5, 8, 11possible: all othersStep-by-step explanation:
Obviously, all multiples of 3 and 7 can be paid.
1 cent can be added by adding a 7-cent stamp and taking away two 3-cent stamps. 2 cents can be added by adding three 3-cent stamps and taking away one 7-cent stamp. Hence any value more than 7 +2(3) = 13 cents can always be accommodated.
Amounts that are impossible:
1, 2, 4, 5, 8, 11 cents
All other positive integer amounts are possible.
smplify the following algebraic expression: 6(2y + 8) - 2(3y - 2)
Answer:
6y +52
Step-by-step explanation:
6(2y + 8) - 2(3y - 2)
Distribute
12y + 48 - 6y +4
Combine like terms
6y +52
a country's population in 1993 was 94 million. in 1999 it was 99 million
Answer:
i dont get it
Step-by-step explanation:
What equation can be solved to find one of the missing side lengths of a triangle?
Answer:
Step-by-step explanation:
1 find out what kind of its is
if its equivelent you might use 60 as thee angles then find out
If A={3,6,9,12 }and B={0,4,8,12}, then find A∩B. *
Answer:
{12}
Step-by-step explanation:
[tex]A= \{3,6,9,12\} \\ B= \{0,4,8,12 \} \\ A \: \cap \: B = \{12\} [/tex]
The total surface area of this cuboid is 112 cm,
Find the value of x.
X cm
2 cm
10 cm
Answer:
x=3
Step-by-step explanation:
The triangle shown below has an area of 444 units^2 2 squared. Find the missing side.
Answer:
2 units
Step-by-step explanation:
khan
Answer:
[tex]\boxed{\tt x=2\: units}[/tex]
Step-by-step explanation:
First, we need to set up an equation using the formula for the area of a triangle.
[tex]\boxed{\tt Area=\cfrac{1}{2} \times \: base\times height}[/tex]
Given:
Area: 4
Base: x
Height: 4
____________________
[tex]\tt 4=\cfrac{1}{2} \times\: x\times4[/tex]
[tex]\longmapsto\tt 4=2x[/tex]
Divide both sides by 2:
[tex]\longmapsto\tt \cfrac{4}{2}=\cfrac{2x}{2}[/tex]
[tex]\longmapsto\tt x=\cfrac{4}{2}[/tex]
[tex]\longmapsto\tt x=2[/tex]
Therefore, the missing side is 2 units.
____________________________
The Lylian is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of p > 0.5, which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the method, which of the following P-values would you prefer and Why?
a. 0.999
b. 0.5
c. 0.95
d. 0.05
e. 0.01
f. 0.001
Answer:
[tex] p_v =P(z>z_{calc}) [/tex]
In order to establishing the success of the method we need to obtain a p value very low in order to reject the null hypothesis because we need enough evidence in favor of the alternative hypothesis, so then the best option would be:
f. 0.001
Step-by-step explanation:
We need to conduct a hypothesis in order to test the claim that one of several methods claimed to increase the likelihood of a baby girl so then the system of hypothesis are:
Null hypothesis:[tex]p\leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The p value for this case is given by:
[tex] p_v =P(z>z_{calc}) [/tex]
In order to establishing the success of the method we need to obtain a p value very low in order to reject the null hypothesis because we need enough evidence in favor of the alternative hypothesis, so then the best option would be:
f. 0.001
I'm very confused as to what the pattern even is, to me I just see a bunch of shapes and numbers. Could any of you help?
2)
Simplify -2(x + 4) + 5x + 10
First distribute through the set of parentheses.
When we distribute, we multiply the number outside
times each of the terms located inside the set.
So we have -2(x) + -2(4) or -2x - 8.
Now we have -2x - 8 + 5x + 10.
Combine like terms → your numbers and your "x" terms.
-2x + 5x is 3x and -8 + 10 is 2.
So we have 3x + 2.
3x + 2 cannot be simplified any further.
If eight trash bags last for thirty days then twenty eight trash bags will last for how many days
Answer:
105 days
Step-by-step explanation:
30 divided by 8 to get the rate which equals 3.75
28*3.75= 105 days
30 POINTS FOR THE GENUIS WHO CAN ANSWER THIS!!
Answer:
Answers are below in bold
Step-by-step explanation:
1) A = 1/2bh Use this equation to find the area of each triangular base
A = 1/2(8)(6) Multiply
A = 1/2(48) Multiply
A = 12cm² Area of each triangular base
2) A = L x W Use this equation to find the area of the bottom rectangular face
A = 20 x 8 Multiply
A = 160 cm² Area of the bottom rectangular face
3) A = L x W Use this equation to find the area of the back rectangular face
A = 20 x 6 Multiply
A = 120 cm² Area of the back rectangular face
4) A = L x W Use this equation to find the area of the sloped rectangular face
A = 20 x 10 Multiply
A = 200 cm² Area of the sloped rectangular face
5) To find the total surface area of the triangular prism, add together all of the numbers.
A = 12 + 12 + 160 + 120 + 200 Add
A = 504 cm² Total area of the triangular prism
The lengths of the sides of a triangle are 3, 3, 32. Can the triangle be a right triangle?
Answer:
No
Step-by-step explanation:
Although two sides are equal, the 32 is simply too big for it to be a triangle.
Answer:
No it is not the sides of right angled triangle.
Step-by-step explanation:
IF a²+b²=c² then the triangle is right
3²+3²=32²
9+9=1024
18=1024
The rectangular floor of colbys room is 9 feet long and 6 feet wide. What is the area of the floor
Answer:
54 ft^2
Step-by-step explanation:
The area is the product of length and width:
A = LW = (9 ft)(6 ft)
A = 54 ft^2
The area of the floor is 54 square feet.
Answer:
area of the rectangular floor = 54 ft²
Step-by-step explanation:
The area of a rectangle is the product of the length and width. The floor is rectangular therefore the area of the floor can be calculated by using the area of a rectangle.
area of the rectangular floor = length × width
length = 9 ft
width = 6 ft
area of the rectangular floor = length × width
area of the rectangular floor = 9 × 6
area of the rectangular floor = 54 ft²
Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of 7 per hour. If it takes approximately 10 minutes to serve each customer, find the mean and variance of the total service time for customers arriving during a 1-hour period. Assume that a sufficient number of servers are available so that no customer must wait for service. What is the probability that the total service time will exceed 2.5 hours? (Use at least four digits after the decimal if rounding.)
Answer:
the mean service time = 70 minutes
the variance of the total service time for customers arriving during a 1-hour period is 700
the probability that the total service time will exceed 2.5 hours is 0.0012
Step-by-step explanation:
Given that:
Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of 7 per hour.
If it takes approximately 10 minutes to serve each customer
From the given information:
The mean total service time= [tex]10 \ minutes * \lambda[/tex] (i.e the average number to turn up during the hour) .
where;
[tex]\lambda =[/tex] the average rate per hour i.e 7
Thus; the mean service time = 10 × 7 = 70 minutes
For a Poisson Distribution;
The variance of the the total service time for customers arriving during a 1-hour period can be expressed by the relation:
[tex]\sigma(aX) = a* \sigma(X). \\ \\ where ; \sigma = {\sqrt{S^2}} \\ \\ \sigma(service \ time) = 10 * \sigma(arrival \ time) \\ \\S^2 (service \ time) = (10* \sigma(arrival \ time))^2 \\ \\ S^2(service \ time) = 100 * S^2(arrival \ time) \\ \\ = 100*\lambda \\ \\ = 100*7 = 700[/tex]
where S² = variance
What is the probability that the total service time will exceed 2.5 hours?
If we convert 2.5 hours to minutes ; we have
2.5 × 60 minutes =150 minutes
The probability that the total service time will exceed 2.5 hours is as follows:
[tex]Z = \dfrac{S-70}{\sqrt {700}} \ \ \ \ follow \ N(0,1) \\ \\ P(S > 150) = \dfrac{S-70}{\frac{\sqrt{700}>(150-70)}{\sqrt{700}}} \\ \\ =P(Z > -2.5512) \\ \\ =0.0012[/tex]
Ian is borrowing $1000 from his parents to buy a notebook computer. He plans to pay them back at the rate of $60 per month
Answer:
whats the question?
Step-by-step explanation:
Does this table represent a function? Why or why not?
Answer:
B
Step-by-step explanation:
Yes because every x value corresponds to exactly one y value.
Answer: B
Step-by-step explanation: The basic idea of a function is you put in some value for x and you get out something for y.
So for a table to be a function, each x term
needs to corresponds to exactly one y-term.
So yes, every x-value corresponds to exactly one y-value.
A common mistake would be to say that this is not a function
because the y-value of 3 repeats twice.
However, that's ok because you don't get
different y-values for the same x.
Mrs. Lowery wants to make as many 3-ounce baggies of almonds as she can. She has an open jar of almonds with 10 ounces left. She also has a full 16-ounce jar of almonds.
Mrs. Lowery will have ＿＿＿ounces of almonds left over.
