(x+3i)(x-3i)
A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, I = √-1 and both a and b are real numbers.
Consequently, a complex number is a straightforward illustration of the addition of two integers, specifically a real number and an imaginary number. It consists of two parts: one that is entirely real, the other entirely fantastical.
Using complex numbers,
x²+81 = x² - (-9i)²
= (x²- 9²i²)
= (x+3i)(x-3i)
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Find the perimeter of a rectangle with a length of 9 yards and a width of 6 yards.
Answer:
30 yards
Step-by-step explanation:
9+9+6+6=30yards
A pair of cars, 70 miles apart, begin at the same time to run toward each other. If car A
from city A runs at a rate that is 5 mph faster than car B from city B, and if they meet 2
hours later, how far is the place they meet away from city A?
Answer: car a must be meet to cannot be so your aner is a
Step-by-step explanation:
Use the equation y-6= to fill in the missing values in the table below
Using the given equation, the missing values in the table are:
x y
32 14
12 9
0 6
-8 4
-36 -3
How to Apply an Equation?Given the equation, y - 6 = x/4, we can rewrite the equation as:
y = x/4 + 6
For x = 12, we have:
y = 12/4 + 6 = 3 + 6
y = 9
For x = 0, we have:
y = 0/4 + 6 = 0 + 6
y = 6
For y = 4, we have:
4 = x/4 + 6
4 - 6 = x/4
-2 = x/4
-8 = x
x = -8
For y = -3, we have:
-3 = x/4 + 6
-3 - 6 = x/4
-9 = x/4
-36 = x
x = -36
Thus, using the given equation, the missing values in the table are:
x y
32 14
12 9
0 6
-8 4
-36 -3
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With steps please, if it’s correct I’ll give full rate please
A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160feett/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute
Given that 1)A gull can fly at a speed of 22 miles per hour and asked to convert its units to foot/hour
2)An AMTRAK train travels at 125 miles per hour and is asked to convert its units to miles/minute
1 mile=5280 feet
22 miles/hour=22 × 5280 foot/hour
22 miles/hour=116,160 foot/hour
1 hour=60 minute
125 miles/hour= 125/60 miles/minutes
125 miles/hour= 2.083 miles/minutes≈ 2.1miles/minutes
Therefore, A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160 feet/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute
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how can you see immediately that two integers add up to 1?
The numbers have absolute values that differ by 1, and the number with the larger absolute value is positive.
Which choice is a term in this expression? 3x − 7(x + 4)
The term in the given expression is -3x − 7(x + 4) (A) -3x.
What exactly do we mean by expressions?A finite combination of symbols that is well-formed according to context-dependent rules is referred to as an expression or mathematical expression.A mathematical expression is a phrase that has at least two numbers or variables, at least one mathematical operation, and at least one mathematical operation.Addition, subtraction, multiplication, and division are all considered math operations.The structure of an expression is as follows: An expression is (Number/variable, Math Operator, Number/variable).Term:
Terms are expression parts that are separated by + or - signs.Because it is separated from the rest of the expression by a - sign, -3x is a term.Therefore, the term in the given expression is (A) -3x.
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The correct question is given below:
Which choice is a term in this expression? -3x − 7(x + 4)
Is the relationship between the side length of a square and its area proportional?
The relationship between the length of a side and the area is non proportional.
The answer is non proportional because the side length is x,
so is the other side lengths.
The side lengths are all equal and to find area you do x squared or x times x.
So they are not proportional because there will be different numbers for each.
For example. X= 2, area ( x squared ) is 4.
Hence, The relationship between the length of a side and the area is non proportional.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In a square, we need to find the relationship between the length of a side and the area.
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Which value of v makes 12=12+v-8/2 a true statement?
Answer:
Step-by-step explanation:
12 = 12 + v - (8/2)
12 = 12 + v - 4
12 - 12 = v - 4
v = 4
Help? fraction multiplication as scaling AYUDA HELP
Answer:
1) 1/2 × 3/5 = 45/150
2) 5/5 × 3/5 = 90/150
3) 2 2/3 × 3/5 = 1 90/150
Explanation below
Explanation belowHope this helps :)
Step-by-step explanation:
1/2 × 3/5 = 3/10
2 2/3 × 3/5 = 8/3 × 3/5 = 24/15
5/5 × 3/5 = 15/25
We need to find the Least Common Multiple (LCM) to order them from least to greatest.
The LCM is 150.
3/10 = 45/150
24/15 = 1 9/15 = 1 90/150
15/25 = 90/150
So the order from least to greatest is ...
1) 1/2 × 3/5 = 45/150
2) 5/5 × 3/5 = 90/150
3) 2 2/3 × 3/5 = 1 90/150
can anyone help me with this question please asap !! thank you in advance !!!!!
Answer:
31/35
Step-by-step explanation:
3/5 + 2/7 = (3 × 7) / (5 × 7) + (2 × 5) / (7 × 5)
= 21/35 + 10/35
= 31/35.
Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = t i t2 j 2 k
The velocity of a particle = i + 2t j
The acceleration of a particle = 2 j
The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]
Here,
The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]
We have to find, the velocity, acceleration, and speed of a particle with the given position function.
What is Velocity of a particle with the given position function?
The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.
Now,
The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]
The velocity of a particle = [tex]\frac{d r(t)}{dt}[/tex]
[tex]r (t ) = ti + t^{2} j +2k[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
The acceleration of a particle = [tex]\frac{d^{2} r(t)}{dt^{2} }[/tex]
[tex]r (t ) = ti + t^{2} j +2k[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
[tex]\frac{d^{2} r(t)}{dt^{2} }= 2j[/tex]
The speed of a particle = [tex]| \frac{d r(t)}{dt}| = |v(t)|[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
[tex]|v(t)|=\sqrt{1 + 4t^{2} }[/tex]
Hence, The velocity of a particle = [tex]i + 2t j[/tex]
The acceleration of a particle = [tex]2 j[/tex]
The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]
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A plane leaves the airport and travels east for 2.5 hours at a speed of 240 miles per hour. It then travels south for 500 miles. a)Calculate the distance of the plane from the airport. b)Calculate the bearing of the plane from the airport.
a) The distance of the plane from the airport is approximately 781.025 miles.
b) The bearing of the airplane in standard position is approximately 320.194°.
How to calculate the distance and the bearing of the bearing from the airport
Let the location of the airport be the origin and the orthogonal axes are oriented to the east and north, respectively. Beside, let consider that the plane moves at constant speed. a) Thus, the distance of the plane can be found by using the Pythagorean Theorem:
d = √[[(240 mi / h) · (2.5 h)]² + (500 mi)²]
d ≈ 781.025 mi
b) And the bearing in standard position is determined by the following inverse trigonometric function:
θ = tan⁻¹ [(- 500 mi) / [(240 mi / h) · (2.5 h)]]
θ ≈ 320.194°
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Express 21 as a product of prime
factors
Answer:
21=1×21 or 3×7
Step-by-step explanation:
21 is a composite number.factors of 21:1,3,7,21.
Prime factorization:21=3×7.
since 3 and 7 are the only prime numbers ...
Thanks!!
Please help solve this equation. -3(5w-3y-2)
Answer:
-15w+9y+6
Step-by-step explanation:
I think that you are asking to simplify the expression. An equation has an equal sign and I do not see one.
We need to distribute the -3 to everything inside of the parentheses.
A negative times a negative is a positive.
A negative times a positive is a negative.
-3(5w-3y-2)
-3(5w) -3(-3y) -3(-2)
-15w + 9y + 6
Hi!
To simplify this, use the Distributive Property:
[tex]\tt{a(b+c)=ab+ac}[/tex] | Basically, we distribute a so that it gets multiplied by b and c.Now, let's simplify the given expression:
[tex]\dashrightarrow\sf{-3(5w-2y-2)}[/tex]
Like the property said, We should distribute -3 so that it's multiplied by each term:
[tex]\bullet\dashrightarrow\sf{-15w+9y+6}[/tex]
Therefore,
[tex]\bullet\dashrightarrow\stackrel{\heartsuit}{\boxed{\boxed{\boldsymbol{-15w+9y+6}}}}}\dashleftarrow\bullet[/tex]
Good luck.- stargazing :')
solve the literal equation for y
4x+1=9+4y show steps please i am confused
The solution to the literal equation is y = x - 2.
What is the solution to inequality?To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.
From the given information:
4x + 1 = 9 + 4y
To solve for y, we have to switch the sides:
9 + 4y = 4x + 1
Subtract 9 from both sides
9 - 9 + 4y = 4x + 1 - 9
4y = 4x - 8
Divide both sides by 4
[tex]\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}[/tex]
y = x - 2
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8 Simplify: 7x² + 4x-x²
[tex] \: \Large \mathbb{SOLUTION:}[/tex]
[tex] \: \: \rm{ {7x}^{2} + 4x - {x}^{2}}[/tex]
[tex] \: \: \text{Reorder and gather like terms}[/tex]
[tex] \: \: \rm{( {7x}^{2} - {x}^{2} ) + 4x}[/tex]
[tex] \: \: \text{Collect coeffiecients of like terms}[/tex]
[tex] \: \: \rm{(7 - 1) {x}^{2} + 4x}[/tex]
[tex] \: \: \text{Calculate the sum or difference}[/tex]
[tex] \: \: \rm{ \underline{ \underline{ {6x}^{2} + 4x}}}[/tex]
[tex] \rm{6x {}^{2} + 4x}[/tex]
Solution:Collect like terms
[tex] \red{7x {}^{2} } + 4x \red{ - x {}^{2} }[/tex]
[tex] \red{6x {}^{2} } + 4x [/tex]
Jim picks a number. he doubles that number, then adds 5, and gets 41 as his result. what was the original number jim picked?
Answer: 18
Step-by-step Explanation:
Subtract: 5 from 41 | 41-5= 36
Divide: by 2 | 36/2= 18
Answer:18
Step-by-step explanation:
SUBTRACT41 FROM 5
THAT GIVES YOU 38
THEN DIVIDE 38/2 AND IT WILL GIVES 18
Irwin has flowering plants in 15% of his garden. Which of the following is equivalent to 15%?
Answer: Im not sure
Step-by-step explanation:
You didnt list the options therefore i cant answer this for you. :I
PLEASE HELP ME!
WILL GIVE BRAINLIEST!
What is the answer to this problem ?
Answer:
11
Step-by-step explanation:
Plug 4 into the x, 6(4) = 24
24 - 13 = 11
Helpppp...
[tex]{e}^{x} = {2e}^{ - x} [/tex]
Pls gv explaination to the solution
A number is chosen at random from the numbers 1-10. What is the probability of selecting the number 7 or a number less than 4?
Answer:
3/25
Step-by-step explanation:
What does it mean for a sample to have a standar deviation of zero? describe the scores in such a sample
Given that sample standard deviation is zero. This indicates that the variance of sample is also zero as square of sample standard deviation is sample Variance. Variance is average of the squared deviations from mean. As shown in below formula
Since Variance = 0 , we substitute in formula and we get the sum of squares of deviations of all data points from mean should be zero. This is only possible if and only if all the data points in the data distribution are same as mean of the data distribution. In the case the variance and standard deviation will be zero.
Variance = Summation n to i = 1 [tex]\frac{(X_{1-X} )^2}{n-1}[/tex]
0 = Summation n to i = 1[tex]\frac{(X_{1-X} )^2}{n-1}[/tex]
Summation n to i [tex]{(X_{1-X} )^2[/tex] = 0
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▼
What, approximately, is the percent uncertainty for the measurement given as 1.59 m²?
Answer: The approximately percent uncertainty for the measurement is 0.62%.
Step-by-step explanation:
The given parameters:
Area of the measurement, A = 1.59 m²
The uncertainty in the measurement of the area = ±0.01 m²
The approximately percent uncertainty for the measurement is calculated as follows;
[tex](0.01/1.59)*100[/tex] %
=0.62%
Thus, the approximately percent uncertainty for the measurement is 0.62%.
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Answer: 0.6 percent.
Step-by-step explanation: to find the uncertainty , we will take that absolute uncertainty _0.01 divided by the measurement of 1.59 _ times by a hundred percent and we get 0.6 percent.
How to I do part (ii)?
Answer:
Step-by-step explanation:
7(i)
[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=\frac{dx}{dx} *(3x-5)^\frac{5}{3}+x*\frac{d}{dx} \{(3x-5)^\frac{5}{3} \}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=1*(3x-5)^\frac{5}{3} +x*\frac{5}{3}*(3x-5)^{\frac{5}{3} -1}*\frac{d}{dx} \{(3x-5)\}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +\frac{x*5*(3x-5)^{\frac{2}{3}}*3 }{3} \\\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +5x*(3x-5)^\frac{2}{3} \\\\[/tex]
[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3}*((3x-5)^{\frac{5}{3}-\frac{2}{3}} + 5x)\\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5)^\frac{3}{3}+5x) \\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5+5x)\\\ \frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(8x-5)*(3x-5)^\frac{2}{3}[/tex]
7(ii)
[tex]\int\limits {(x*(3x-5)^\frac{2}{3}) } \, dx \\Let\ \sqrt[3]{3x-5} =u\\Hence,\\(\sqrt[3]{3x-5})^3=u^3\\ 3x-5=u^3\\3x-5+5=u^3+5\\3x=u^3+5\\[/tex]
Divide both parts of the equation by 3:
[tex]\displaystyle\\x=\frac{u^3+5}{3}\\\\dx=\frac{d}{du} \{\frac{u^3+5}{3}\} \\dx=\frac{3u^2}{3} du=\\\\dx=u^2du\\Hence,\\\\\int\limits {\frac{u^3+5}{3}* u^2*u^2} \, du =\\\\\int\limits {\frac{u^3+5}{3} *u^4} \, du =\\\\\int\limits {\frac{u^7+5u^4}{3} } \, du =\\\\\frac{1}{3} \int\limits {u^7} \, du +\frac{1}{3}\int\limits {5u^4} \, dxu =\\\\[/tex]
Kyrie and Jayla were trying to describe parts
of the expression (5p+ 3)(p+1).
Jayla said, "The entire expression is the
sum of 5 terms."
Kyrie said, "The entire expression is the
product of 4 factors."
Step-by-step explanation:
did you leave something out ?
(5p + 3)(p + 1) = 5p×p + 5p×1 + 3×p + 3×1 =
= 5p² + 5p + 3p + 3 = 5p² + 8p + 3
at no point do we have 5 terms to sum up. but 4 and then finally 3, yes.
but we always have also additions, not only multiplications (products).
so, none of the 2 options is correct.
we could, of course. start with the initial expression, that shows the product of 2 factors and multiply by 1×1
(5p + 3)(p + 1)×1×1
then we have the expression as product of 4 factors.
in the same way we could bump up the sum scenario by adding one or 2 0s : tadah ! sum of 5 terms.
I strongly suspect there is something missing in the problem description.
Answer:
Neither is correct.
Step-by-step explanation:
If p(a | b) = 0.4, p(b) = 0.8, and p(a) = 0.5, are the events a and b independent?
The events A and B are not independent.
Given that,
P(A|B) = 0.4
P(A) = 0.5
P(B) = 0.8
Two events A and B are said to be independent, if P(A∩B) = P(A) P(B)
We have, P(A|B) = P(A∩B)/P(B)
Therefore, P(A∩B) = P(A|B) P(B) = 0.4 x 0.8 = 0.32
Now P(A) P(B) = 0.5 x 0.8 = 0.4
So P(A∩B) ≠ P(A)P(B)
Therefore, the events A and B are not independent.
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Three numbers are in the ratio 2:5:7 and their lcm is 490 find the square root of the largest number
Answer:
49
Step-by-step explanation:
The ratio of three numbers = 2:5:7
Then the numbers are 2x,5x and 7x
Given that the LCM of these numbers = 490
LCM of 2x,5x,7x is 2×5×7×x = 70x
Then, we have 70x = 490
x = 7
Hence, the numbers are 14, 35 and 49
Largest number = 49
∴The square root of the largest number = 7
Consider the points p such that the distance from p to a ( 1,5,3) is twice the distance from p to b (6, 2, 2) . show that the set of all such points is a sphere, and find its center and radius
The set of all such points is a sphere center c = ( 23/3 , 19/3 , 3 ) r = 2√83/9
what is the sphere?
sphere, The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.The standard form of the equation of a sphere with center (a ,b ,c) and radius r is
( x -a)² + ( y-b)² + ( z - c)² = r²
We let P = ( x, y,z ) be an arbitrary point which satisfies the given conditions. Then
[tex]\sqrt{(x - 1)^{2} + ( y - 5)^{2} + (z - 3)^{2} } = 2 \sqrt({x - 6)^{2} + ( y - 2 )^{2} +( z - 3)^{2} }[/tex]
Squaring both sides of this equation and simplifying yields
( x - 1)² + ( y - 5)² + ( z -3)² = 4 [ (x - 6)² + ( y- 6 )² + ( z - 3)²
( 3x² - 46x + 143 ) + ( 3y² - 38y + 119 ) + ( 3z² - 18z + 27 ) = 0
Next, we complete the square for each variable to obtain
( x - 23/3)² + ( y - 19/3)² + ( z - 3 )² = 332/9
Thus the set of all such points P forms a sphere, with
center c = ( 23/3 , 19/3 , 3 ) r = 2√83/9
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A scale that allows one to determine only if there is more, less, or an equal amount of the attribute in comparison to another observation is called a(n) _____ scale.
Ordinal is the answer.
In the given statement is:
A scale that allows one to determine only if there is more, less, or an equal amount of the attribute in comparison to another observation is called a(n) ____ scale.
Ordinal Scale is the 2nd level of measurement that reports the ranking and ordering of the data without actually establishing the degree of variation between them. Ordinal level of measurement is the second of the four measurement scales. "Ordinal" indicates "Order".
Hence, The answer is Ordinal
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