On comparing, we get {a} = 0 and {b} = 4.
What is the general form of a complex number?The general form of a complex number is -
z = a + ib
Given is the number as -
√-16
We can write the number √-16 in the form of (a + ib) as follows. We have -
√-16
√(- 1 x 16)
√(i² x 16)
√i² x √16
i√16
0 + i√16
0 + 4i
Therefore, on comparing, we get {a} = 0 and {b} = 4.
To solve more questions on complex number, visit the link -
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1. Write an integer that can
represent 200 years ago?
someone please help with this question!! i will give you brainly if it’s right
Answer:
2000 ft
x= 175/ tan5 which is approximately 2000.
#The extremities of the diagonal of a square are (1,1 )and (-2, -1).Obtain the two other vertices and the equation of a next diagonal.
#
find the area of the triangle with vertices(1,2),(2,3),and(4,5).what inference can you draw about the points from your upshot?
Answer:
(i) (-3/2, 3/2) and (1/2, - 3/2)
6x + 4y = - 3
(ii) Points are col linear
Step-by-step explanation:
Let the coordinates of the point(lower) be (a, b) and that of upper be (x, y).
Using mid point formula,
Mid point of diagonal(using the given points) is:
= ( (-2+1)/2 , (-1+1)/2) = (-½ , 0)
Using (a, b) and (x, y) :
= ( (a+x)/2 , (b+y)/2 ) = (-1/2, 0)
Which means, a+x= -1 & b + y = 0
Therefore, x = - 1 - a & b = - y
Using distance formula, diagonal = √(-2-1)² + (-1-1)² = √13
Knowing the relation in diagonal and side, side = diagonal/√2 = √13/√2 = √(13/2)
Again using distance formula, diagonal = √13
=> √(x - a)² + (y - b)² = √13
=> (-1-a -a)² + (-b - b)² = 13
=> a² + b² + a = 3 ... (1) [solved directly]
Length of side = √(13/2)
=> √(a-(-2))² + (b-(-1))² = √(13/2)
=> a² + b² + 4a + 2b = 3/2 ...(2)
On solving (1) and (2):
a = 1/2 or -3/2, but a lies in 4th quadrant so a > 0, thus, a = 1/2
b = -3/2 or 3/2, but b lies in 4th quadrant so b < 0, b = -3/2
Therefore,
x = - 1 - a = -1 - 1/2 = -3/2
y = - b = - (-3/2) = 3/2
Vertices are (x, y) = (-3/2, 3/2) and (a, b) = (1/2, -3/2)
Equation is just a relation in y and x, for a relation:
Subtract (1) from (2):
3a + 2b = -3/2 => 6a + 4b = - 3
By merely replacing a, b by x, y
6x + 4y = -3 is the required equation
(ii):
Ar. of ∆ = ½ | 1(3 - 5) + 2(5 - 2) + 4(2 - 3) |
Ar. of ∆ = ½ | -2 + 6 - 4 | = 0
As the area of the ∆ is 0, the given points don't form ∆, they are col linear.
Someone know this? Pls I really need help
Answer:
Step-by-step explanation:
d₃₄ = Value in the 3rd row and 4th column
= 0
m₁₃ = Value in the 1st row and 3rd column
= 2
k₂₁ = Value in the 2nd row and 1st column
= 1
What is the area of the school crossing sign represented below?
15 inches 15 inches
15 inches
15 inches
help me plsss
Last month we had only five sunny days. There were 30 days in all last month.
What was the ratio of sunny days to the total number of days? What was the ratio
of sunny days to days that were not sunny?
Answer:
6
Step-by-step explanation:
30 ÷ 5 = 6
Answer:
6
Step-by-step explanation:
it is 6
Eric went for a car rental for the weekend. He can choose one of two plants. The first plant has an initial fee of $44 and cost an additional $.12 per mile driven. The second plan has an initial fee of $57 and cost an additional eight cents per mile driven. For what amount of driving do the two plants cost the same?
Answer:
325
Step-by-step explanation:
.12x + 44 = .08x + 57
.04x = 13
x= 325
please help i have been stuck on this for 3 hours
Answer:
The one you selected is the correct one
Answer:
(5/7) x 56 = 40 is correct
Step-by-step explanation:
How have you been stuck on this for 3 hours
Please help will give brainliest
Answer:
angle a+angle b+angle c=180°
90°+38°+angle c=180°
128°+angle c=180°
angle c=180°-128°
angle c =52°
52°+n°=180°
n=180°-52
n=128°
What is the missing length?
A. 15
B. 30
C. 8
D. 7
Answer:
red and blue are not a Selection!!!!!
) Cars are parked in line as they come off the assembly lines. There are three models: red cars which take up 2 spaces, blue cars which also take up 2 spaces, and green cars which take up only 1 space. Let an be the number of ways of filling the first n parking spaces with red, blue and green cars.
Answer:
Hello your question has some missing information below is the complete question
answer :
[tex]a_{n} = a_{n-2} + a_{n-2} + a_{n-1}[/tex]
Step-by-step explanation:
Red car and Blue car take up 2 spaces each
Green cars take up 1 space
lets determine the number of ways of filling up the parking spaces
i) First lets assume the last space is filled by Green car then there will be [tex]n^{th}[/tex] space occupied hence there will be ( n - 1 ) spaces left to be filled in [tex]a_{n-1}[/tex] ways
ii) lets assume the last space is filled by either a Red car or a Blue car then there will be [tex]n^{th} + ( n -1 )^{st}[/tex] parking space occupied hence there will be
( n - 2 ) spaces left to be filled in [tex]a_{n-2}[/tex] ways
Hence A closed formula for [tex]a_{n}[/tex]
[tex]a_{n} = a_{n-2} + a_{n-2} + a_{n-1}[/tex]
where : a1 = 1 way , a2 = 3 ways
I can't figure this out
9514 1404 393
Answer:
143 in²
Step-by-step explanation:
The figure is dimensioned in such a way that it can be divided easily into three rectangular areas. The top rectangle is 10 in wide and 7 in high. The vertical rectangle below that is 4 in wide and 12 in high, and the square appendage on the right is 5 in square.
Then the total area is the sum of products of length and width:
A = (10 in)(7 in) + (4 in)(12 in) + (5 in)(5 in) = (70 +48 +25) in²
A = 143 in²
The area of the irregular figure is 143 in².
A paper weight is made in the shape of a triangular pyramid. The dimensions of the paper weight are shown. A triangular pyramid. The base has a base of 9 centimeters and height of 6 centimeters. The height of the pyramid is 7 centimeters. [Not drawn to scale] The formula for the volume of a triangular pyramid is V = one-third B h. Which expression can be used to find the value of B, the area of the base of the pyramid? B = one-half (9) (6) B = (9) (6) B = one-third (9) (7) B = (9) (7)
Answer:
B=one half (9) (6)
Step-by-step explanation:
I took the test
Please help will give brainliest
Answer:
A+B=180°(linear pair)
a+ 52°=180°
a=180°-52°
a=128° is your answer
In order to play on the 7th grade basketball team you must buy a team uniform. Last year a uniform cost $40, but this year a uniform cost $48. What is the percent of change?
Show your work here:
INCLUDE ANSWER AND TY
Answer:
20%
Step-by-step explanation:
The uniform cost $8 more than last year.
Last year was $40
Find what percent of 40 is 8.
8/0.4 = 20
the percent change is 20%
Calculus helpppppppppppppppp
Answer:
[tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
FunctionsFunction NotationExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Logarithms and Natural LogsLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex]Logarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Derivatives
Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Logarithmic Derivative: [tex]\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x\sqrt[3]{1 + x^2}[/tex]
Step 2: Rewrite
[Equality Property] ln both sides: [tex]\displaystyle lny = ln(x\sqrt[3]{1 + x^2})[/tex]Logarithmic Property [Multiplying]: [tex]\displaystyle lny = ln(x) + ln(\sqrt[3]{1 + x^2})[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle lny = ln(x) + ln \bigg[ (1 + x^2)^\bigg{\frac{1}{3}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = ln(x) + \frac{1}{3}ln(1 + x^2)[/tex]Step 3: Differentiate
ln Derivative [Implicit Differentiation]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx} \bigg[ ln(x) + \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{d}{dx} \bigg[ \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{1}{3}\frac{d}{dx}[ln(1 + x^2)][/tex]ln Derivative [Chain Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \frac{d}{dx}[(1 + x^2)][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \bigg( \frac{d}{dx}[1] + \frac{d}{dx}[x^2] \bigg)[/tex]Basic Power Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot (2x^{2 - 1})[/tex]Simplify: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot 2x[/tex]Multiply: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{2x}{3(1 + x^2)}[/tex][Multiplication Property of Equality] Isolate y': [tex]\displaystyle y' = y \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex]Substitute in y: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex][Brackets] Add: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{5x^2 + 3}{3x(1 + x^2)} \bigg][/tex]Multiply: [tex]\displaystyle y' = \frac{(5x^2 + 3)\sqrt[3]{1 + x^2}}{3(1 + x^2)}[/tex]Simplify [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Implicit Differentiation
Book: College Calculus 10e
Please help, brainliest for correct answer
Answer:
The correct answer is m∠2 = 120°
Step-by-step explanation:
There is a triangle rule that states the outer angle of an angle in a triangle is equal to the sum of the remaining two angles in that triangle, which means that m∠2 = 52° + 68° = 120°. This can be proven correct because the sum of two of the angles in the triangle is 120°, which means the final angle is 60°. Since m∠2 is the outer angle of 60°, that means it will be 180° - 60° or 120°.
Answer:
m<2+= 60
Step-by-step explanation:
what is the value of x in each figure
PLEASE DON'T GIVE ME A LINK
Answer:
x=43
Step-by-step explanation:
3x+17+x-9=180
4x+8=180
4x=180-8
4x=172
x=43
P = 3. Q = -2. Solve 4PQ
Answer:
-24
Step-by-step explanation:
4(3)(-2) = -24
plz, help. I need it...
Answer: (6, 3)
Step-by-step explanation:
answer and show proof for branliest
Answer:
-2(4 - 1)
Step-by-step explanation:
Choice A: ❌
9-(-17)
9 + 17 = 26
Choice B: ❌
(4 - 16)/(-2)
(-12)/(-2)
6
Choice C: ✅
-2(4 - 1)
-2(3)
-6
Choice D: ❌
3 x (-2) x (-1)
-6 x (-1)
6
Answer:
- 2(4 - 1)
Step-by-step explanation:
9 - (- 17)
9 + 17 = 26
[tex]\frac{4 - 16}{-2}[/tex] = 12
- 2(4 - 1)
- 2(3) = - 6
3 × - 2 × - 1 = 6
1 . What is the distance between the two points.
(0,5 1,3), (-0,4, -1,3) ?
2. What is the distance between the two points
(6, -3), (2, -4)
In ABC, the measure of the largest angle is 16 less than 4 times the smallest angle. The measure of the middle angle is 7 more than half the measure of the largest angle. What is the measure of the middle angle?
Answer:
Step-by-step explanation:
Let A ≤ B ≤ C
largest angle is 16 less than 4 times the smallest angle
C = 4A-16
middle angle is 7 more than half the measure of the largest angle
B = C/2 + 7
A+B+C = 180°
A = 28 ⅐°
B = 55 2/7°
C = 96 4/7°
Answer choices
4 feet
5feet
6feet
8feet
Please help if you send a link I will report
Answer:
d
Step-by-step explanation:
only reasonable answer
Need help if you have the time and i need explanation for this (NO LINKS PLS)
Answer:
ask ur question i will try to help
Step-by-step explanation:
Calculate the slope of a line that goes through points (3, 4) and (0, 0).
Question 5 options:
3/4
3
4
4/3
Answer:
4/3
Step-by-step explanation:
0-4/0-3
-4/0-3
-4/-3
4/3
Answer:
Step-by-step explanation:
3\4
what is 4 1/8 - 2 2/3 to the nearest whole number
Answer:
1 11/24
Step-by-step explanation:
:))
Help me I need this really bad and I need a good grade I’m behind on school
Answer:
If you share 7 apples equally with 3 people, then there are 2 1/3 apples per person.
The number 2 represents the number of whole apples each individual gets.
The denominatior, 3, represents how many times an apple will have to be split to divide equally
The numerator, 1, represents how many 3rds each person gets.
-2y + x +
3
How many terms are in the expression
Answer:3
Step-by-step explanation:
In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student chosen randomly from the class has a cat or a dog?
Has a cat Does not have a cat
Has a dog 9 2
Does not have a dog 4 5
Answer:
0 students have a cat and 92 students have a dog
The probability that a student is chosen randomly from the class has a cat or a dog is 15/20.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
The class has a cat and a dog = 9
Has a dog and does not have a cat = 2
Does not have a dog and has a cat = 4
Does not have dog and cat = 5
The total strength of the class is 20
The probability that a student is chosen randomly from the class has a cat or a dog = Number of favorable outcomes / total number of outcomes
P(E) = 15 /20
Hence, The probability that a student is chosen randomly from the class has a cat or a dog is 15/20.
Learn more about probability :
https://brainly.com/question/795909