If the three numbers of a square in the complex plane are [tex]-19+32i,-5+12i and -22+15i[/tex] , then the fourth complex number [tex]-2+19i[/tex].
Given [tex]-19+32i,-5+12i and -22+15i[/tex] are three numbers.
Complex numbers are those numbers which extends the real numbers with an imaginary i. In this [tex]i^{2}=-1[/tex]. Major complex numbers are in the form a+ bi where a and b are real numbers.
let the fourth complex numbers be [tex]x+yi[/tex]. Then according to question;
=[tex](-22+15i)-(-5+12i)[/tex]
=(cos π/2+i sin π/2) [tex](x+yi)-(-5+12i)[/tex]
[tex]-17+3i=-y+12[/tex][tex]+(x+5)i[/tex]
Now solving for x and y by equating both sides.
x=-2 and y=29
Put the value of x and y in [tex]x+yi[/tex]
Z=-2+29i
Hence if the three numbers which forms vertices of a square are [tex]-19+32i,-5+12i,-22+25i[/tex] then the fourth complex numbers be [tex]-2+29i[/tex].
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The function f(x) = -√x is shown on the graph.
-6
43
4-
N
-7-6-5-4-3-2-₁ 1 2 3 4 5 6 7 x
-2+
-3-
-4
Which statement is correct?
The domain of the function is all real numbers less
than or equal to -1.
The range of the function is all real numbers greater
than or equal to 0.
O The range of the function is all real numbers less
than or equal to 0.
The domain of the function is all real numbers less
than or equal to 0.
Answer: The range of the function is all real numbers less
than or equal to 0.
The correct statement for the given function f(x) = -√x is "The range of the function is all real numbers less than or equal to 0." So, the correct option is C.
The domain of the function is all real numbers that are greater than or equal to 0 but we know that the square root of a negative number is in the real number system.
The graph of the function shows that for each positive input i.e. the range values we get the output values that are negative or zero.
Therefore, the range of the function is all real numbers less than or equal to 0, which is option C.
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HELP PLEASE GIVING BRIANLEST
Answer:
Maybe the answer will be C. P (A and B )
Ans: C
Explanation:
I think it is option c , P(A and B)
as this is the only option which has the value of 80, which we got from the table
A cylindrical barrel of water has a base radius of 30 cm and is 110 cm high.
a) Find it’s volume in cm³.
b) Find it’s capacity in litres
( Hint is 1 cm³= 1 ml )
c) Find the number of bottles of water that can be filled from the barrel if each bottle holds 0.73 litres.
The volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
We have:
The radius of the cylindrical barrel r = 30 cm
Height of the cylindrical barrel h = 110 cm
Volume:
[tex]\rm V = \pi (30)^2 (110)[/tex]
V = 311017.67 cubic cm
The volume of litres:
V = 311.017 cubic ml (1 liter = 1000 cubic cm)
Number of bottles = 311.017 /0.73= 426 bottles
Thus, the volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.
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1. If x³ +3x²-4=0 has x=-2 as a root (zero), find the other two roots.
Answer:
1 and -2 (has a multiplicity of 2)
Step-by-step explanation:
so since x=-2 is a root then (x+2) is a factor of the polynomial. This means you can divide the polynomial by (x+2) by using synthetic or long division. So for this example I'll using synthetic division which is much more simple than long division
-2 | 1 3 0 -4
-2 -2 4
1 1 -2 0
(x+2)(x²+x-2)
Now you can factor the quadratic into
(x+2)(x-1)
x+2 = 0
x = - 2
x-1 =0
x = 1
What is the area of rectangle ABCD?
coordinate plane with rectangle ABCD at A 0 comma negative 1, B 0 comma 4, C 4 comma 4, and D 4 comma negative 1
Answer:
Area = 20 units
Step-by-step explanation:
A (-1,0)
B (0,4)
C (4,4)
D (4,-1)
i hope this is right
Answer:
Area = 20
Step-by-step explanation:
A (0,-1)
B (0, 4)
C (4, 4)
D (4, -1)
[tex] \frac{1 }{4 } \times \frac{3}{4} \div \frac{10}{3} [/tex]
What is the answer to the above equation?
Answer:
Step-by-step explanation:
Solution
This (after combining the top 2 fractions, is a 4 tier fraction.
1/4*3/4 = 3/16
So the question now becomes 3/16 ÷ 10/3
The rule for such a question is invert (turn up side down) the second fraction and multiply.
3/16 * 3/10 Combine
(3*3)/(16* 10)
9 / 160
0.05625
[tex]\bf{\dfrac{1}{4}\times\dfrac{3}{4}\div\dfrac{10}{3} }[/tex]
Multiply 1/4 by 3/4 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\bf{\dfrac{1\times3}{4\times4}\div\dfrac{10}{3} \ \ \to \ \ \ Multiply.}[/tex]
Do the multiplications in the fraction 1 × 3 / 4 × 4.
[tex]\bf{\dfrac{3}{16}\div\dfrac{10}{3} }[/tex]
Divide 3/16 by 10/3 by multiplying 3/16 by the reciprocal of 10/3.
[tex]\bf{\dfrac{3}{16}\times\left(\dfrac{3}{10}\right) }[/tex]
Multiply 3/16 by 3/10 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\bf{\dfrac{3\times3}{16\times10 } \ \ \to \ \ \ Multiply }[/tex]
Do the multiplications in the fraction 3 × 3 / 16 × 10
[tex]\bf{\dfrac{9}{160} \ \ \to \ \ Answer }[/tex]
[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer: Choice D) x is a real number
Reason:
We can replace x with any number we want without any restriction. There's no issues dealing with division by zero errors for instance, and we also don't have negatives under square roots to worry about. The domain of any linear function is always "the set of all real numbers".
Extra info: The domain in interval notation is [tex](-\infty, \infty)[/tex] which could be thought of as [tex]-\infty < x < \infty[/tex], i.e. x is between negative infinity and positive infinity.
Answer:
d
Step-by-step explanation:
What is the equation of the line that passes through the point (1,4) and has a slope of 4
Answer:
y = 4x
Step-by-step explanation:
Equation of line in point -y intercept form:
[tex]\sf \boxed{\bf y-y_1=m(x- x_1)}[/tex]
[tex]\sf x_1 = 1 \ ; \ y_1=4 \ \& \ m = 4[/tex]
y - 4 = 4(x -1)
y - 4 = 4*x - 4*1
y - 4 = 4x - 4
Add 4 to both sides
y = 4x - 4 + 4
y =4x
Fluffy the bunny ate 1/2 of a carrot in the morning, and he ate some more at night. By the end of the day, he still had 1/3 of the carrot left to eat. How much of the carrot did Fluffy the bunny eat at night?
Answer:
1/6
Step-by-step explanation:
the total carrot is 1/1 and fluffy ate 1/2 of it . this means half has been eaten and it is left with half so now 1/2 -1/3 ( carrot left in the morning - the carrot left now ) this will be 1/6
Lines l1 and l2 are parallel and l3 is a transversal.
Which statement is true?
A
m∠2+m∠4=180°
B
m∠2+m∠3=180°
C
m∠1=m∠4
D
m∠1=90°
Answer:
C. m∠1 = m∠4
Step-by-step explanation:
A. m∠2 + m∠4 = 180°
∠2 and ∠4 are vertically opp. angles which means m∠2 = m∠4.
Hence, it's a false statement.
B. m∠2 + m∠3 = 180°
∠2 and ∠3 are corresponding angles which means m∠2 = m∠3.
It's a false statement.
C. m∠1 = m∠4
∠1 and ∠4 are another pair of corresponding angles which clearly states that m∠1 = m∠4.
Therefore, it's a true statement.
D. m∠1 = 90°
As clearly visible in the diagram;
It's a false statement.
Calculate the area of the Parallelogram.
I will mark as brainliest, Please help quick!
Answer:
A = 42 cm²
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 6 and h = 7 , then
A = 6 × 7 = 42 cm²
In the square pyramid shown below, the slant height is 12 centimeters and the height of the pyramid is 7 centimeters.
To the nearest whole number, find the diagonal length of the base of the pyramid. In your final answer, include your calculations with reasoning for each step.
The diagonal of the square pyramid will be equal to 33.10 centimetres.
What is diagonal?The lines which connect the two opposite corners of any quadrilateral are called diagonal. here we have a square pyramid whose slant height and the vertex height are given and we have to find the diagonal length of the base.
Let the side of the square base of the pyramid is "a". Now the side will be calculated by the following relation.
[tex](\dfrac{a}{2})^2[/tex] = s² - H
[tex](\dfrac{a}{2})^2[/tex] = 12² - 7 = 137
a² = 137 x 4 = 548
a = √548 = 23.40 cm
Now the diagonal will be calculated by using the Pythagorean theorem
D² = 23.04² + 23.40²
D² = 548 + 548
D = √1096
D = 33.10 centimeter
Therefore the diagonal of the square pyramid will be equal to 33.10 centimetres.
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Use the Pythagorean theorem to find the distance on the coordinate plane.
Could someone help me with this question real quick?
Answer:
Width is 46 meter
Length is 86 meter
Given:
width = wlength = (w + 40)Formula:
Area of rectangle = Length × WidthTrial and improvement:
1st try with w = 50
w(w + 40) = 4000
50(50 + 40) = 4000
4500 ≠ 4000
Value too high.
2nd try with w = 45
w(w + 40) = 4000
45(45 + 40) = 4000
3825 ≠ 4000
Value too small
3rd try with w = 46
w(w + 40) = 4000
46(46 + 40) = 4000
3956 ≠ 4000
This value is somewhat near to the area value.
It is found that width = 46 m then length = (w + 40) = (46 + 40) = 86 m
Write the fraction as a decimal.
six tenths
0.6
0.06
6.0
1.6
Answer:
[tex]\huge\boxed{\dfrac{6}{10}=0.6}[/tex]
Step-by-step explanation:
[tex]0.6=\dfrac{6}{10}[/tex]
one digit after the decimal point - one zero in the denominator
[tex]0.06=\dfrac{6}{100}[/tex]
two digits after the decimal point - two zeros in the denominator
[tex]6.0=6[/tex]
[tex]1.6=1\dfrac{6}{10}\ \text{or}\ 1.6=\dfrac{16}{10}[/tex]
Write an equation for each translation of y=|x|
13 units down
y-13= |x|
y=1x1-13
y=1-13x1
y=1x1+13
The answer is y=|x|-13.
Answer:
y=|x|-13
Step-by-step explanation:
(08.01)
A new video game is expected to sell 120 copies the first hour at a local game store. After that, the sales will follow the function s(x) = 15(=
1) where x is the number of hours. What is the function that shows total sales, including the first hour?
Answer:
f(x)=15x+120
Step-by-step explanation:
trust
PLEASE HELP ME TO ANSWER THIS QUESTION THANK YOU!
Answer:
Step-by-step explanation:
a. 4cm * 9cm * 2cm = 72 cm^3
b. 5m * 4m * 9m = 180 m^3
c. 10dm * 36 dm^2 (because the square could also be represented as 6cm * 6cm) =360 dm^3
d. (56mm)^3 = 175616 mm^3
e. 10 m * 1 m^2 (because of the square) = 10m^3
To tell which cubic unit of measure that should be used:
⇒ we should examine the unit of the side lengths
First question (a):
a rectangular prism that is 4cm by 9 cm by 2cm⇒ must use cm³ as cubic unit of measure
⇒ as all sides are centimeters
⇒Answer: cubic centimeters or cm³
Second question(b):
a rectangular prism that is 5m by 4m by 9m⇒ must use m³ as cubic unit of measure
⇒ as all sides are meters
⇒Answer: cubic meters or m³
Third question(c):
a rectangular prism that gives only two side length: 10dm, 6dm⇒must use dm³ as cubic unit of measure
⇒ as all of the sides given are in decimeter
⇒Answer: cubic decimeter or dm³
Fourth question(d):
a cube that gives only one side length: 56mm⇒ must use mm³ as cubic unit of measure
⇒ as all the given sides with side lengths are in millimeters
⇒ Answer: cubic millimeters or mm³
Fifth question(e):
a rectangular prism with two side length: 1m, 10m⇒ must use m³ as cubic unit of measure
⇒ as all given sides with side lengths are in meter
⇒Answer: cubic meter or m³
In general:
⇒ when faced with these problems
⇒ look to the unit of measure of the majority of the side lengths
⇒ look to the unit of measure that the problem wants for the answer
Hope that helps!
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HURRRRYYY
Hurry pleaseee use elimination show your work
15y - 9x =-9 -8y+9x=12
Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
The solution to the exponential expression is as follows:
[tex]\mathbf{\dfrac{(2\times 3^{-2})^3(5\times 3^2)^2}{(3^{-2})(5\times 2)^2} = 2}[/tex][tex]\mathbf{=(3^3)(4^0)^2(3\times 2)^{-3}(2^2)=\dfrac{1}{2}}[/tex][tex]\mathbf{\dfrac{(3^7\times 4^7)(2 \times 5)^{-3}(5^2)}{12^7\times 5^{-1}\times 2^{-4}} = 2}[/tex][tex]\mathbf{\dfrac{(2\times 3)^{-1}\times 2^0}{(2\times 3)^{-1}}= 1}[/tex]What are exponential expressions?Exponential expressions are convenient ways to express the mathematical power of a number in short forms.
Simplifying the following expressions given:
1.
[tex]\mathbf{\dfrac{(2\times 3^{-2})^3(5\times 3^2)^2}{(3^{-2})(5\times 2)^2} }[/tex]
Applying the exponent rule: [tex]\mathbf{(a\times b)^n = a^n b^n}[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 5^2\times 81}{3^{-2}\times 5^2\times2^2} }[/tex]
cancel out the common factor, we have:
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 81}{3^{-2}\times2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^4}{3^{-2}\times2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^6}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times 3^6}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times729}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 }{2^2} = 2}[/tex]
2.
[tex]\mathbf{=(3^3)(4^0)^2(3\times 2)^{-3}(2^2)}[/tex]
= [tex]\mathbf{\dfrac{1}{2}}[/tex]
3.
[tex]\mathbf{\dfrac{(3^7\times 4^7)(2 \times 5)^{-3}(5^2)}{12^7\times 5^{-1}\times 2^{-4}} = 2}[/tex]
4.
[tex]\mathbf{\dfrac{(2\times 3)^{-1}\times 2^0}{(2\times 3)^{-1}}= 1}[/tex]
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True or false for 1 and 3
Step-by-step explanation:
I think 1 is true.
3 is false. it's $10 per hour
Linear equations in two variables
Graph y = -4 then explain why it is not a function, can somone ELI5
Answer:
y=-4 is a function
Step-by-step explanation:
It passes the vertical line test, and each x has only one y, so it is a function.
x = -4 is NOT a function because one x has multiple y values. It does not pass the vertical line test.
Find the surface area of a hexagonal prism if the length of each side of the hexagonal base is 4 cm and the height is 7 cm.
The surface area of a hexagonal prism willl be 251.13844 cm².
What is the surface area?The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.
A=6ah+3√3a²
A=6×4×7+3√3×4²
A≈251.13844
Hence the surface area of a hexagonal prism willl be 251.13844 cm².
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PLEASE HELP i WOULD GREATLY APPERTICATE IT
Answer:
Factor 4x^3 - 7x^2y+15y-30y
Factor:4x^3-7x^2-30/y+15:
⬇
4x^3y-7x^2y+15y-30
y
give me da answer.........................................................................
Answer:
Ok ya sure I would love to. :)
Step-by-step explanation:
Oh wait….
*Crickets chirping*
Matching a Table to a Graph On a coordinate plane, a line goes through points (negative 1, 0), (0, 1), and (1, 2). Which table goes with the graph? A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled y with entries 0, 4, 6, 8. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled y with entries 0, 2, 4, 6. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled y with entries 0, 1, 2, 3.
At x = -1 , 0 ,1 ,2 , the y value = 0, 1, 2, 3, Option C is the correct answer.
What is a Function ?A function is a law that relates a dependent variable to an independent variable.
The points of line are
(- 1, 0), (0, 1),(1, 2).
The equation of the line formed will be
y = mx +c
[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
m = 1
y = x +c
at x = 0 , y =1
c = 1
The equation is
y = x+1
The option 1 is
x = - 1, 0, 1, 2.
y1 = 0, 4, 6, 8.
y2= 0, 2, 4, 6
y3 =0, 1, 2, 3.
From the equation
at x = -1 , 0 ,1 ,2
the y value = 0, 1, 2, 3
Therefore Option C is the correct answer.
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Here is a sketch of y=x^2 +bx+c
Answer:
Step-by-step explanation:
NEED HELP ASAPP PLEASE!!
Each step of the proof are:
a || b∠1 ≅ ∠5∠1 ≅ ∠5∠5 ≅ ∠7∠5 ≅ ∠7∠1 ≅ ∠7∠1 ≅ ∠7How to complete the proof?The given parameter is:
Lines a and b are parallel.
This is represented as; a || b
Corresponding angles are equal.
∠1 and ∠5 are corresponding angles.
So, we have: ∠1 ≅ ∠5
Also, they are congruent.
So, we have ∠1 ≅ ∠5
Vertical angles are equal.
∠5 and ∠7 are vertical angles.
So, we have: ∠5 ≅ ∠7
Also, they are congruent.
So, we have ∠5 ≅ ∠7
According to the transitive property;
If ∠1 ≅ ∠5 and ∠5 ≅ ∠7, then ∠1 ≅ ∠7
Hence, it has been proved that ∠1 ≅ ∠7
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[tex]10 ^{k - 2} = 100[/tex]
find the value of k
Answer:
k = 4
Explanation:
[tex]\sf 10^{k-2}=100[/tex]
make bases similar
[tex]\sf 10^{k-2}=10^2[/tex]
cancel out the bases
[tex]\sf k-2=2[/tex]
add '2' on both sides
[tex]\sf k-2+2=2+ 2[/tex]
simplify the following
[tex]\sf k =4[/tex]
[tex]\frac{4x}{x-1} -\frac{5x}{x-2}=\frac{2}{x^{2} 3x+2}[/tex]
The value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2
How to solve the equation?The equation is given as:
[tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex]
Start by taking the LCM
[tex]\frac{4x(x - 2) - 5x(x - 1)}{(x - 1)(x -2)} = \frac{2}{x^2 - 3x + 2}[/tex]
Expand the denominator
[tex]\frac{4x(x - 2) - 5x(x - 1)}{x^2 -3x +2} = \frac{2}{x^2 - 3x + 2}[/tex]
Cancel out the common factor
4x(x - 2) - 5x(x - 1)= 2
Expand
[tex]4x^2 - 8x - 5x^2 + 5x = 2[/tex]
Evaluate the like terms
[tex]-x^2 - 3x = 2[/tex]
Rewrite as:
[tex]x^2 + 3x + 2 = 0\\[/tex]
Expand
[tex]x^2 + 2x + x + 2 = 0[/tex]
Factorize
x(x + 2) + 1(x + 2) = 0
Factor out x + 2
(x + 1)(x + 2) = 0
Solve for x
x = -1 or x = -2
Hence, the value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2
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