By dividing the complex number 5 / -5[tex]i}[/tex] we get the answer as :
5 / -5[tex]i}[/tex] = [tex]i}[/tex]
Simplification:A complex number is a number system that extends the real numbers with a specific element denoted I known as the imaginary unit, and satisfying the equation [tex]i^{2}[/tex] = -1; each complex number can be expressed in the form a + bi, where a and b are real numbers.
Steps to simplify complex number:
On both the numerator and the denominator, multiply the given complex number by the conjugate of the denominator.Distribute the number in the numerator and denominator to remove the parentheses.Simplify i's powers.Given complex number , 5 / -5[tex]i}[/tex]
multiply the numerator and denominator with conjugate [tex]-i /-i[/tex]
= [tex]5(-i)/-5i(-i)[/tex]
by again simplifying we get ,
= [tex]-5i/-5[/tex]
-5 common from numerator and denominator is eliminated
so we get ,
5 / -5[tex]i}[/tex] = [tex]i[/tex]
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mom walks at a speed of 6 miles per hour. how long will it take her to walk 1 mile?
The Distributive Property Determine if the given expressions are equivalent
1. 3x + 12 and 3( 4 + x ) 2. 2( 3x - 30 ) and 6 - 30 3. 4 ( 5 - 4x ) and 20x - 16
The given expressions have been evaluated to be equivalent or not equivalent as follows:
3(4 + x) and 3x + 12: Equivalent.2(3x - 30) and 6 - 30: Not equivalent.4(5 - 4x) and 20x - 16: Not equivalent.What is the distribution property?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a specific number, the same output (result) would be produced as when each addend is multiplied respectively by the number, and the products are added together.
Mathematically, the distributive property of multiplication is given by this expression:
a(b + c) = ab + ac.
Next, we would determine whether or not the given expressions are equivalent:
3x + 12 and 3(4 + x):
Opening the bracket, we have:
3(4 + x) = 3x + 12 (Equivalent).
2(3x - 30) and 6 - 30;
Opening the bracket, we have:
2(3x - 30) = 6x - 60
2(3x - 30) = 6 - 30 (Not equivalent).
4(5 - 4x) and 20x - 16;
Opening the bracket, we have:
4(5 - 4x) = 20 - 16x
4(5 - 4x) = 20x - 16 (Not equivalent).
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Please help immediately!!
Complete the table with ordered pairs that give coordinates of points that lie on the line shown in the graph
Use the tangent identity to
find tan x.
sin x =
44
45
tan x =
COS X =
[?]√]
√89
4
Answer:
[tex]tan(x)=\frac{44\sqrt{89}}{89}[/tex]
Step-by-step explanation:
tan is defined as: [tex]tan(x)=\frac{opposite}{adjacent}[/tex]
sin is defined as: [tex]sin(x)=\frac{opposite}{hypotenuse}[/tex]
cos is defined as: [tex]cos(x)=\frac{adjacent}{hypotenuse}[/tex]
We can also define tan as: [tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
because plugging in the definitions of sin and cos in we get: [tex]tan(x)=\frac{(\frac{opposite}{hypotenuse})}{(\frac{adjacent}{hypotenuse})}\\\\tan(x)=\frac{opposite}{hypotenuse}*\frac{hypotenuse}{adjacent}\\\\tan(x)=\frac{opposite}{adjacent}[/tex]
which you'll notice is the original definition of tan(x)
So using this definition of tan(x) we can use the givens sin(x) and cos(x) to find tan(x)
[tex]sin(x)=\frac{44}{45}\\\\cos(x)=\frac{\sqrt{89}}{45}\\\\tan(x)=\frac{sin(x)}{cos(x)}[/tex]
plugging in sin(x) and cos(x) we get:
[tex]tan(x)=\frac{\frac{44}{45}}{\frac{\sqrt{89}}{45}}\\\\tan(x)=\frac{44}{45}*\frac{45}{\sqrt{89}}\\\\tan(x)=\frac{44}{\sqrt{89}}[/tex]
We usually don't like square roots in the denominator, and from here we want to rationalize the denominator which we do by removing the square root from the denominator.
We can do this by multiplying the fraction by: [tex]\frac{\sqrt{89}}{\sqrt{89}}[/tex] which doesn't change the value of the fraction since it simplifies to 1, but it gets rid of the square root in the denominator
[tex]tan(x)=\frac{44}{\sqrt{89}}*\frac{\sqrt{89}}{\sqrt{89}}\\\\tan(x)=\frac{44\sqrt{89}}{89}[/tex]
B.10 Midpoint formula: find the midpoint 2YG
A line segment has the endpoints U(19, 6) and V(17, -3). Find the coordinates of its midpoint
M.
Write the coordinates as decimals or integers.
M =
Submit
Work it out
Please help
Answer:
Midpoint formula is given as [(x1+x2)÷2, (y1+y2)÷2], where x and y are coordinates of the points.
Midpoint = [(19+17)÷2, (6+(-3))÷2]
= (36÷2, 3÷2)
= (18, 1.5)
write the equation of the line in point-slope form, that is parallel to y=5/2x + 1 and passes through the point (-3,1)
Answer:
[tex]\sf y = \dfrac{5}{2}x +\dfrac{17}{2}[/tex]
Step-by-step explanation:
[tex]\sf y =\dfrac{5}{2}x+1[/tex]
m= 5/2
Parallel lines have same slope.
Slope y-intercept form: y = mx +b
Here, m is the slope and b is the y-intercept
[tex]\sf y = \dfrac{5}{2}x + b[/tex]
Point (-3,1) passes through the required line. Substitute (-3,1) in the above equation and find 'b'.
[tex]\sf 1 = \dfrac{5}{2}*(-3)+b\\\\1 =\dfrac{-15}{2}+b\\\\[/tex]
[tex]\sf 1 +\dfrac{15}{2}=b\\\\\dfrac{2+15}{2}=b\\\\\\ \boxed{b= \dfrac{17}{2}}[/tex]
[tex]\sf \bf y = \dfrac{5}{2}x+\dfrac{17}{2}[/tex]
Use the parabola tool to graph the quadratic function f (X) =x2 - 12x +27
Answer:
Step-by-step explanation:
[tex]f(x)=x^2-12x^2+27\\f(x)=x^2-2(x)(6)+6^2-6^2+27\\f(x)=x^2-2(x)(6)+6^2-36+27\\f(x)=(x-6)^2-9[/tex]
This is the graph of the function f(x)=x² shifted right about the x-axis
by 6 units and dropped down about the y-axis by 9 units
(Scientific Notation in the Real World MC)
A TV show had 5.6 x 105 viewers in the first week and 4.1 x 105 viewers in the second week. Determine the average number of viewers over the two weeks and write the final answer in scientific notation.
9.7 x 1010
9.7 x 105
4.85 x 1010
4.85 x 105
The average number of viewers over the two week is D. 4.85 x 10^5.
How to calculate the value?It should be noted that the scientific notation simply has to do with writing of numbers that are either too large or too small. This will be illustrated thus:
In this case, the TV show had 5.6 x 10^5 viewers in the first week and 4.1 x 10^5 viewers in the second week.
Therefore, the average number of viewers over the two weeks will be:
= (5.6 × 10^5) + (4.1 × 10^5) / 2
= 4.85 × 10^5
Note that we had to divide by 2 since it's average.
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What is the slope of the line represented by the equation y = 4/5x -3?
Answer: 4/5
Step-by-step explanation:
y = mx + b
m represents the slope in this line.
Answer:
4/5
Step-by-step explanation:
Equation is in slope intercept form:
[tex]y = mx + b[/tex]
where m is the slope and b us the y-intercept
so, slope is 4/5
If the quadratic equation is
y=x²
what is y when x = 3
Plug in 3 in the place of x and simplify
[tex]y=(3)^{2} \\y=3*3\\y=9[/tex]
y=9
"I NEED HELP PLS" The following figure is made of 1 triangle and 2 rectangles.
Find the area of each part of the figure and the whole figure.
Figure Area (square units)
Rectangle A
Triangle B
Rectangle C
Whole figure
The value of the area are;
Rectangle A = 54 square units
Triangle B = 2 square units
Rectangle C = 6 square units
Whole figure = 62 square units
How to determine the area of the composite figureThe formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleFrom the figure shown, we have two rectangles
Area of the bigger rectangle;
Length = 9
Width = 6
Now, substitute the value
Area = 9(6)
Multiply through
Area = 54 square units
Area of the smaller rectangle
Length = 9 - 7 = 2
Width = 9 - 6 = 3
Substitute the values
Area = 2(3)
Multiply through
Area = 6square units
The formula for area of a triangle is expressed as;
Area = 1/2 base× height
Base = 9 - 6 = 3
Height = 9 - 2 = 3
Substitute the value
Area = 1/ 2 ×2(3)
Area = 6/ 3
Area = 2
The total area = Rectangle A + rectangle B + Triangle
Total area = 54 + 6 + 2
Total area = 62 square units
Hence, the area is 62square units
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Answer:
A=54 B=3 Whole=73
Step-by-step explanation:
I know this because i did this aswell
Consider a rectangular prism with a volume of 24 cubic centimeters. What could be the dimensions of the rectangular prism? Match each set of length and width with the correct height to complete the possible dimensions of rectangular prisms with volumes of 24 cubic centimeters. Prism M Length = 4 cm Width = 1 cm Prism W Length = 2 cm Width = 2 cm Prism Z Length = 6 cm Width = 1 cm Prism J Length = 2 cm Width = 4 cm Prism R Length = 2 cm Width = 3 cm Prism F Length = 1 cm Width = 8 cm
The dimensions of the rectangular prisms are:
Prism M: l=4 cm , w=1 cm and h=6 cm
Prism W: l=2 cm , w=2 cm and h=6 cm
Prism Z: l=6 cm , w=1 cm and h=4 cm
Prism J: l=2 cm , w=4 cm and h=3 cm
Prism R: l=2 cm , w=3 cm and h=4 cm
Prism F: l=1 cm , w=8 cm and h=3 cm
Given, a rectangular prism with a volume of 24 cm³
Dimensions of the prism if the volume is 24 cm³.
Prism M:
l=4 cm and w=1 cm
we know that volume = h×l×w
h×4×1=24
4h=24
h=24/4
h=6 cm
Prism W:
l=4 cm and w=2 cm
we know that volume = h×l×w
h×2×2=24
4h=24
h=24/4
h=6 cm
Prism Z:
l=4 cm and w=1 cm
we know that volume = h×l×w
h×6×1=24
6h=24
h=24/6
h=4 cm
Prism J:
l=2 cm and w=4 cm
we know that volume = h×l×w
h×2×4=24
8h=24
h=24/8
h=3 cm
Prism R:
l=2 cm and w=3 cm
we know that volume = h×l×w
h×2×3=24
6h=24
h=24/6
h=4 cm
Prism F:
l=1 cm and w=8 cm
we know that volume = h×l×w
h×1×8=24
8h=24
h=24/8
h=3 cm
hence we get the required dimensions.
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an airline has 30 airplanes in los angeles (la), 12 airplanes in st. louis (sl), and 8 airplanes in dallas (d). during an eight-hour period, 20% of the planes in la fly to sl and 10% fly to d. of the planes in sl, 25% fly to la and 50% fly to d. of the planes in d, 12.5% fly to la and 50% fly to sl. how many planes are in each city after 8 hours?
Using proportions, the number of planes in each city after 8 hours is given as follows:
Los Angeles: 25.St. Louis: 13.Dallas: 12.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division, with the given ratios.
One example of application of proportions is for percentage problems, as the total amounts are multiplied by the decimal equivalent of the percentage to find the equivalent amounts.
The planes in Los Angeles after 8 hours are given as follows:
70% of 30 (that were already in Los Angeles).25% of 12(planes that were in St. Louis).12.5% of 8(planes that were in Dallas).Hence the amount is:
0.7 x 30 + 0.25 x 12 + 0.125 x 8 = 25.
The planes in St. Louis after 8 hours are given as follows:
20% of 30 (planes that were in Los Angeles).25% of 12(planes that were already in St. Louis).50% of 8(planes that were in Dallas).Hence the amount is:
0.2 x 30 + 0.25 x 12 + 0.5 x 8 = 13.
Initially, there were 50 planes, and 25 + 13 = 38 are in either Los Angeles or St. Louis, hence the remaining 50 - 38 = 12 are in Dallas.
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how do I find the correct answer for the blank?
5.36 mixed number simplest form
To write a given number 5.36 in the mixed number is [tex]5\frac{36}{100}[/tex] and in the simplest form it is written as 134 / 25 .
As given in the question,
Given number in decimal form is equal to 5.36
5 is the whole number and 0.36 can be written as 36 /100.
Mixed number of the given number 5.36 is equal to
= 5 ( 36 / 100)
Reduced the mixed number to get the simplest form :
5 ( 36 / 100)
= 5 ( 9 / 25)
= 134 / 25
Therefore, to write a given number 5.36 in the mixed number is [tex]5\frac{36}{100}[/tex] and in the simplest form it is written as 134 / 25 .
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what is the value of 7 in the number 345.79
Answer: 345.79 - The value of the digit 7 is 7 thousandths, or 0.007.
sorry if this doesn't help..
Multiply. 1. (5.2x)(1.9x)
Answer:
9.88x
Step-by-step explanation:
multiply both numbers together
10^-3 x 10^6
please write in the form of powers/ index notation (for example, 7^5 or 10^-4)
It should be noted that 10^-3 × 10^6 in scientific notation is 10³.
How to illustrate the information?It should be noted that scientific notation is simply used in Mathematics to express the numbers that are either too small or too large.
This will be illustrated based on the information given. In this case, we want to multiply 10^-3 × 10^6. This will be illustrated thus:
= 10^-3 × 10^6.
It should be noted that since the question is about multiplication, the powers will be added.
= 10^-3 × 10^6.
= 10³
The answer is 10³.
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Question 2 (10 points)
Answer:
125.
Step-by-step explanation:
5^3
= 5 * 5 * 5
= 25 * 5
= 125.
A rectangle with a width of x feet and height of StartFraction 7 over 2 EndFraction feet.
Jack is building a rectangular fence for his ferret. He has 20 feet of fencing and wants the short side of the fence to be 7
2
feet. How long will the other side of the fence be? Write the answer in decimal form.
The long side will be
feet.
The other side of the fence based on the information illustrated is 6.5 feet.
How to calculate the length?It should be noted that the perimeter of a rectangle is illustrated as:
= 2(length + width)
In this case, the width is given as 7/2 = 3.5 feet.
It should be noted that the perimeter is given as 20 feet.
Therefore, the length will be:
2(length + width) = 30
2(length + 3.5) = 20
2Length + 7 = 20
2L = 20 - 7
2L = 13
L = 13/2
L = 6.5
Therefore, the length is 6.5 feet.
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PLEASE, PLEASE HELP WILL GIVE BRAIBNLIEST PLEASE HELP!!! QUESTION IN THE IMAGE BELOW.
Answer:
25/6
Step-by-step explanation:
We determine the scale factor by comparing the lengths of corresponding sides of the square.
The length of O’N’=15 and the length of ¯¯¯¯¯¯¯¯¯¯¯ON=9
The equation for the scale factor, k is then given by:
O’N’=kON
15=9k
K= 15/9= 5/3.
The scale factor is k= 5/3
what percent of 30 is 36
Answer:
10.8
Step-by-step explanation:
30% of 36
= 30/100 * 36
= 3/10 * 36
= 108/10
= 54/5
= 10.8
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the following question
Answer:
angle ODC=30°
Step-by-step explanation:
Parallel to the line now draw another line PQ
If I have £450 and I’m going away to India and currency conversion is £1=99.40 how much would I have
Answer:
Step-by-step explanation:
450 * 99.40 = 44730
What is the equation of the line that is perpendicular to y = 2x + 3 and passes through the point (−4, 8).
y = 2x + 16
y = 2x − 20
y equals negative one-half times x
y equals negative one-half times x plus 6
The equation of the line that is perpendicular to y = 2x + 3 and passes through the point (−4, 8) is y = - 1 / 2 x + 6(y equals negative one-half times x plus 6)
How to find equation of a line?The equation of the line is perpendicular to y = 2x + 3 and passes through the point (−4, 8).
Therefore, perpendicular lines follows the rule:
m₁m₂ = -1
Hence,
2m₂= -1
m₂ = - 1 / 2
Therefore, let's find the slope of the line using (-4, 8)
8 = - 1 / 2 (-4) + b
b = 8 - 2
b = 6
Therefore, the equation of the line is y = - 1 / 2 x + 6
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Answer: The answer is D- y= -1/2x+6
omsomfigure2.52base a 20 cmfigure B:ta20 cm5 pmfigure.boromomsomfigure D:tasarea 2018.paretAmong these figures, gureand figurehave the same volume
We will compute the volume of each figure.
1) Figure A
We have a cone with:
• Ab = base area = 20 cm²,
,• h = heigh = 5 cm.
The volume of the cone is:
[tex]V_A=\frac{1}{3}\cdot A_b\cdot h=\frac{1}{3}\cdot(20cm^2)\cdot5\operatorname{cm}\cong33.3cm^3\text{.}[/tex]2) Figure B
We have a cylinder with:
• Ab = base area = 20 cm²,
,• h = heigh = 6 cm.
The volume of the cylinder is:
[tex]V_B=A_b\cdot h=20cm^2\cdot6\operatorname{cm}=120cm^3.[/tex]3) Figure C
We have an inclined cylinder with:
• Ab = base area = 20 cm²,
,• h = heigh = 5 cm.
The volume of the inclined cylinder is:
[tex]V_C=A_b\cdot h=20cm^2\cdot5\operatorname{cm}=100cm^3.[/tex]4) Figure D
We have a parallelepiped with:
• Ab = base area = 20 cm²,
,• h = heigh = 5 cm.
The volume of the parallelepiped is:
[tex]V_D=A_b\cdot h=20cm^2\cdot5\operatorname{cm}=100cm^3.[/tex]5) Figure E
We have an inclined square pyramid with:
• Ab = base area = 20 cm²,
,• h = heigh = 10 cm.
The volume of the square pyramid is:
[tex]V_E=\frac{1}{3}\cdot A_b\cdot h=\frac{1}{3}\cdot(20cm^2)\cdot10\operatorname{cm}\cong66.67cm^3\text{.}[/tex]Answer
Among these figures, figure C and figure D have the same volume.
omg im so sorry but i need help again guys:(
The expression for the side length of the bulletin board is √n (option B).
What is the expression for the side length?A square is an object with four sides that are of equal length. The sum of angles in a square is 360 degrees. A square has two diagonals that are of equal length that bisect each other at a right angle.
The area of a square can be determined by calculating the square of a side length.
The area of a square = length x length
= length²
If the area of a square is given, to determine its side length, find the square root of the area.
Length of a side = √area
√n
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another one i don’t get them that’s why
Answer:
x° = 100°
Step-by-step explanation:
Straight line angles add up to be 180°
Angles opposite eachother aka "vertical angles" are the same measurements.
a poker hand consists of five cards randomly dealt from a standard deck of 52 cards. the order of the cards does not matter. determine the following probabilities for a 5-card poker hand. write your answers in percent form, rounded to 4 decimal places.
The probabilities listed here, in percent form and rounded to the fourth decimal place, are 29.9474 for a 5-card poker hand.
How do probabilities work?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
According to given information;
C(4,3)C(48,2)/C(52,5) - 3 of 4 aces, 2 of 48 non-aces 0.1736%
C(13,5)/C(52,5) - 5 of 13 spades 0.0495%
There are 4 face cards, ace, king, queen, jack, and 4 suits for each. 16 face cards, and 36 non-face cards - C(16,3)C(36,2)/C(52,5) 13.5747%
There are 44 cards that are not aces or kings - C(4,2)C(4,2)C(44,1)/C(52,5) 0.0609%
There is 1 jack and 48 non-jacks C(4,1)C(48,4)/C(52,5) = 29.9474%.
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