Solve for z in the following equation: 2-3iz = 3 + 2iz$
The value of 'z' for the given linear equation is [tex]- \frac{1}{5i}[/tex].
What is a linear equation?A linear equation is an equation where there are one or multiple variables. However, the highest power of any variable is one.
Given linear equation is
[tex]2-3iz = 3 + 2iz[/tex]
⇒ [tex]2iz + 3iz= 2-3[/tex]
⇒ [tex]5iz = -1[/tex]
⇒ [tex]z = \frac{-1}{5i}[/tex]
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f(x)= 2x-3x^2 evaluate f(-3)
A. -33
B. 6
C. 33
D. -21
ymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is
C(x) = 3250 + 5x + 0.1x2 (0 ≤ x ≤ 500).
Gymnast Clothing sells the cleats at $110 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?
what is 2x+square root x+1=8 solve for x
You and your brother are readibg the same novel you wnat to get ahead of him in the book so you decide to read 30 minutes longer than your brother reads how many minutes will you read if your brother reads for 15 minutes
Answer:
45 minute 30+15= 45 easy
Step-by-step explanation:
97 cars making up a freight train,56 are boxcars and 41 are not.Find the fraction of the cars that are not boxcars?
An oil storage tank is a cylinder 30 feet high. The base of the tank is a circle with a diameter of 50 feet. When full, how many gallons are in the tank? 1 gallon equals approximately 0.13 cubic feet.How many gallons are in the tank?
Answer: 7653.75 gallons
Step-by-step explanation:
Given : Height of cylinder = 30 feet
Diameter : d= 50 feet
Radius : [tex]r=\dfrac{d}{2}=\dfrac{50}{2}=25\text{ feet}[/tex]
The volume of a cylinder is given by :-
[tex]V=\pi r^2 h\\\\\Rightarrow\ V=(3.14)(25)^2(30)\text{ cubic feet}[/tex]
Also, 1 gallon equals approximately 0.13 cubic feet.
Then , the number of gallons of water in the tank :-
[tex]V=(3.14)(25)^2(30)(0.13)=7653.75\text{ gallons}[/tex]
What is the base 8 representation for 112
In base 8 (also known as octal), the conversion of the decimal number 112 is done by repeatedly dividing by 8 and considering the remainder. Following this process, the base 8 representation of 112 is 160.
Explanation:In base 8 (also known as octal), each position in a number represents a power of 8. To convert the decimal number 112 to base 8, we need to determine how many times 8 can fit into 112, along with the remainder.
Here's how we do it:
Divide 112 by 8. The result is 14 with no remainder. There's your first Octal digit, at the least significant digit (rightmost). Now divide the whole number quotient from the previous step (14) by 8. The result is 1 with a remainder of 6. The whole number quotient (1) is the next Octal digit, and keep 6 as the next step's quotient.Finally, you have 1 (from the last step) which can be divided by 8, results in 0 and a remainder of 1. So, the remainder is the final Octal digit, at the most significant digit (leftmost).So, the base 8 representation for 112 is 160.
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Ivy corporation gave 90 people a bonus. If ivy had given 8 more people bonuses, ivy would have rewarded 2/3 of the workforce. How large is Ivy's workforce?
What is the gcf of 14 and 22
A reel of electrical cable holds 80 metres when full.
3/16 of the reel has been used.
How much cable is there left on the reel?
Estimate the sum 458+214
Final answer:
To estimate the sum of 458+214, round each number to the nearest ten to get 460 and 210, then add to find the estimated sum of 670. The actual sum is 672, confirming the estimate's accuracy.
Explanation:
To estimate the sum of 458+214, you can round each number to the nearest ten and then add them together. You would round 458 to 460 and 214 to 210. When you add 460 and 210, you get 670. Therefore, an estimate for the sum of 458 and 214 is 670.
To verify if our estimation is accurate, we can perform the actual addition: 458 + 214 equals 672. Our estimate of 670 is very close to the actual sum, demonstrating the effectiveness of the estimation method.
When given an algebraic expression involving subtraction, why is it best to rewrite the expression using addition before identifying the terms?
The service elevator in a high-rise building travels between the lowest underground parking level and the seventeenth story of the building. The lowest parking level is 15 meters below street level, and the seventeenth story is 51 meters above street level. If the elevator rises at a rate of 2 meters per second, how long, in seconds, could a person ride the elevator when starting from the lowest level? Assume the elevator makes no extra stop.
15 +51 = 66 meters total
66 /2 = 33 seconds
and that is your answer
The person will reach to the seventeenth in 33 seconds.
Given that,
The lowest parking level is 15 meters below street level, and the seventeenth story is 51 meters above street level.
To determine how long, in seconds, could a person ride the elevator when starting from the lowest level.
Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
Here,
Total height to cover = height of lowest parking to street level + height of 17 stories from street level.
Total height = 15 + 51
Total height = 66 meters
Time to reach to the 17th story
Speed = distance / time
2 = 66 / time
time = 66 / 2
Time = 33 seconds
Thus, the person will reach to the seventeenth in 33 seconds.
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A cell phone that is on sale for $70 has a markdown of 45% off the regular price. What is the regular price of the cell phone? Round to the nearest cent.
What is the median of the following string of values?
55, 18, 58, 49, 8, 77, 62, 26, 7, 91
A.55
B.52
C.49
D.58
Answer:
Option B is correct
The median of the following string of values is 52
Step-by-step explanation:
Median defined as the median is the middle number.
To find the median of the following string of values:
55, 18, 58, 49, 8, 77, 62, 26, 7, 91
Arrange the string of values from least to greatest.
7, 8, 18 , 26, 49, 55, 58, 62, 77, 91
As you can see that we have two numbers, there is no middle number.
Simply, take the mean of the two middle numbers.
then;
Median = [tex]\frac{49+55}{2} = \frac{104}{2} = 52[/tex]
Therefore, the median of the following string of values is 52
A line passes through the point (d, d) and has a slope of k. Which equation models the line?
HELLLLPPPPP MMMEEEEE!
you have 2 angles given 50 and 110
50+110 = 160
so 180-160 = 20
A = 20 degrees
Ms. Ache is paid $1250 per week but it's fined $100 each day she is late to work Ms.A che wants to make at least $3,000 over the next three weeks so she can take a vacation. over the next three weeks, what is the maximum number of days she can be late to work and still reach her goal of making at least $3000?
Answer:
7 days
Step-by-step explanation:
Given: Ms. Ache is paid $1250 per week but it's fined $100 each day she is late to work.
To Find: maximum number of days she can be late to work and still reach her goal of making at least $3000?
Solution:
per week payment of Ms. Ache =[tex]\$[/tex] [tex]1250[/tex]
Fine for getting late a day = [tex]\$[/tex] [tex]100[/tex]
let number of days Ms. Ache gets late = [tex]\text{x}[/tex]
Amount Ms. Ache wants to make in three weeks = [tex]\$[/tex] [tex]3000[/tex]
maximum earning potential of Ms. Ache in 3 weeks = [tex]1250\times3[/tex]= [tex]\$[/tex] [tex]3750[/tex]
Net earning = maximum earning potential of Ms. Ache in 3 weeks - total fine
=[tex]\$ 3750 - 100\text{x}[/tex]
To reach a goal of [tex]\$[/tex] [tex]3000[/tex]
[tex]\$ 3750 - 100\text{x}[/tex] ≥ [tex]3000[/tex]
[tex]100\text{x}[/tex]≤[tex]750[/tex]
[tex]\text{x}\leq 7[/tex]
Maximum number of days she can be late to work and still reach her goal of making at least $3000 is [tex]7[/tex] [tex]\text{days}[/tex]
347,456 round to the place value of the underlined digit. The four being in the ten thousand places
The area of a circle is 99 in.² what’s the radius
Use Cramer's Rule to solve the following system: –2x – 6y = –26 5x + 2y = 13
What radius of a circle is required to inscribe a regular hexagon with an area of 210.44 cm2 and an apothem of 7.794 cm?
Answer:
The answer is D) 9cm
6 equilateral triangles in a regular hexagon
210.44
6
= 35.073 cm2
The apothem cuts each equilateral triangle into two right triangles.
35.073
2
= 17.5367 cm2
Base of each right triangle.
area =
1
2
bh
17.5367 =
1
2
b(7.794)
b = 4.5
Thus, the sides of each equilateral triangle is 2b = 2(4.5) = 9; which is also the radius of the circle needed to construct the inscribed regular hexagon.
Brainliest? You can read me work unlike the other
What is 6,403.5 rounded to the nearest thousand?
The quotient of nine and the difference of four and a number
The quotient of nine and the difference of four and a number is obtained by dividing nine by the difference of four and the number (4 - x), after subtracting the number from four first. This expression can be simplified to get the final result.
Explanation:The quotient of nine and the difference of four and a number can be expressed as:
9 / (4 - x)
To simplify this expression, we need to subtract the number x from 4 first, and then divide 9 by the result. For example, if the number x is 2, the expression would be:
9 / (4 - 2) = 9 / 2 = 4.5
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A bear, awakening from winter hibernation, staggers directly northeast for 15 m and then due east for 15 m. Show each displacement graphically and graphically determine the single displacement that will take the bear back to her cave to continue her hibernation.
The total displacement east is:
15 cos(45) + 15
= 25.607 m
The total displacement north is:
15 sin(45)
= 10.607 m
The magnitude of the total displacement is:
sqrt(25.607^2 + 10.607^2)
= 27.717 m = 27.7 m
Its direction is N x E where:
tan(x) = 25.607 / 10.607
x = 67.5 deg
The return displacement is therefore of the same magnitude
but in the opposite direction.
Displacement 27.7 m, direction S 67.5 deg W
Starting from the same place, Sara walks due west and Ammad walks due east. On the number line, 0 represents their starting point, negative values represent the distance traveled west and positive values represent the distance traveled east. A number line with a point for Ammad at coordinate 480 and a point for Sara at coordinate -240. How many feet apart are Sara and Ammad on the number line? Enter your answer in the box.
It's 720, because all you need to do is 240 + 480 = 720.
Hope it helps,
Find the equation of the line that contains the given points. P1(−8, 5), P2(−8, −5)
For the equation, 2x^4 -5x^3+10=0 find the number of complex roots and the possible number of real roots.
A. 3 complex roots; 0, 2 or 4 real roots
B. 3 complex roots; 1 or 3 real roots
C. 4 complex roots; 0, 2 or 4 real roots
D. 4 complex roots; 1 or 3 real roots
Which of the following is not an isometry?
rotation
dilation
translation
Answer:
B. Dilation.
Step-by-step explanation:
We are asked to find which transformation is not isometric.
We know that isometry preserves length.
We know that the length of a figure remains unchanged after rotation and dilation as they preserves length.
We also know that dilation either enlarges length or shrinks length of a figure, therefore, the correct choice is dilation.