Please help! Which linear system has this matrix of constants? `[[12],[11],[4]]` A, B, C, or D
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Solve the following equation:
[tex]z {}^{4} + z {}^{2} - i \sqrt{3} = 0[/tex]
Note that:
[tex]i = \sqrt{ - 1} [/tex]
× Irrelevant answers will be blocked and reported.
Complete the square.
[tex]z^4 + z^2 - i\sqrt 3 = \left(z^2 + \dfrac12\right)^2 - \dfrac14 - i\sqrt3 = 0[/tex]
[tex]\left(z^2 + \dfrac12\right)^2 = \dfrac{1 + 4\sqrt3\,i}4[/tex]
Use de Moivre's theorem to compute the square roots of the right side.
[tex]w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)[/tex]
[tex]\implies w^{1/2} = \pm \dfrac{\sqrt7}2 \exp\left(\dfrac i2 \tan^{-1}(4\sqrt3)\right) = \pm \dfrac{2+\sqrt3\,i}2[/tex]
Now, taking square roots on both sides, we have
[tex]z^2 + \dfrac12 = \pm w^{1/2}[/tex]
[tex]z^2 = \dfrac{1+\sqrt3\,i}2 \text{ or } z^2 = -\dfrac{3+\sqrt3\,i}2[/tex]
Use de Moivre's theorem again to take square roots on both sides.
[tex]w_1 = \dfrac{1+\sqrt3\,i}2 = \exp\left(i\dfrac\pi3\right)[/tex]
[tex]\implies z = {w_1}^{1/2} = \pm \exp\left(i\dfrac\pi6\right) = \boxed{\pm \dfrac{\sqrt3 + i}2}[/tex]
[tex]w_2 = -\dfrac{3+\sqrt3\,i}2 = \sqrt3 \, \exp\left(-i \dfrac{5\pi}6\right)[/tex]
[tex]\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}[/tex]
The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and point A is reflected across the x-axis to obtain point C. What are the coordinates of points B and C?
B(2, 3) and, C(−2, −3)
B(−2, −3) and C(2, 3)
B(2, −3) and C(−2, 3)
B(−2, 3) and C(2, −3)
Answer: B(2, -3) and C(-2, 3) which is choice 3
Further Explanation:
The rule for a y-axis reflection is [tex](\text{x}, \text{y}) \to (-\text{x}, \text{y})[/tex] meaning the x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same.
Therefore, point A(-2,-3) moves to B(2, -3) when reflecting over the y-axis.
A similar rule is [tex](\text{x}, \text{y}) \to (\text{x}, -\text{y})[/tex] to describe an x-axis reflection. This time the y coordinate flips in sign, and the x coordinate stays the same.
In this case, we move from A(-2,-3) to C(-2, 3)
The graph of all three points is shown below. I used GeoGebra to make the graph, but Desmos is another option. I also recommend graphing by hand on graph paper to get practice that way if possible.
need heeeelp please
Answer:
[tex]\dfrac{3x+6}{x^2+x-6}[/tex]
Step-by-step explanation:
Notice that we can factor the expression [tex]x^2-x-2[/tex] as [tex](x-2)(x+1)[/tex]. Similarly, we can express [tex]3x+3[/tex] as [tex]3(x+1)[/tex]. Now, we can multiply the fraction together as [tex]\dfrac{(x+2)(3)(x+1)}{(x-2)(x+1)(x+3)} = \dfrac{3(x+2)}{(x-2)(x+3)} = \boxed{\dfrac{3x+6}{x^2+x-6}}[/tex].
Line passes through the point (8,4) and a slope of 5/4. Write equation in slope-intercept
Answer:
Step-by-step explanation:
y - 4 = 5/4(x - 8)
y - 4 = 5/4x - 10
y = 5/4x - 6
what is the solution I need help
Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is less than 0.4
Square root of numbersThe square root of numbers is is expressed using the square root sign. In order to determine the square root os 0.15 given, we need need to determine the square of perfect square before and after the given number.
For the square root of √0.09
√0.09 = 0.3
Similarly for the square root of √0.16
√0.16 = 0.4
Since the resulting value is 0.3 and 0.4, hence the square root of 0.15 must be between these two values on the number line.
Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is less than 0.4
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Which of the following is NOT part of a scatter plot graph?
Key
Source
Labels
Scale
Which of the following is the scale on each axis based on?
Averages
Percents
Data
Number of data poin
The first step in the area method to estimate the line of best fit is to ______.
divide the data points equally with a horizontal line
draw a line around all of the data points
place two x's centered in each half of the data points
divide the data points equally with a vertical line
The complete statements are:
The Key is not part of a scatter plotThe scale on the axes of a scatter plot is based on the number of data pointsThe first step in the area method to estimate the line of best fit is to draw a line around all of the data pointsHow to complete the statementsPart of a scatter plot
The parts of a scatter plot are
LabelSourceScaleThe dataThe axesThis means that the Key is not part of a scatter plot
The scale on the axes
Here, the scale is determined by the number of data points that exists on the scatter plot
This means that scatter plots that have 10 and 100 data points might not be represented on the same scale
The line of best fit
This is determined by drawing a line through the data points on the scatter plot.
The line is know as the line of best fit
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Simplify [tex]\frac{6a^2 b^-^2}{8a^-^3 b^3}[/tex] Assume a≠0 and b≠0
Answer:
sorry i thought i knew it
Step-by-step explanation:
Answer:
3rd option
Step-by-step explanation:
using the rules of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] : nm > n
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] : n > m
[tex]\frac{6a^2b^{-2} }{8a^{-3b^3} }[/tex] ← separate the variables
= [tex]\frac{6}{8}[/tex] × [tex]\frac{a^2}{a^{-3} }[/tex] × [tex]\frac{b^{-2} }{b^3}[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2-(-3)}[/tex] × [tex]\frac{1}{b^{3-(-2)} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2+3}[/tex] × [tex]\frac{1}{b^{3+2} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{5}[/tex] × [tex]\frac{1}{b^{5} }[/tex]
= [tex]\frac{3a^{5} }{4b^{5} }[/tex]
Amanda works as a waitress. She earns $50 a day plus 75% of the tips her customers leave.(The rest of the tips go to the kitchen
staff and bussers.) The table of values represents Amanda's earnings on different days. Write a linear equation that represents
the relationship between earnings and tips.
Tips ($)
20.00
50.00
100.00
Total Earnings ($)
65.00
87.50
125.00
The linear equation that represents the relationship between earnings and tips will be y = 0.75x + 50.
What is a linear equation?The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Working as a waitress is Amanda. She receives $50 every day in addition to 75% of the tips her clients leave.
Let 'x' be the tip amount and 'y' be the total earning.
y = 0.75x + 50
Check:
At (20,65), then we have
65 = 0.75(20)+50
65 = 15+50
65=65
At (50,87.5), then we have
87.5 = 0.75(50)+50
87.5 = 37.5+50
87.5=87.5
At (100,125), then we have
125 = 0.75(100)+50
125 = 75+50
125=125
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A plant is 30cm tall when planted in a garden it increases by 10 percent each week how long will it take to reach 1 meter
Answer:
12.63 weeks ~~ 13 weeks
Step-by-step explanation:
This is much like a banking question with compounded interest
FV = PV ( 1 + i)^n FV = Future value = 1 m PV = present value = .3
i = periodic interest = .10 n = periods
1 = .3(1 + .1)^n solve for n = the number of weeks
1/.3 = 1.1^n
log (1/.3) / log 1.1 = n = 12.63 weeks
20 is 50% of what number? If necessary, round to the nearest tenth.
Answer:
20 is 50% of 40.
Step-by-step explanation:
1% = 1/100
50% = 50/100 or 1/2
1/2 = 20/n
1*20/2*20 = 20/n
20/40 = 20/n
n = 40
if a rectangular piece of metal has 27.75 square inches what is the length and width?
We cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations.
What are the dimensions of a rectangular piece of metal?
By geometry we know that the area of the piece of metal is equal to the product of its length and width, then we must find two real numbers such that:
l · w = 27.75, where l, w > 0.
Unfortunately, we cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations. We need at least one equation to find an unique solution.
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NEED HELP QUICK
Select the correct answer.
Firewood can be sold in cords. The wood is cut into equal lengths and stacked evenly in a rack.
Which geometric shape can be used as a model to calculate the volume of the cord of wood?
A.
cylinder
B.
pyramid
C.
rectangular prism
D.
cone
The volume of the cord of wood will be similar to the volume of a rectangular prism. Then the correct option is C.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
The rectangular prism is the most typical geometric form used to approximate the volume of a cord of wood.
The wood is evenly cut into identical lengths, and when stacked, it forms a rectangular prism.
Therefore, C. rectangular prism is the right response.
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Elena is 56 inches tall. (Note: 100 inches = 254 centimeters)
Round your answers to the nearest thousandth. Type the answers in the boxes below.
1. What is her height in centimeters? centimeters
2. What is her height in meters?
Elena's height in centimeters is 142.24 cm.
Elena's height in meters is 1.42 meters.
What is Elena's height in centimeters and meters?The mathematical operations that would be used to determine the answers ae division and multiplication.
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Multiplication is the operation that is used to determine the product of two or more numbers.
In order to determine the height in centimeters, first determine how many cenitmeters make 1 inch
1 inch = 254 / 100
1 inch = 2.54 cm
Now, convert 56 inches to cm : 56 inches x 2.54 = 142.24 cm
In order to determine the height in meters, first find the unit of conversion of inches to meters
1 inch = 0.0254 meters
0.0254 x 56 = 1.42 meters
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which theorem can be used to show that LJKL is the same as LMNP
a. AA similarity
b. SSS similarity
c. ASA similarity
d. SAS similarity
4- Evaluating Expressions
11) (2 + y - x); use x = 4 and y = 6
13) P(+²); use a = 7 and p=6
6
5-Solving Inequalities
16) 1 ≤
10 11 12
18) 6v> 54
13 14 15 16 17 18
8 9 10 11 12 15 14 15 16 17 18
12)3(8a-5b)-2(a + b); use a = 3 and b = 2
14) 3m-2+
use m = 5 and n = 6
17) 20
19) 82/2
4
14 15 16 17 15
9 10 11 12
14 15 16 17 15
Answer:
The answer is 4'
Step-by-step explanation:
The answer is 4, 123456789, 6 12, 18, 24, 30, 36, 42, 48.
(a+b)² - 11(a+b) -42
pls show the work
Answer:
(a+b)² - 11(a+b) -42
Step-by-step explanation:
Thoughtfully split the expression at hand into groups, each group having two terms,
Group 1: -11b-11a
Group 2: a2+2ab
Group 3: b2-42
Pull out from each group separately :
Group 1: (a+b) (-11)
Group 2: (a+2b) (a)
Group 3: (b2-42) (1)
Looking for common sub-expressions :
Group 1: (a+b) (-11)
Group 3: (b2-42) (1)
Group 2: (a+2b) (a)
final answer:(a+b)² - 11(a+b) -42
Answer:
(a+b+3)(a+b-14)
Step-by-step explanation:
let a+b be x,
= x²-11x-42
=x²-(14-3)x-42
=x²-14x+3x-42
=x(x-14)+3(x-14)
=(x+3)(x-14))
replacing x by a+b,
=(a+b+3)(a+b-14)
what’s the volume of the sphere
Answer:
[tex]\pi[/tex]([tex]r^{2}[/tex]h)
Step-by-step explanation:
r = radius
h = height
QUESTION IS DOW BELOW 15 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
WILL GIVE BRAINLIEST FOR ACCURATE ANWSER
a. Applying the angle of intersecting chord theorem, m∠AEB = 57°.
b. Applying the , angle of intersecting tangents or secants theorem, VW = 106°.
What is the Angle of Intersecting Chords Theorem?According to the angle of intersecting chord theorem, the angle formed inside a circle (i.e. angle AEB) by two chords (i.e. AC and BD) have a measure that is equal to half of the sum of the measures of intercepted arcs AB and CD.
What is the Angle of Intersecting Tangents or Secants Theorem?According to the angle of intersecting tangents or secants theorem, the angle formed outside a circle (i.e. angle VZW) have a measure that is equal to half of the positive difference of the measures of intercepted arcs XY and VW.
a. m∠AEB = 1/2(measure of arc AB + measure of arc CD) [angle of intersecting chord theorem]
Substitute
m∠AEB = 1/2(53 + 61)
m∠AEB = 57°
b. 35 = 1/2(VW - 36) [angle of intersecting tangents or secants theorem]
Multiply both sides by 2
2(35) = VW - 36
70 = VW - 36
Add 36 to both sides
70 + 36 = VW
VW = 106°
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I really need your help ASAP!
Answer:
Option 4
Step-by-step explanation:
See the attached image.
Enter the letter for the function graphed
below.
1
a) y = √x - 5
b) y = √√√x-5
c)y=5-√√x
d) y = √x +
e) y = √√√x +
Answer:
e) y = √(x) +5
Step-by-step explanation:
The graph shown is the graph of the square root function shifted upward 5 units. There is no translation left or right.
Translated functionA function can be translated h units right and k units up by the following:
g(x) = f(x -h) +k
Translated square rootWhen the function is f(x) = √x, and it is translated 5 units up, but none left or right, we have ...
g(x) = f(x-0) +5
y = √(x) +5 . . . . . . matches choice e
What is the equation of the line described below in slope-intercept form?
The line passing through point (-1, 5) and parallel to the line whose equation is x + y = 10
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]x + y = 10\implies y = -x+10\implies y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+10 \leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so, we're really looking for the equation of al ine whose slope is -1 and that passes through (-1 , 5)
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-1}( ~~ x-\stackrel{x_1}{(-1) ~~ }) \\\\\\ y-5 = -(x+1)\implies y-5=-x-1\implies y=-x+4[/tex]
A pail holds 3 1/2 gallons of water. How much is this in cups?
A chemical company makes two brands of antifreeze. The first brand is 30% pure antifreeze and the second brand is 55% pure antifreeze. In order to obtain 160 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answer:
64 gallons 30%96 gallons 55%Step-by-step explanation:
The amount of each brand can be found by writing and solving an equation that makes use of the given relations.
SetupLet x represent the quantity of 55% pure antifreeze needed in the mixture. Then the quantity of the 30% brand is (160-x). The amount of pure antifreeze in the mixture is ...
0.55x +0.30(160 -x) = 0.45(160)
SolutionSubtracting 0.30(160), we have ...
x(0.55 -0.30) = 160(0.45 -0.30)
x = 24/0.25 = 96 . . . . . simplify, divide by the coefficient of x
96 gallons of the 55% brand, and 64 gallons of the 30% brand must be used.
__
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What insult is meat shield I never understood it if someone calls a person a meat shield what does the insult mean
Answer: someone who is viewed as obsolete or a person you can use to save yourself from any problem/situation
Step-by-step explanation:
Answer:
The term "meat shield" is often used as an insult to refer to someone who is used by others as a protective barrier, especially in a dangerous or violent situation. The implication is that the person being referred to is expendable and not valued for their own merits or abilities.
Here are a few examples of insults that use the term "meat shield":
"You're nothing more than a meat shield for your boss."
"You're just a disposable meat shield to your friends."
"You're nothing but a human meat shield to your team."
"You're just a weak and pitiful meat shield."
"You're just a coward who hides behind others like a meat shield."
Again, it's important to remember that using insults is never a productive or kind way to communicate with others. It's always better to try to address the issue in a respectful and constructive manner.
What is the answer to this equation?
Answer:W ^10
Step-by-step explanation:
The solution is in the
Perform the following mathematical operation, and report the answer tot he correct number of significant figures 0.396/0.5
Answer:
answer 0.8
Step-by-step explanation:
Solution
0.396 has 3 significant digits
0.5 has 1 significant digit.
Therefore the answer should be 1 significant digit.
0.396 / 0.5 = 0.792
Rounded to 1 sig dig, the answer = 0.8
What is the best estimated volume of the figure?
can anyone solve this for me with a detailed explanation step by steps and reasoning so i can grasp concepts
The answer is 756 m³.
The formula to find volume is : length × width × height
To estimate, round each dimension to the nearest whole number.
⇒ 12.3 ≅ 12
⇒ 7.2 ≅ 7
⇒ 8.6 ≅ 9
Volume = 12 × 7 × 9
Volume = 84 × 9
Volume = 756 m³
Answer:
The ans to this question is 756 which is Option (B)
Step-by-step explanation:
Estimate volume = rounding every digit
= 12.3 = 12
= 7.2 = 7
= 8.6 = 9
= 12x7x9 = 756
Colby needs to wash the windows on the second floor of a building.
He only has a 12 ft ladder and because of dense shrubbery, he hasto put the base of the ladder 5 feet from the building. How many feet above the ground would the windows need to be in order for Colby to reach them with his 12 ft ladder?
If the length of ladder is 12 feet then the height of windows from the ground is 10.91 feet.
Given that the length of ladder is 12 feet and the base is 5 feet.
We are required to find the height of the windows from the ground.
When we graph all the things like ladder and all that we will get a right angled triangle.
We can find the height of window by using pythagoras theorem.
Pythagoras theorem says that the square of the hypotenuse is equal to sum of squares of base and perpendicular of right angled triangle.
[tex]H^{2} =P^{2} +B^{2}[/tex]
P=[tex]\sqrt{H^{2} -B^{2} }[/tex]
Height of wall=[tex]\sqrt{12^{2} -5^{2} }[/tex]
=[tex]\sqrt{144-25}[/tex]
=[tex]\sqrt{119}[/tex]
=10.908
After rounding off it will be 10.91 feet.
Hence if the length of ladder is 12 feet then the height of windows from the ground is 10.91 feet.
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A manufacturer has a steady annual demand for 22,638 cases of sugar. It costs $7 to store 1 case for 1 year, $33 in set up cost to produce each batch, and $15 to produce each case. Find the number of cases per batch that should be produced to minimize cost
The number of cases per batch that the manufacturer should produce to minimize cost is 462 cases per batch.
How can inventory costs be minimized?To minimize inventory costs, especially setup and holding costs, the economic order quantity (EOQ) technique is deployed.
The EOQ model refers to the ideal order or batch quantity a company should purchase per order or produce per batch to minimize its inventory costs.
Some of a company's inventory costs include holding costs, shortage costs, setup, and ordering costs.
Using the EOQ model shows the ideal minimum units that the manufacturer should produce per batch to minimize costs.
The EOQ formula is square root of: [2(setup costs)(demand rate)] / holding costs.
Data and Calculations:Annual demand = 22,638 cases
Storage cost per case = $7
Setup cost per batch = $33
Product unit cost = $15 per case
EOQ = square root of: [2(setup costs)(demand rate)] / holding costs.
= square root of 2 x $33 x 22,638/$7
= square root of 213,444
= 462
Number of batches = 49 (22,638/462)
Thus, the number of cases per batch that the manufacturer should produce to minimize cost is 462 cases per batch.
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