Consequently, there exist four numbers z:
√3/2 ± I 1/2
-√3/2 ± I 1/2
The three unique vertices of an equilateral triangle are 0, z, and z3: (z^3=0)= e ^iπ/3(z -0 ) ⇔ z^3=e^(±iπ/3)z
=(z^2-e^±iπ/3)z=0⟺z=0
or z^2=e^±iπ/3
Since we have z[tex]\neq[/tex]0, z=e^±iπ/6= ±(√3/2 ± I 1/2 )
There are thus four numbers in z:
√3/2 ± I 1/2
-√3/2 ± I 1/2
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#16 23.8 divided by 5.6
Answer:
23.8/5.6=4.25
Step-by-step explanation:
Answer:
4.25
Step-by-step explanation:
[tex] \sf \: 23.8 / 5.6 =4.25[/tex]
[tex] \sf----------------------------------[/tex]
What is a good job for people with dyslexia, but also love mathamatics?
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Use the Pythagorean theorem to solve for c using the lesser two sides.
The answer is A.
i need help fast pls be correct
1) The rule of transformation is described as; A: A rotation 90° clockwise about the origin
2) The value of x is; 2
3) The value of x is 10
4) The slope of the line is; 2
How to Interpret rule of transformation?
1) The rule of transformation for When the point M (h, k) is rotated through 90° clockwise about the origin, the point M (h, k) takes the image M' (k, -h). Thus, that is the rule here.
2) From the given image, we can tell that the angles 50° and 26x - 2 are corresponding angles. Thus, they are congruent and we have;
26x - 2 = 50
26x = 52
x = 2
3) From the given image, we can see that the given angles are supplementary and as such they add up to 180 degrees. Thus;
9x + 15 + 6x + 15 = 180
15x + 30 = 180
15x = 150
x = 10
4) Slope is;
m = (y2 - y1)/(x2 - x1)
m = (1 - (-3))/(1 - (-1))
m = 4/2
m = 2
5) Same question as the first one.
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according to a survey of adults, 64% have money in a regular savings account. if we plan on surveying 50 randomly selected adults, find the mean number of adults who would have regular savings accounts.
By using Binomial probability distribution, the mean number of adults who would have bank savings accounts is 32.
For every survey, there are only two possible outcomes.
First- they have bank savings accounts,
second- they do not.
So, by using the binomial probability distribution we can solve this problem.
Probability of exactly Y successes in ‘n’ repeated trials, with ‘p’ probability.
Probability = p
Successes repeated = n times
The value of the binomial distribution is:
E(Y) = n x p
In this problem, we have that:
p = 0.64
If we were to survey among 50 randomly selected adults, the mean number of adults who would have bank savings accounts is,
E(Y) when, n = 50
So,
E(Y)= n x p
= 50 x 0.64
= 32
Hence ,our required answer is 32 adults who would have bank savings accounts
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Factorise fully 3x² -75
Answer : 3(x - 5)(x + 5)
example 3(x 2 - 25)
3x2 - 75
sorry about what happened but I hope this helps have a great day
I need help on number 10! asap!!
Answer:
6
Step-by-step explanation:
on a popular fictional game show, contestants are given the opportunity to win money by reaching into a bag after being blindfolded and selecting a chip with a dollar amount written on it. assume all chips are identical. the bag contains four chips with a $0 amount, six chips with $1, five chips with $5, two chips with $10, and one chip with $100. the chips are mixed in the bag before the contestant draws their chip. a. construct a probability mass function (pmf) for x, the dollar amount won by a contestant in this game. b. what is the expected value for x?
Construct a probability mass function (pmf) for x, the dollar amount won by a contestant in this game is 1/18.
What is a probability math example?
Probability is the measurement of how likely something is to happen. As an example, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head. We write P(heads) = 12 here. The four most popular approaches to probability are axiomatic, classical, empirical, and subjective.from above total number of chips =4+6+5+2+1 =18
hence Probabilty of win 0 P(0)=4/18
P(1) =6/18
P(5) =5/18
P(10) =2/18
P(100)=1/18
x P(x) xP(x)
0 0.22 0.00
1 0.33 0.33
5 0.28 1.39
10 0.11 1.11
100 0.06 5.56
8.39
therefore expeted value =8.39
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What rules of exponents do you use to solve 10^3*10^-7*10^2? Choose all answers that apply.
Product Rule
Negative Rule
Quotient Rule
Power Rule
The rules of exponents which can be used to solve the expression as given in the task content are; Product rule, Negative rule and Quotient rule.
What rules of exponents do you use to solve 10³ * 10-⁷ * 10² as given in the task content?It follows from the task content that the rules which can be used to correctly solve the expression as given in the task content be determined.
Since the expression given is;
10³ * 10-⁷ * 10²
We can therefore have rewrite 10-⁷ using the negative rule so that we have; 1/10⁷.
Also, the product rule can be used on; 10³ * 10² so that we have; 10⁵.
Ultimately, the quotient rule can be used on the resulting expression; 10⁵/10⁷ so that we have; 10-².
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Miranda has the following income and expenses:
$550 bi-weekly paychecks
$60 cell phone
$85 car insurance
●
$195 car payment
• $55 HULU
• $575 rent
How much are Miranda's total monthly expenses?
The amount of Miranda's total monthly expense is $970.
What is the meaning of an expenses?Basically, an expense refers to any cost of operations that a company incurs to generate revenue. It also means the cost that one is required to spend on obtaining something.
In a typical firm, the common expenses include a payment to suppliers, employee wages, factory leases, equipment depreciation etc.
in the question context, the expenses are:
$60 cell phone$85 car insurance$195 car payment$55 HULU$575 rentTotal monthly expenses = $60 + $85 + $195 + $55 + $575
Total monthly expenses = $970.
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if there are 36 apples and 6 bananas for a fruit basket, fill out all the possible ratios of apples to banana that could be made
b^2=48, how do you answer a question like this? (also the words have nothing to do with the equation, i'm just confused)
The solution of the equation b² = 48 is b = 4√3
How to solve equation?The equation can be solved as follows;
b² = 48
Therefore, we are to find the value of b in the equation.
The value of b comes with a square sign, so we have to remove the square to make b stand alone in the equation.
By removing the square sign we have to square root both sides.
Hence,
b² = 48
square root both sides of the equation
b² = 48
√b² = √48
Therefore,
b = √16 × 3
b = 4√3
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math assignment(not to be confused with assessment) that I need help with
The statements that are true in the lines of construction of the straightedge and compass construction which makes use of congruent circles, are;
Line EF is the perpendicular bisector of segment BD
Line EF is the bisector of angle BAC
How are a compass and straightedge used to construct geometric figures?Geometric figures are constructed using a compass and a straightedge, by using outlined steps or procedures.
From the diagram, given that the circumference of the circle with center B passes through the center of the circle with center D, and vice versa, we have;
Circle B is congruent to circle D
Construction of Perpendicular Bisector to Line BDThe steps to construct a perpendicular bisector to the segment BD includes;
Placing the compass at point B and draw an arc above and below segment BC then place the compass at point D then draw arcs above and below the segment BD to intersect the previous arcs drawn from point B. at points E and FJoin the point of intersection of the two arcs which are the points E and F to complete the the construction of the perpendicular bisector of segment BDTherefore;
Line EF is the perpendicular bisector of segment BDThe steps to construct the angle bisector of angle BAC
The angle bisector can be constructed by using the following steps
Place the compass at point A which is the vertex of the angle, and draw arcs to intersect the arms of the angle at B and D Place the compass at points B and D and draw arcs above BD to intersect at point F which is on the of BD away from point AJoin FAV to complete the construction of the bisector of angle BACWhich gives;
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PLEASE HELP WILL GIVE BRAIBNLIEST!
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 the corresponding segment ON =9.
Then, we compute the scale factor:
O’N’=kON
15=9k
k=15/9=5/3.
The scale factor is k=5/3.
determine the body mass index of a person 65 inches tall with a weight of 175 pounds
The body mass index of a person 65 inches tall with a weight of 175 pounds is 29.12
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
The body mass index (BMI) is given by:
BMI = [mass in pounds / (height in inches)²] * 703
Given mass = 175 pounds, height = 65 in, hence:
BMI = [175/65²] * 703 = 29.12
BMI = 29.12
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the given family of functions is the general solution of the differential equation on the indicated interval. find a member of the family that is a solution of the initial-value problem. y
the given family of functions is the general solution of the differential equation on the indicated interval y=[tex]7/2e^{x} -7/2e^{-x}[/tex]
What is differential equation?
Equations which involves functions and its derivative is known as differential equation. these equations are highly used to model behaviour of complex system.
How to solve?
y(x) = [tex]C_{1} e^{x}+C_{2}e^{-x}[/tex]
y(0) = [tex]C_{1} +C_{2}[/tex]
0 =[tex]C_{1} +C_{2}[/tex] --------------------------------------------------(1)
y'(x) = [tex]C_{1}e^{x} -C_{2}e^{-x}[/tex]
y'(0) = [tex]C_1- C_{2} }[/tex]
7 = [tex]C_{1}-C_{2}[/tex] -------------------------------------------------(2)
From Equation 1 and 2
[tex]C_{1} +C_{2}[/tex] = 0
[tex]C_{1} -C_{2}[/tex] = 7
[tex]C_{1}[/tex] = 7/2
[tex]C_{2}[/tex] = -7/2
y=[tex]7/2e^{x} -7/2e^{-x}[/tex]
the complete question is
The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1ex + c2e−x, (−∞, ∞); y'' − y = 0, y(0) = 0, y'(0) = 7
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Find the measure of each arc. For each arc, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.
m arcQS
Answer:
m arcRP = 125°
m arcQS = 125°
m arcSP = 55°
m arcQR = 55°
Step-by-step explanation:
An arc is the curve between two points on the circumference of a circle.
An arc measure equals its corresponding central angle measure.
Vertical Angles Theorem: When two straight lines intersect, the opposite vertical angles are congruent.
Angles on a Straight Line Theorem: The sum of angles formed on a straight line is equal to 180°.
Arc RPAs m∠ROP = 125°
Therefore, m arcRP = 125°
Given the measure of angle ROP is 125°, and an arc measure equals its corresponding central angle measure, the measure of arc RP is 125°.
Arc QSUsing the Vertical Angles Theorem:
⇒ m∠QOS = 125°
Therefore, m arcQS = 125°
Using the Vertical Angles Theorem, the measure of angle QOS is equal to the measure of angle ROP, so the measure of angle QOS is 125°. As an arc measure equals its corresponding central angle measure, the measure of arc QS is 125°.
Arc SPUsing the Angles on a Straight Line Theorem:
⇒ m∠SOP = 180° - 125° = 55°
Therefore, m arcSP = 55°
Using the Angles on a Straight Line Theorem, the measure of angle SOP is 55°. As an arc measure equals its corresponding central angle measure, the measure of arc SP is 55°.
Arc QRUsing the Angles on a Straight Line Theorem:
⇒ m∠QOR = 180° - 125° = 55°
Therefore, m arcQR = 55°
Using the Angles on a Straight Line Theorem, the measure of angle QOR is 55°. As an arc measure equals its corresponding central angle measure, the measure of arc QR is 55°.
Write as fraction
4. 6.025
Answer: In simplest form it would be 6 1/40
Step-by-step explanation:
[tex] \frac{241}{40} [/tex]
but in mixed number
[tex]6\frac{1}{4} [/tex]
josie took a total of 24 quizzes over the course of 6 weeks. after attending 10 weeks of school this quarter, how many quizzes will josie have taken in total? solve using unit rates.
In linear equation, 42 units quizzes will josie have taken in total.
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y.When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.josie took a total = 24 quizzes
the course = 6 weeks
quizzes will josie have taken = 24/6 = 4
after attending 10 weeks of school this quarter = 10 * 4 = 40 units
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30 kilograms of beans cost $5 how many beans can you buy for $1
Answer:
6kg
Step-by-step explanation:
5 to 30 ratio
1 to 6 ratio
Answer:
30/5=6
6 kg beans for $1
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A stack of 30 science flashcards includes a review card for each of the following 10 insects, eight trees eight flowers, 4 birds. What is the probability of randomly selecting a TREE or a FLOWER?
From the statement, we know that stack of 30 science flashcards has:
• 10 with insects,
,• 8 with trees,
,• 8 with flowers,
,• 4 with birds.
The probability of selecting a tree or a flower is given by:
[tex]P(\text{tree or flower})=\frac{\text{\# of trees + \# of flowers}}{\text{total \# of cards}}=\frac{8+8}{30}=\frac{16}{30}=\frac{4}{15}.[/tex]Answer4/15
A hot utensil kept away from the flame and cools down. Name and define the process of heat transfer invloved in given example
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∠1 and ∠4 are supplementary angle in transversal line .
What is a transversal angle?
When a transversal splits two parallel lines, the two intersections create a number of angles. Transversal angles are what those are.A transversal is a line that crosses a network of lines, according to the definition. Transversals include, for instance, a line that crosses a set of two parallel lines.A transversal line is one that crosses two other lines at two different locations. Line l meets a and b in the picture below at two different locations, P and Q. Line l is the transversal line as an outcome.1) ∠6 ≅ ∠8 congruent angle.
2) ∠6 = ∠1 and ∠8 = ∠3 are Verical angles.
3) ∠1 and ∠4 are supplementary angle.
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A force of 40.0 N accelerates a 5.0-kg block at 6.0 m/s2 along a horizontal surface. what is the net force acting on the block
The value of the net force acting on the block will be equal to 79N.
Force may be defined as the product of mass and acceleration, and it acts on the body in order to move the body. Since, the external force is acting on the block there will be a frictional force which opposes the block to move. The frictional force may be represented by f(k) and is given by
f(k) = external force - (ma)
f(k) = 40N - (5×6)
f(k) = 40N - 30N
f(k) = 10N and since it opposes the external force then the sign will be negative that is f(k) = -10N.
Also, there is a force of gravity acting on the body which will be equal to mg where 'g' is the acceleration due to gravity.
Now, force of gravity = mg
= 5×9.8 = 49N
Now, net force acting on the block = 40N - 10N + 49N
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A field has width x and and length 2x+1 the area of the field is 600m^2 find the width and the length of the field
The length and width of the rectangular field is found as width x = 2.08 m and length = 5.16 m.
What is termed as the rectangle?A rectangle is indeed a closed two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal as well as parallel. Because a rectangle is a two dimensional shape, it has two dimensions: length and width. The length of the rectangle is the longer side, and the width seems to be the shorter side.The given values in the question are-
The width of the field = w.
The length of the field = 2x+1
The area of the field = 600 m².
The formula of area of rectangular field;
A = length×width
Put the values;
600 = (2x+1)x
Simplifying the equation;
600 = 2x² + x
2x² + x - 600 = 0.
Find the factors of the above quadratic equation using quadratic formula.
x = 2.08, neglecting negative value.
Thus, the width is x = 2.08 m.
length = 2x + 1
length = 5.16 m.
Thus, the length and width of the rectangular field is found as width x = 2.08 m and length = 5.16 m.
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If f(x) = x² + 5, then what is the remainder when f(x) is divided by x + 5?
Step-by-step explanation:
you can ask questions for clarification
Answer:
3
Please refer to the photo below:
5. Which number is the smallest?
2.2458103 x 10^-6
2x10^-5
3.215 × 10^-7
3x10⁰
HELP
Answer: 3.215 × 10^-7
Step-by-step explanation:
The exponent is smaller than all of the others, so it's the smallest.
Help plhyhrfdhfgtsgf
Answer:
60000
Step-by-step explanation:
Answer:
60000
Step-by-step explanation:
6 × [tex]10^{4}[/tex] =
6 × 10000 =
60000
a farmer grew 8,914 bushels of corn. he delivered corn to different stores using his truck. his truck can carry 336 bushels of corn in one load. what was the least number of loads the farmer made to deliver all the corn to the stores?
Answer:
The farmer had to do 27 loads.
Step-by-step explanation:
Basically the easy way to do this is to grab a calculator (or the paper and pen way) and keep adding 336 until you get to 8914.
Once you add it all you will see there is a remainder of his corn left (that has not been delivered):178
Even though it isn't a full 336, the farmer would still have to make another trip.
336*26=8,736
So, adding the remainder into it's own load, we would get:
27.
What is the image of (-8,6) after a reflection over the line y=-x
The image of (-8,6) after a reflection over the line y = -x is (-6, 8).
What is reflection transformation?In geometry, a reflection is referred to as a flip. A reflection is the shape's mirror image. A line, called the line of reflection, is where an image will reflect. Changes in position during reflection may also result in translation. The coordinate system may be referred to by the reflection transformation(X and Y-axis).Given:
The image of (-8,6) after a reflection over the line y = -x.
The x-coordinate and y-coordinate of a point change positions and are negated when it is reflected across the line y = -x.
So, the reflection of the point (-8, 6) across the line y = -x is (-6, 8).
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