Answer:
To find the sum of two complex numbers on the complex plane, we can simply add their real and imaginary parts separately. The real part of a complex number is the x-coordinate on the complex plane, while the imaginary part is the y-coordinate.
In this case, the two complex numbers are (-4-4i) and (4+2i). To find their sum, we add their real and imaginary parts separately:
Real part: -4 + 4 = 0
Imaginary part: -4 + 2 = -2
So, the sum of (-4-4i) and (4+2i) is 0 - 2i, which can be represented as a point on the complex plane with x-coordinate 0 and y-coordinate -2.
Step-by-step explanation:
Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if Z′(10, 8).
y = 1
x = −8
y-axis
x-axis
Answer:
(d) x-axis
Step-by-step explanation:
You want the line of reflection that transforms Z(10, -8) to Z'(10, 8).
Line of reflectionThe line of reflection is the perpendicular bisector of the segment between a point and its image.
Here, the segment ZZ' is on the vertical line x=10, so the bisector will be a horizontal line whose y-value is the average of the y-values of Z and Z':
y = (-8 +8)/2 = 0/2 = 0
The line y=0 is the x-axis. The line of reflection is the x-axis.
__
Additional comment
Rather than go to the trouble of considering perpendicular bisectors, you can simply make use of your knowledge of reflection over the axes:
(x, y) ⇒ (-x, y) . . . . reflection over the y-axis
(x, y) ⇒ (x, -y) . . . . reflection over the x-axis ←
(x, y) ⇒ (-x, -y) . . . . reflection over both axes, or reflection across the origin
Answer:
(d) x-axis
Step-by-step explanation:
Find the circumference of a closed semicircle with diameter 20 cm.
Answer: 10π + 20, or 51.4159, cm
Step-by-step explanation:
The circumference of a circle is calculated using πd. Our d, or diameter, is 20, so the circumference of a full circle would be 20π. However, we only have half of a circle, so that number is halved, resulting in 10π. Now, we just have to add on the cross section, which is equal to the diameter, giving us 10π + 20, or 51.4159, cm.
Question 4(Multiple Choice Worth 2 points)
(Circumference LC)
What is the circumference of the circle? Use 3.14 for TT.
Answer:
A. 12 TT
B. 6 TT
C. 9 TT
D. 18 TT
The correct answer is D. 18 TT. The formula for circumference is C = 2TT x radius, so with TT equal to 3.14, the circumference of the circle is 18.28 TT which is approximately equal to 18 TT.
Roller Coaster Engineering. The
height, y m, of a rider above the
ground in a section of roller coaster
ride is given by y=1/3x²- 2x + 8,
where x m is the rider's horizontal
distance from the start of the ride.
(i) Express the function in the form
y = a(x - h)² + k.
(ii) Find the rider's minimum height
above the ground.
(iii) If the rider is 8 m above the dw
ground after the ride starts, find
the rider's horizontal distance from
the start of the ride.
a) The vertex-form definition of the quadratic function is given as follows: y = 1/3(x - 3)² + 5.
b) The rider's minimum height above the ground is of: 5 meters,
c) The horizontal distance is given as follows: x = 0 m and x = 6 m.
How to obtain the features?The quadratic function in the context of this problem is defined as follows:
y = x²/3- 2x + 8.
In which:
x is the horizontal distance.y is the vertical distance.The coefficients are given as follows:
a = 1/3, b = -2, c = 8.
The x-coordinate of the vertex is given as follows:
x = -b/2a = -(-2)/(2/3) = 3.
Hence the y-coordinate of the vertex is given as follows:
y = (3)²/3 - 2(3) + 8 = 5 meters.
Hence the vertex-form definition of the equation is given as follows:
y = 1/3(x - 3)² + 5.
As the function is concave up, the minimum height is of 5 meters.
For the horizontal distance at a height of 8m, we have that:
x²/3 - 2x + 8 = 8
x²/3 - 2x = 0
x(x/3 - 2) = 0.
Hence:
x = 0 m and x = 6 m.
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Which angle measure is equivalent to 144°?
Send help, I don’t understand
Answer: 8.9 and 6.7
Step-by-step explanation:
These are right triangles, so you can use the Pythagorean theorem, a² + b² = c², where a and b are the legs, or shorter sides, of the triangle and c is the hypotenuse, or the longest side.
1. 4² + 8² = c²
16 + 64 = c²
80 = c²
c = √80
c = 8.9
2. 6² + 3² = c²
36 + 9 = c²
45 = c²
c = √45
c = 6.7
suppose that in a barn, there is a cow, a horse, a pig, and a goat. if two of the animals leave the barn, what is the probability that one of them is the goat?
Answer:
50% or 1/2
Step-by-step explanation:
Because there are 4 animals in the barn, if two animals leave (out of 4), then there are 50% of the animals in the barn and 50% of the animals leaving the barn.
Hope this helps! If you find my answer helpful, please consider marking brainliest! If you have any questions, feel free to ask in the comments!
2) A music store is offering piano lessons for $78 per month. A piano book costs
$25. How many months of lessons could a student take if he had $649 to spend on
the lessons and book?
Variable:
means:
The student can take 8 months of lessons if he has $649 to spend on lessons and the book.
Describe Division?The arithmetic action of division is the opposite of multiplication. It is employed to determine how frequently one quantity is included within another. Divide the dividend by the divisor to execute a division, which can be represented with the division symbol () or a fraction bar (/). The outcome of division is the quotient, which shows how many times the dividend can be divided by the divisor. For instance, if you divide 8 apples into 4 equal portions, each portion would include 2 apples.
First, let's find the total cost of the lessons by multiplying the cost per month by the number of months:
$78/month × n months = $78n, where n is the number of months of lessons.
Next, we add the cost of the book to find the total cost:
$78n + $25 = $649.
Now, we can solve for n by subtracting the cost of the book from both sides of the equation:
$78n = $649 - $25 = $624.
Finally, we divide both sides of the equation by 78 to find the number of months of lessons:
n = $624 ÷ $78/month = 8 months.
So, the student can take 8 months of lessons if he has $649 to spend on lessons and the book.
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3x-2y<6 in slope intercept form
Answer:
y=-3/2+3
Step-by-step explanation:
so you have to solve for y
If a hypothesis test is performed and the null hypothesis is rejected in favor of the alternative hypothesis, does the test prove that the alternative hypothesis is correct? ExplainChoose the correct answer below.A.The test does not prove the alternative hypothesis correct, because only one test was done, and it takes at least β hypothesis tests to prove a claim about a population parameter.B.The test does not prove the alternative hypothesis correct, because of the possibility of rejecting the null hypothesis when the null hypothesis is true.C.The test proves the alternative hypothesis correct, because once the null hypothesis is rejected, the only possibility that remains is for the alternative hypothesis to be true.D.The test proves the alternative hypothesis correct, because it shows that all the evidence suggests that the alternative hypothesis is true.
The test does not prove the alternative hypothesis correct, because of the possibility of rejecting the null hypothesis when the null hypothesis is true.
The test does not prove the alternative hypothesis correct, because when performing a hypothesis test, the null hypothesis is rejected in favor of the alternative hypothesis. However, rejecting the null does not necessarily mean that the alternative hypothesis is true. It is possible for the null hypothesis to be rejected even when it is true, due to the occurrence of random fluctuations. Therefore, the test does not prove that the alternative hypothesis is correct, as there is always a possibility that the null hypothesis is true despite being rejected. To prove that the alternative hypothesis is correct, a series of hypothesis tests must be conducted to show that the population parameter is consistent with the alternative hypothesis.
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what is the probability that at least two of the faces match when you roll three fair six-sided dice? express your answer as a common fraction.
The probability that we get the same faces when we roll 3 fair six-faced dice is 44.44%.
What is probability?Simply put, the probability is the likelihood that something will occur.
We can discuss the likelihood of several outcomes or the potential of one outcome when we are unsure of how something will turn out.
Statistics is the study of events that fall into a probability distribution.
Therefore, there is a chance that each one is unique:
6/6 * 5/6 * 4/6 = 120/216
Therefore, the likelihood that at least two of them will display the same face is:
1 - 120/216 = 96 / 216 =44.44%
Therefore, the probability that we get the same faces when we roll 3 fair six-faced dice is 44.44%.
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Tyee is working two summer jobs, making $10 per hour washing cars
and $6 per hour walking dogs. Last week Tyee worked twice as many
hours walking dogs as he worked washing cars and earned a total of
$88. Write a system of equations that could be used to determine the
number of hours Tyee worked washing cars last week and the number
of hours he worked walking dogs last week. Define the variables that
you use to write the system.
Ethan is 1.85 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 28.45 meters. He stands 24.3 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
Step-by-step explanation:
The tree is .0564 meters
Answer:
Step-by-step explanation:
de chill de chill
Consider the function g(x)=x−4‾‾‾‾‾√3.
Which ordered pair lies on the inverse of the function?
the ordered pair will be (3,-1) lies in the inverse function.
What is inverse function?
A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1
Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.
function g(x)=∛(x−4)
So the inverse of the function
g ¬(x) = x³+4
So the ordered pair will be (3,-1)
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Lowest value of x x4 2 2 + + is
The lowest value of the equation is at x = -2 when (x + 2) = 0.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
Given the function,
x² + 4x + 2
to find the lowest value,
factorize the function,
x² + 4x + 2
add and subtract 4 from the function,
x² + 4x + 2 + 4 - 4
x² + 4x + 4 - 2
(x + 2)² - 2
here (x + 2)² is always positive,
and lower value will be x = -2 when (x + 2) = 0
Hence lowest value will be at x = -2.
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The correct question is,
Lowest value of x² + 4x + 2.
Ella wants to learn how to hang glide. At "Hope You Live" hang gliding school, it is $140 deposit and $55 a lesson. At "Try Your Luck" hang gliding school, it is $60 deposit and $75 a lesson. At how many lessons would both schools be the same?
Answer:
4 Lessons
Step-by-step explanation:
55 * 4 = 220 + 140 = 360
75 * 4 = 300 + 60 = 360
Price per lesson, times number of lessons, plus deposit cost, equals total amount when the lessons will be the same price.
Hope this helps!
1+sin^2-cos^x / 2sin^2x =?
The simplified expression of 1+sin^2-cos^x / 2sin^2x issin^2(x) / 2(1 + cos(x)) + 1 / 2(1 - cos(x))
What is the simplified expressionTo simplify this expression, we can first simplify the numerator by combining the terms inside the parentheses:
1 + sin^2(x) - cos(x) = sin^2(x) + 1 - cos(x)
Next, we can factor the denominator trigonometric identity sin^2(x) + cos^2(x) = 1:
2 sin^2(x) = 2(1 - cos^2(x)) = 2 - 2cos^2(x)
Now we can substitute these simplified expressions into the original expression:
(1 + sin^2(x) - cos(x)) / (2 sin^2(x))
= (sin^2(x) + 1 - cos(x)) / (2 - 2cos^2(x))
= [(1 - cos(x)) + sin^2(x)] / [2(1 - cos(x))(1 + cos(x))]
1+sin^2-cos^x / 2sin^2x = [sin^2(x) / 2(1 + cos(x))] + [1 / 2(1 - cos(x))]
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What value of q is a solution to this equation?
q +13= 20
Answer: 7
Step-by-step explanation: 13 + 7 = 20
Answer: 7
Step-by-step explanation:
q+13=20
subtract 13 on both sides and you get
q=7
A color printer prints 41 pages in 12 minutes. How many minutes does it take per page?
Answer:
3.41
Step-by-step explanation:
41/12
evaluate ( 6^2 - 4^2 ) x ( 1/4 )^2
The evaluation of expression is 5/4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
The expression; ( 6^2 - 4^2 ) x ( 1/4 )^2
=( 6^2 - 4^2 ) x ( 1/4 )^2
=(36-16)*(1/16)
=20*1/16
=5/4
Therefore, the algebraic expression answer will be 5/4.
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true or false: of the range, the interquartile range, and the variance, the interquartile range is least influenced by an outlying value in the data set.
The interquartile range is least affected by an outlying value in the data set of the range, interquartile range, and variance is True.
Max to min value is the range. Range can substantially change if there are any outliers.
Since the threshold values for Q3 and Q1 are not outliers, the IQR won't change.
Outliers cause variance to be misinterpreted since they vastly increase variance.
Interquartile range:
You may determine the spread of the midpoint of your distribution using the interquartile range.
The interquartile range contains half of the values for any distribution that is ordered from low to high. The first 25% of values are found in the first quartile (Q1), while the last 25% are found in the fourth quartile (Q4).
The third quartile (Q3) less the first quartile (Q1) is the interquartile range (Q1). This provides us with the data set's middle half's range.
The interquartile range is calculated using only 2 values, much like the range. The IQR, however, is less impacted by outliers because the two values are more likely to be average scores because they are drawn from the middle of the data set.
The IQR provides a reliable indicator of variability for both skewed and normal distributions.
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Can somebody please explain the answers for these? Its a simple question but for me its confusing!
Thanks !!!!!!!!!!!!!!
HELP ASAPPPP!!!!!!!!!!!!!!!!!!!!!
The options which are equal to, or a good estimate of the ratio include:
8 out of 1, 000 :
0. 8 % less than 1 %8 / 100 :
2 out of 25Almost 10 %How to find the ratios ?8 out of 1, 000 is a ratio that can be shown to be :
= 8 / 1, 000 x 100 %
= 0. 008 x 100 %
= 0. 8 %
0. 8 % is less than 1 %.
8 / 100 is a ratio that would be:
= 8 / 100 x 100 %
= 8 %
This is almost 10 % as it is 2 % away.
8 / 100 = 0. 08
2 / 25 = 0. 08
These two ratios are therefore equal.
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Find the ratio of 35 min to 1 hr tell me this question ans i have a test tommorow
A fish swims a distance of 6 km in 5 minutes. What is the average speed in m/s
Answer:
Step-by-step explanation:
6 km = 6000 m
5 min = 300 s
6000m / 300s = 20 m/s
Answer:
20 m/s
Step-by-step explanation:
The average speed of the fish can be calculated by dividing the distance traveled by the time taken.
First, we need to convert the distance from km to meters:
6 km = 6,000 meters
Next, we need to convert the time from minutes to seconds:
5 minutes = 5 × 60 = 300 seconds
Finally, we divide the distance traveled by the time taken:
Average speed = 6000 meters / 300 seconds = 20 m/s
So, the average speed of the fish is 20 m/s.
Find the particular solution of the differential equation that satisfies the initial condition. (Enter your solution as an equation.)
Differential Equation:
dT+k(T-60)dt=0
Initial Condition:
T=139 when t=0
Answer:
T = 79e^(-kt) +60
Step-by-step explanation:
You want the particular solution to the differential equation ...
dT +k(T -60)dt = 0 . . . . T(0) = 139
SolutionThis is a separable differential equation, so we can solve it by separating the variables and integrating each side:
[tex]\dfrac{dT}{T-60}=-k\,dt\\\\\displaystyle \int{\dfrac{dT}{T-60}}=\int{-k}\,dt\\\\\ln{(T-60)}=-kt+C\\\\T-60=e^{-kt+C}=Ce^{-kt}\qquad\text{take antilogs; values of $C$ are different}[/tex]
Applying the initial condition, we have ...
139 -60 = C = 79
Then the particular solution is ...
[tex]\boxed{T=79e^{-kt}+60}[/tex]
Help asap ? Need to be turned in by end of class aka 8:40
Answer:
All the answers are bolded in the step-by-step explanation.
Hope it helps :)
Step-by-step explanation:
The radius of the top of a cylinder is always the same length as the radius of the base of a cylinder.
Radius of the base of can A: 10 cm
Radius of the base of can B: 18 cm
To find the area of the bases, use the area formula that you put as your first answer.
Area of the base of can A:
[tex]A=\pi (10^{2} )[/tex]
[tex]A=100\pi[/tex]
[tex]A=314[/tex] cm (Assuming we're only using 3.14 and not any other decimals)
Area of the base of can B:
[tex]A=\pi (18^{2} )[/tex]
[tex]A=324\pi[/tex]
[tex]A=1017.36[/tex] cm (Again, assuming we're only using 3.14 and not any other decimals)
The base of can B has a greater Area
To find the height, look at the diagram
Height of can A: 28cm
Height of can B: 9cm
Can A has a greater height
To find the volume, use the equation that you put as your answer for question 2 or just multiply the area of the base times the height.
Volume of can A:
[tex]314*28=V[/tex]
[tex]V=8792[/tex]
Volume of can B:
[tex]1017.36*9=V[/tex]
[tex]V=9156.24[/tex]
Can B holds more paint
solution to 4d+9=21?
Answer:
d = 3
Step-by-step explanation:
4d+9=21
4d = 12
d = 3
Let's check
4(3) + 9 = 21
12 + 9 = 21
21 = 21
So, d = 3 is the correct answer.
Answer: 3 = d
Step-by-step explanation:
4d + 9 = 21
- 9 - 9
4d = 12
— —
4 4
d = 3
Is it possible to form a triangle with side lengths , , and ? If so, will it be scalene, isosceles, or equilateral?A.Yes; scaleneB. Yes; isoscelesC. Yes; equilaterald. no
No. A triangle cannot be formed with side lengths of 2, 4, and 5. option (d)
The sum of the lengths of the two shorter sides (2 + 4 = 6) must be greater than the length of the longest side (5). This is known as the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, to form a triangle, the sum of the lengths of the two shorter sides must be greater than the length of the longest side. In this case, the two shorter sides do not meet this requirement, so it is not possible to form a triangle with these side lengths.
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Complete Question:
Is it possible to form a triangle with side lengths 2, 4, and 5? If so, will it be scalene, isosceles, or equilateral?
A.Yes; scalene
B. Yes; isosceles
C. Yes; equilateral
d. no
John bought 9. 25m of cloth for Php 425. 50. Find the cost price per metre. *
A. Php 26. 00
B. Php 36. 00
C. Php 46. 00
D. Php 56. 00
The cost price of cloth that John bought per meter is Php 46.00 (Option C). To find the cost price per meter, divide the total cost by the number of meters of cloth.
In this case, the total cost is Php 425.50 and the number of meters is 9.25. By dividing the total cost by the number of meters, we get Php 46.00 per meter. This means that John paid Php 46.00 for every meter of cloth he bought. This is the cost price per meter and it is option C, Php 46.00.
The specific value that corresponds to the unit price that was purchased is reflected in retail systems by the cost price. In some stock market theories, this value is used to determine the value of stock holdings, and it is used as a key factor in determining profitability.
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a radio program has a quiz consisting of 3 multiple-choice questions, each with 3 choices. a contestant wins if he or she gets 2 or more of the questions right. the contestant answers randomly to each question. what is the probability of winning?
The probability of winning the quiz is 0.19 or 19% when the contestant answers randomly to each question.
The number of possible outcomes for answering 3 multiple-choice questions with 3 choices each is [tex]3^3[/tex] = 27. Out of these 27 possible outcomes, 9 of them result in the contestant getting 2 or more questions correct.
So, the probability of winning the quiz can be calculated as follows:
P(Winning) = 9/27 = 1/3 = 0.3333...
Rounding to two decimal places, the probability of winning the quiz is approximately 0.33 or 33%.
However, since the contestant is answering randomly to each question, the probability of winning can also be expressed as the sum of the probabilities of getting exactly 2, or 3 questions right. This is calculated using the binomial distribution. The probability of getting exactly 2 questions right is:
P(X = 2) = (3 choose 2) * [tex](1/3)^2 * (2/3)^1[/tex] = 3 * 1/9 * 2/3 = 2/9The probability of getting exactly 3 questions right is:
P(X = 3) = (3 choose 3) * [tex](1/3)^3 * (2/3)^0[/tex]= 1 * 1/27 * 1 = 1/27The sum of these probabilities gives the total probability of winning:
P(Winning) = P(X = 2) + P(X = 3) = 2/9 + 1/27 = 5/27Rounding to two decimal places, the probability of winning the quiz is approximately 0.19 or 19%.
Since the contestant is answering randomly to each question, the probability of winning is approximately 0.19 or 19%.
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