A segment with endpoints X Left parenthesis negative 6 comma 2 right parenthesis and Y Left parenthesis negative 1 comma negative 3 right parenthesis is rotated 90º about the origin. What are the coordinates of X Prime and Y Prime?
A. X prime Left parenthesis negative 1 comma negative 3 right parenthesis and Y prime Left parenthesis negative 6 comma 2 right parenthesis.
B. X prime Left parenthesis 2 comma 6 right parenthesis and Y prime Left parenthesis negative 3 comma 1 right parenthesis.
C. X prime Left parenthesis negative 2 comma negative 6 right parenthesis and Y prime Left parenthesis 3 comma negative 1 right parenthesis
D. X prime Left parenthesis 6 comma negative 2 right parenthesis and Y prime Left parenthesis 1 comma 3 right parenthesis
Answers
Answer:
The correct answer is C.
Step-by-step explanation:
This can be done using complex numbers and its relations with plane geometry. The endpoints of the segment are X(-6,2) and Y(-1,-3). These points can be seen as complex numbers, just recall the geometric interpretation of complex numbers.
So, the complex counterpart of [tex]X(-6,2) is x=-6+2i[/tex], and the complex counterpart of [tex]Y(-1,-3) = -1-3i[/tex]. Moreover, a rotation about the origin has an interpretation as multiplication by a complex number of modulus 1. In this particular case, a rotation of 90 degrees is equivalent to multiply by the complex unit: [tex]i=\sqrt{-1}[/tex].
Then,
[tex] x' = (-6+2i)\times i = -2-6i[/tex] which gives the point [tex]X'(-2,-6)[/tex]
[tex] x' = (-1-3i)\times i = 3-1i[/tex] which gives the point [tex]Y'(2,-1)[/tex].
The other option is to use a software to make geometrical constructions as Geogebra. Bellow there is an image attached made with Geogebra with the solution of the exercise.
Related Questions
What is Henry's speed
Answers
Therefore, for every hour henry travels 60 miles
Patrick is making 8 pizzas. he has 15 2/3 cups of mozzarella cheese that he wants to divide evenly among the pizzas.
how many cups of cheese should he put on the pizzas?
Answers
47/3 and divide it by 8 but you have to convert the division in to multiplication and use the reciprocal of 8 which would be 8 = its reciprocal 1/8. We are now left with 47/3 x 1/8 = 47/24; take 47/24 and simplify by taking 47 divided by 24 and we would have 1 23/24 cups per pizza.
Dan the detective looked for a number. he found a two-digit number less than 50. the sum of its digits was 12. their different was 4. what number did da find
Answers
for numbers that you cannot quickly tell, suppose the one's digit is x, and the tens' digit is y
in this case, x+y=12 and x-y=4.
add the two equation to eliminate y: 2x=16, x=8
y=x-4=4
the number is 48
Mark earns $400 a week plus 5% commission on all sales. Which inequality represents s, what mark's sales must be in order for him to earn at least $700 for the week?
Answers
Tanya planted seedlings in her garden over the weekend. The instructions that came with the seedlings stated that they need to be planted 0.2 meters apart. Tanya has a measuring tape that has values in centimeters. Help Tanya convert meters to centimeters.
Answers
Answer:
20 centimeters apart.
Step-by-step explanation:
Tanya planted seedlings in her garden over the weekend.
The instructions that came with the seedlings stated that they need to be planted 0.2 meters apart.
Tanya has a measuring tape that has values in centimeters.
As we know 1 meter = 100 centimeters
therefore, 0.2 meter = 0.2 × 100 = 20 centimeters
So Tanya need to be planted 20 centimeters apart.
How to turn a fraction into a percentage?
Answers
i hope i helped
Which decimal number is equal to 2/3 ?
A. 0.6
B. 0.66
C. 0.6
D. 0.67
Answers
The answer should be B.
Decimal number equal to 2/3 is 0.67.
What is a Decimal and fractional Numbers?
Decimal numbers include those numbers which have a whole number and the fractional part separated by a decimal point. Example -
2.33, 4.55, 5.6
A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percent, or with a negative exponent. Example -
2/5, 5/6, 7/9
We have a fraction 2/3.
The decimal number equal to 2/3 is 0.67.
Hence, decimal number equal to 2/3 is 0.67.
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What is the length of side AB
Answers
7x+y=13 y=2x-0.5 elim
Answers
7x + y = 13 ---> 7x + y = 13
y = 2x - 0.5 ---> + 2x - y = 0.5
9x = 13.5
/9 /9
x = 1.5
y = 2x - 0.5
y = 2(1.5) - 0.5
y = 3 - 0.5
y = 2.5
Therefore the solution to the linear system is (1.5, 2.5) or (3/2, 5/2)
Write the expression in algebraic form. [hint: sketch a right triangle.] tan(arcsec(x/3))
Answers
Sketch a right triangle having adjacent side(A) is given as “3”, hypotenuse side (H) is “x” and assigning angle “a” as the angle between A and H. Using Pythagorean theorem, you will get “square root of x-squared minus 9” as the opposite side (O). Using SOH CAH TOA function, and since secant is the reciprocal of cosine, sec(a) = x/3. Thus, a = arcsec(x/3). The remaining expression tan(a) is Opposite side over Adjacent side which is equal to “square root of x^2 - 9” over "3". Therefore, the algebraic expression would be: tan(arcsec(x/3)) = “sqrt (x^2 -9)” /3. Different answers can be made depending on which side you consider the “3” and “x”.
the scale of a map is 1 cm :50 mi. Determine the distance between two cities that are
4.2 cm apart on the map
Answers
The actual distance between two cities that are 4.2 cm apart on a map with a scale of 1 cm : 50 mi is 210 miles. The distance was calculated using a direct proportion based on the map's scale.
Explanation:To determine the actual distance between two cities that are 4.2 cm apart on a map with a scale of 1 cm : 50 mi, you can use the following method:
First, understand that the scale means for every 1 cm on the map, the actual distance is 50 miles. Therefore, you can set up a direct proportion to solve for the actual distance.
Scale of map: 1 cm : 50 mi
Distance on map: 4.2 cm
Setting up the proportion, we get:
1 cm / 50 mi = 4.2 cm / x miNow, solve for 'x' which represents the actual distance between the two cities.
x = (4.2 cm × 50 mi) / 1 cmx = 210 miThe actual distance between the two cities is 210 miles.
Erin had $35 more than Angie who had 3 times as as money as Jacob. If they had $196 altogether, how much money did Jacob have?
Answers
j+3j+3j+35=196
7j=161
j=23
Jacob had $23
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Geometry
The polynomial function y = x3 -3x2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
A) The function has one imaginary zero.
B) The function has one real zero and two imaginary zeros.
C) The function has one real zero and one imaginary zero.
D) The function has one imaginary zero and two real zeros.
Answers
The sum of two numbers is 66 . the larger number is eight more than the smaller number. what are the numbers?
Answers
x = 8 + y
y = x - 8
37 + 29 = 66
x = 37
y = 29
(The larger number is 37, and the smaller one is 29).
I hope that helped you! c:
I NEED MATH HELP, QUICK! PLEASE HELP ME!
The graph of the equation y = 3x + 4 is shown. Determine the value of y for the point
(-1, y).
Answers
To find the value of y for the point (-1, y) in the equation y = 3x + 4, plug in -1 for x and solve: y = -3 + 4, which simplifies to y = 1. Thus, the value of y is 1.
The student needs to determine the value of y when x is -1 for the equation y = 3x + 4. To find y, we substitute -1 in place of x and solve the equation:
y = 3(-1) + 4
y = -3 + 4
y = 1
Therefore, the value of y for the point (-1, y) is 1.
enter the correct word and unit of measurement to complete the conversion
1 nanosecond = one ___
of a __
Answers
1 nanosecond = one billionth of a second
In other words, it takes 1 billion nanoseconds to elapse for one whole second to pass by. It's a very small amount of time.
Answer:
1 nanosecond = 1 billionth of a second
Step-by-step explanation:
A nanosecond (ns) is an SI unit of time equal to one billionth of a second, that is, 1⁄1 000 000 000 of a second, or 10^−9 seconds. The term combines the prefix nano- with the basic unit for one-sixtieth of a minute. A nanosecond is equal to 1000 picoseconds or 1⁄1000 microsecond.
Find three consecutive even integers such that the sum of twice the smallest number and three times the largest is 42.
Answers
the second x +2
the third x+ 4
twice the smallest 2x
three times the largest 3(x+4 )
2x + 3(x+4 )=42
2x +3x +12 = 42
5x= 30
x=6 the second is 8 the third is 10
iana started to evaluate the function f(x) = 2x2 – 3x + 7 for the input value 2.
f(x) = 2(2)2 – 3(2) + 7
= 2(4) – 3(2) + 7
What is the value of the function when x = 2?
9
10
16
17
Answers
Answer:
f(2) = 9.
Step-by-step explanation:
Given : f(x) = 2x² – 3x + 7.
To find : What is the value of the function when x = 2.
Solution : We have given that f(x) = 2x² – 3x + 7.
For, x = 2
f(2) = 2(2)² – 3(2) + 7.
f(2) = 2 *4 -6 +7
f(2) = 8 - 6 +7.
f(2) = 2 +7
f(2) = 9.
Therefore, f(2) = 9.
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Answers
- Two supplementary angles add up to 180°, forming a straight angle (the angle formed by a straight line)
- The interior angles of a triangle add up to 180°
Given those, we notice that the one unlabeled angle in the figure shares a line with 156°. In fact, this angle is supplementary to 156°, which means that the two add up to 180°. To find the measure of this mystery angle, we can subtract 156 from 180 to obtain 180 - 156 = 24°.
Now, let's look at the triangle. We already know the measure of one of the angles is 24°, and the other two are x°. What else do we know about the angles of a triangle? From the two facts listed at the beginning, we know their interior angles add up to 180°, so let's use that fact to solve for x.
We have:
[tex]x+x+24=180[/tex], or [tex]2x+24=180[/tex]
Solving for x:
[tex](2x+24)-24=180-24\\2x=156\\(2x)/2=(156)/2\\x=78[/tex]
So, x = 78°.
For question 5, the definition of a pair of parallel lines is a pair of lines which never intersect, so "always" would be the appropriate answer.
Um navio esta situado exatamente a 10 milhas a leste de um ponto A. Um observador, situado exatamente a sul do navio, ve o ponto A sob um angulo de 40°. Qual a distância entre o observador e o navio?
Answers
Com estes 3 pontos formamos um triangulo.
O angulo OAN vale 40º
O lado AN vale 10 milhas
O que queremos saber é a distância entre o observador e o navio: lado NO
2) Para isso calculamos a tangente deste angulo: tg 40º= angulo oposto/ angulo adjacente.
angulo oposto é o NO e o lado adjacente ao angulo é o AN que vale 10
Se fores à calculadora vês que tg40º é 0,83.
0,83= angulo oposto/ 10
ang oposto= 8,3 milhas
o observador e o navio estao a 8,3 milhas de distancia
What is the product 4.6(-5.2)
Answers
Final answer:
The product of 4.6 and -5.2 is 20.12.
Explanation:
The product of 4.6 and -5.2 is calculated by multiplying the two numbers together. To do this, we can use the following steps:
Multiply the whole numbers: 4 * 5 = 20Multiply the decimal parts: 0.6 * 0.2 = 0.12Add the results: 20 + 0.12 = 20.12Therefore, the product of 4.6 and -5.2 is 20.12.
Eight subtracted from five times a number is -138. what is the number?
Answers
You add 8 to each side
5n= -130
Divide by 5 on each side
n = -26
Have a wonderful day
Answer:
8-5n= -138
You add 8 to each side
5n= -130
Divide by 5 on each side
n = -26
Step-by-step explanation:
Find the points on the curve given below, where the tangent is horizontal. (round the answers to three decimal places.) y = 7 x 3 + 6 x 2 - 8 x + 7
Answers
To find the points where the tangent is horizontal on the given curve, find the values of x for which the derivative is zero.
Explanation:To find the points on the given curve where the tangent is horizontal, we need to find the values of x for which the derivative of the curve is equal to zero. This is because the derivative represents the slope of the tangent line. Setting the derivative equal to zero and solving for x will give us the x-coordinates of the points.
The given curve is y = 7x³ + 6x² - 8x + 7. To find the derivative of this curve, we use the power rule of differentiation. The derivative is dy/dx = 21x^2 + 12x - 8.
Setting dy/dx equal to zero, we have 21x² + 12x - 8 = 0. To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). Using this formula, we can find the values of x that make the derivative equal to zero.
Keywords: curve, tangent, horizontal, derivative, quadratic equation
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which inequality best represents the following situation: A driver is on the highway, with a speed limit of 70 miles per hour, and is not breaking the law?
Answers
2m= p-q/r
solve for p
Answers
Add q/r on both sides of the equal sign
2m+q/r=p
Therefore...
p=2m+q/r
Answer: The required solution for p is [tex]p=2mr+q.[/tex]
Step-by-step explanation: We are given to solve the following equation for the variable p :
[tex]2m=\dfrac{p-q}{r}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation for p, we must take p on one side of the equation and all other terms on the other side.
From equation (i), we get
[tex]2m=\dfrac{p-q}{r}\\\\\Rightarrow 2mr=p-q~~~~~~~~~~~~~~[\textup{Cross-multiplication}]\\\\\Rightarrow p=2mr+q.[/tex]
Thus, the required solution for p is [tex]p=2mr+q.[/tex]
A video game arcade offers a yearly membership with reduced rates for game play. A single membership costs $60 per year. Game tokens can be purchased by members at the reduced rate of $1.00 per 10 tokens. Which statements represent the function of the yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Check all that apply. The slope of the function is $1.00. The y-intercept of the function is $60. The function can be represented by the equation y = 1/10x + 60. The domain is all real numbers. The range is {y| y ≥ 60}.
Answers
The function can be represented by the equation y=1/10x+60
The range is {y| y ≥ 60}
A firework exploded 1,360 meters away and the sound of the firework took 4 seconds to reach you. At what speed did the sound travel?
Answers
Answer:
Speed of sound, v = 340 m/s
Step-by-step explanation:
It is given that,
A exploded 1360 meters away, d = 1360 meters
time taken, t = 4 seconds
We need to find the speed of the travelled sound. Speed of sound is equal to the distance covered divided by total time taken i.e.
[tex]v=\dfrac{d}{t}[/tex]
[tex]v=\dfrac{1360\ m}{4\ s}[/tex]
v = 340 m/s
So, the speed with which sound is travelled is 340 m/s. Hence, this is the required solution.
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What are the steps for using a compass and straightedge to construct the bisector of ∠G?
Drag the steps and drop them in order from start to finish.
A. Use the straightedge to draw GK−→−.
B. Place the point of the compass on point H and draw an arc in the interior of the angle.
C. Place the point of the compass on point G and draw an arc that intersects the sides of ∠G. Label the points of intersection as points H and J.
D. Without changing the opening of the compass, place the point of the compass on point J and draw another arc in the interior of the angle.
E. Label the intersection of the arcs in the interior of the angle as point K.
Answers
You need to create an arc that intersects the angle. That is providing the equal sections for the bisections. Where the arcs intersect in E is the midpoint between the two rays. GK is the bisector of the angle.
Answer:
C, B, D, E, A.
Step-by-step explanation:
A recipe calls for 1 1/2 cups of flour,but you only have 2/3 of a cup.How much more flour do you need?
Answers
First, make 1 1/2 an Improper fraction:
1 1/2 = 3/2
Next, Subtract:
3/2 - 2/3 = 5/6
Your answer would be 5/6
♡ Hope I helped ♡
Determine whether the lines l1 and l2 are parallel perpendicular or neither
Answers
The lines l1 and l2 are perpendicular to each other. They form a 270° angle which means they form three right angles. Hence they are indeed perpendicular due to the fact they intersect at a point if one line is extended by 180°.
Explanation:In this case, we are asked to determine if the lines l1 and l2 are parallel, perpendicular or neither. One critical information presented is that the two lines are perpendicular and form a 270° angle between each other.
Typically, when two lines are perpendicular, they form a right angle, which is 90°. However, a 270° angle suggests they make three right angles, meaning they do not directly intersect at a right angle, but do meet at a point if you extend one line 180° further. Hence, they are indeed perpendicular.
So, although it might seem a bit unusual, based on this information, the lines l1 and l2 are perpendicular to each other.
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