Triangle ABC was rotated about the origin. Which rule
describes the rotation?
A) Ro,90°
B) Ro,180°
C) Ro,270°
D) Ro,360°
Answers
The R stands for "rotation". The "O" as a small subscript means "origin" which is where the x and y axis cross. The 90 degrees means we rotate 90 degrees counterclockwise. This is equivalent to 270 degrees clockwise, but writing [tex]R_0, 270^{\circ}[/tex] is not correct as we don't rotate 270 degrees counterclockwise.
The solution is Option A.
The rotation angle is given by R0 ( 90° )
What is Rotation?The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the triangle be represented as ABC
The coordinate of A = A ( 1 , 4 )
The coordinate of B = B ( 3 , 4 )
The coordinate of C = C ( 3 , 2 )
Now , when the triangle ABC is rotated 90° counterclockwise rotation: (x,y) becomes (-y,x)
Substituting the values in the equation , we get
The coordinate of A' = A' ( -4 , 1 )
The coordinate of B = B ( -4 , 3 )
The coordinate of C = C ( -2 , 3 )
Hence , the rotation is 90° counterclockwise
To learn more about rotation click :
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Related Questions
a group of 12 friends want to see a movie, only 7 seats are available for the current show, they draw straws to determine who will watch the movie and who will go to a leter show. how many different groups are posssible for the current showing of the movie? a 426 b 95,040 c 792 d 33, 264
Answers
Because 12choose7= 792
Please help answer this question Minni has to buy stickers, erasers, and a pencil. She can only spend $4. A sticker costs $0.35, an eraser costs $0.99, and a pencil costs $0.59. Can Minni buy 2 stickers and 2 erasers? [Use the inequality 0.35x + 0.99y + 0.59 ≤ 4] (1 point) Select one: a. Yes, because the total will be $3.27 b. Yes, because the total will be $1.93 c. No, because the total will be $4.27 d. No, because the total will be $5.93
Answers
Answer: A
Since you already have an equation just put in how many stickers and erasers she wants to get: 0.35(2)+0.99(2)+0.59≤4.
Then you multiply: .35(2)=.70. .99(2)=1.98.
Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 so the answer is A
Answer:
A. yes, because the total will be $3.27
Step-by-step explanation:
0.35x + 0.99y + 0.59 ≤ 4
0.35(2) + 0.99(2) + 0.59 ≤ 4
0.70 + 1.98 + 0.59 ≤ 4
3.27 ≤ 4
10 + 3² - 6 = 7 10 11 13
Answers
Answer:
13
Step-by-step explanation:
Evaluate 3² then add and subtract, that is
10 + 3² - 6
= 10 + 9 - 6
= 19 - 6
= 13
Create a table of values for the function f(x) = (1/3)^–x
Answers
Answer:
See the explanation
Step-by-step explanation:
The function given to us is:
f(x) = (1/3)⁻ˣ
We can convert the negative power into positive one by interchanging the numerator and denominator.
f(x) = (3/1)ˣ
f(x) = 3ˣ
Substitute value for x= -3 , -2, -1, 0, 1, 2, 3
f(-3) = 3⁻³ = 0.037
f(-2) = 3⁻² = 0.111
f(-1) = 3⁻¹ = 0.333
f(0) = 3⁰ = 1
f(1) = 3¹ = 3
f(2) = 3² = 9
f(3) = 3³ = 27
f(4) = 3⁴ = 81
and so on
The table of the found values of f(x) or y for the corresponding values of x, along with their graph is given below.
Need help with trig problem in pic
Answers
Answer:
a) [tex]cos(\alpha)=-\frac{3}{5}\\[/tex]
b) [tex]\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]
c) [tex]\frac{4+3\sqrt{3} }{10}\\[/tex]
d) [tex]\alpha\approx 53.1^o[/tex]
Step-by-step explanation:
a) The problem tells us that angle [tex]\alpha[/tex] is in the second quadrant. We know that in that quadrant the cosine is negative.
We can use the Pythagorean identity:
[tex]tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}[/tex]
Where we have used that the secant of an angle is the reciprocal of the cos of the angle.
Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:
[tex]cos(\alpha)=-\frac{3}{5}[/tex]
b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:
[tex]cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]
where we took the positive value, since we know that the angle is in the first quadrant.
c) We can now find [tex]sin(\alpha -\beta)[/tex] by using the identity:
[tex]sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\[/tex]
Notice that we need to find [tex]sin(\alpha)[/tex], which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:
[tex]sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}[/tex]
Then:
[tex]sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}[/tex]
d)
Since [tex]sin(\alpha)=\frac{4}{5}[/tex]
then [tex]\alpha=arcsin(\frac{4}{5} )\approx 53.1^o[/tex]
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
Answers
Answer:
B. Quadratic Function
Quadratic Term: 15x^2
Linear Term: 9x
Constant Term: -6
Step-by-step explanation:
1. F.O.I.L (firsts, outers, inners, lasts) the function
BREAK APART: 3x(5x - 2) and 3(5x - 2)
(fx) = 15x^2 - 6x + 15x - 6
f(x) = 15x^2 + 9x - 6
There is a square in the function, therefore it is quadratic. The quadratic term is the term being squared, and you go from there.
Find the volume of the prism shown. Use Cavalieri’s principle. ANSWERS: 336 cm3 2,696 cm3 1,084 cm3 164 cm3
Answers
Answer:
336 cm3
Step-by-step explanation:
Using Cavalieri’s principle, this volume is the same as for a right rectangular prism with these dimensions. Apply the formula for volume of a rectangular prism:
V = lwh
V = (6)(4)(14)
V = 336 cm3
HELP QUICK ILL GIVE A Brainliest to the first person Which of the answer choices is a coordinate point from the table below?
Answers
Answer:
2/$5.00
Step-by-step explanation:
It's the only one that makes sense
Answer:
4,10
It is the only option on the table
Step-by-step explanation:
5. Solve the inequality.
-4(3-X) > 8
a. -5
b. x < -5
c. 5< x
d. x < 5
Answers
Answer:
x >5
Step-by-step explanation:
-4(3-X) > 8
Divide by -4, remembering to flip the inequality
-4/-4(3-X) < 8/-4
3-x < -2
Subtract 3 from each side
3-x-3 < -2-3
-x <-5
Divide by -1, remembering to flip the inequality
x >5
Answer:
[tex]c.[/tex] [tex]5<x[/tex]
Step-by-step explanation:
[tex]-4(3-x)>8\\3-x>-2\\-x>-5\\x>5[/tex]
Can you help to solve this and explain how thanks in advance
Answers
Hey there! :)
Answer:
5.
Step-by-step explanation:
The pattern of this puzzle is to take the bottom two numbers of the triangle, find the sum, then divide by the top number. For example:
8 + 4 = 12 --> 12/3 = 4.
5 + 13 = 18 --> 18/6 = 3.
9 + 5 = 14 --> 14/2 = 7.
Therefore:
14 + 6 = 20 --> 20/4 = 5. The missing number is 5.
Answer: 5
Step-by-step explanation:
The trisectors of angles $B$ and $C$ of scalene triangle $ABC$ meet at points $P$ and $Q$, as shown. Angle $A$ measures 39 degrees and angle $QBP$ measures 14 degrees. What is the measure of angle $BPC$?
Answers
Answer:
BPC=52 degreees
Step-by-step explanation:
ROWAN IS CHEAT
Answer:
133 degrees
Step-by-step explanation:
I saw this answer in the comments and it is correct.
What is the solution to the equation √x^2+2x-25=√x+5 x = –6 x = 5 x = 6, x = –5 x = –6, x = 5
Answers
Answer:
x = 5, -6
Step-by-step explanation:
Step 1: Write out equation
x² + 2x - 25 = x + 5
Step 2: Move everything to one side
x² + x - 30 = 0
Step 3: Factor
(x - 5)(x + 6) = 0
Step 4: Find roots
x - 5 = 0
x = 5
x + 6 = 0
x = -6
Sam has a collection of yellow and red cards. Yellow cards are worth 3 points and
red cards are worth 5 points. He has at most 15 cards, totaling at least 45 points.
This can be modeled by the following system.
y + r < 15
3y + 5r > 45
Graph the system. Then use the graph to determine which combination is a
solution.
1. 3 yellow and 9 red
2. 6 yellow and 4 red
3. 9 yellow and 3 red
4. 12 yellow and 8 red
Answers
Answer:1.
1. 3 yellow and 9 red
Step-by-step explanation:
r, the amount of red cards, is represented ox x-axisy, the amount of yellow cards, is represented ox y-axisIn the picture attached, the system is represented. The darker area shows all the points that are a solution to the system of inequalities.
The combinations can be rewritten as a coordinate pair, as follows:
1. 3 yellow and 9 red -> (9,3)
2. 6 yellow and 4 red -> (4,6)
3. 9 yellow and 3 red -> (3,9)
4. 12 yellow and 8 red -> (8,12)
As we can see in the picture, only the first option is a solution.
What is the slope of the line shown below? A. -1/3 B. 1/3 C. -3 D. 3
Answers
Answer:
C. -3
Step-by-step explanation:
Plugging both of those points into the slope formula gets you a slope of -3.
Find the x-intercepts of the graph y = StartFraction 2 Over x squared EndFraction?
a.
(2, 0) and (-2,0)
c.
There are no x-intercepts
b.
(-1,0) and (1, 0)
d.
x-intercept is (3, 0)
Answers
Answer:
The answer is option c.
There are no x-intercepts
Hope this helps
please help i dont understand it
30 POINTS
Answers
Answer:
0.16 P(Yellow or Brown)=0.16
Answer: 0.44
Step-by-step explanation:
0.4 + 0.28 = 0.68
1.00 - 0.68 = 0.32
0.32 divided by 2.0 = 0.16
Total answer is 0.44
GLAD TO HELP:)
HAVE A NICE DAY!
BTW: I WAS DOING A TEST, BUT TOOK MY TIME TO HELP YOU! :)
PLEASE BRAINLEST ME!
The probability of a randomly selected adult in one country being infected with a certain virus is 0.003. In tests for the virus, blood samples
from 29 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined
sample to test positive? Note that the combined sample tests positive if at least one person has the virus.
The probability that the combined sample will test positive is
(Round to three decimal places as needed.)
Answers
Answer:
The probability that the combined sample tests positive for the virus is 0.083
Since the probability that combined sample test positive for the virus is greater than 0.05, it is not likely for such a combined sample to test positive.
The probability that the combined sample will test positive is 0.083
Step-by-step explanation:
Given that:
The probability of a randomly selected adult in one country being infected with a certain virus is 0.003.
P = 0.003
number of blood sample size n = 29
The probability mass function of X is as follows;
[tex]P(X=x) = \left[\begin{array}{c}{29}&x\\\end{array}\right] (0.003)^x (1-0.003)^{29-x}[/tex]
Thus; the required probability is;
[tex]P(X \geq 1) = 1 - P ( X < 1)[/tex]
[tex]P(X \geq 1) = 1 - P ( X =0)[/tex]
[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} \dfrac{29!}{0!(29-0)!} \ \ \times 0.003)^0 \times (1-0.003)^{29-0}}\end{array}\right][/tex]
[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} 1 \times 1 \times ( 0.9166)\end{array}\right][/tex]
[tex]P(X \geq 1) = 1 - 0.9166[/tex]
[tex]P(X \geq 1) = 0.0834[/tex]
Therefore; the probability that the combined sample tests positive for the virus is 0.083
Is it unlikely for such a combined sample to test positive?
P(combined sample test positive for the virus ) = 0.0834
Since the probability that combined sample test positive for the virus is greater than 0.05, it is not likely for such a combined sample to test positive.
The probability of a randomly selected adult in one country being infected with a certain virus is 0.003.
P = 0.003
number of blood sample size n = 29
The probability mass function of X is as follows;
[tex]P(X=x) = \left[\begin{array}{c}{29}&x\\\end{array}\right] (0.003)^x (1-0.003)^{29-x}[/tex]
Thus; the required probability is;
[tex]P(X \geq 1) = 1 - P ( X < 1)[/tex]
[tex]P(X \geq 1) = 1 - P ( X =0)[/tex]
[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} \dfrac{29!}{0!(29-0)!} \ \ \times 0.003)^0 \times (1-0.003)^{29-0}}\end{array}\right][/tex]
[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} 1 \times 1 \times ( 0.9166)\end{array}\right][/tex]
[tex]P(X \geq 1) = 1 - 0.9166[/tex]
[tex]P(X \geq 1) = 0.0834[/tex]
The probability that the combined sample will test positive is 0.083
what is the square of 5.5?
Answers
Answer:
30.25
Step-by-step explanation:
Answer: 2.345
Step-by-step explanation:
The square root of 5.5 is 2.345.
HURRY I NEED HELP for 20 points
Beginning at the origin, how far do you travel along the y-axis when plotting the point below? (6, 12)
Answers
Answer:
the answer is 12
Step-by-step explanation:
because (6, 12) x axis is 6, and the 12 is the y axis. Meaning that you would go 12 along the y axis.
Answer:
I believe the answer is 12
Help help please.....Thanks
Answers
Hey there! :)
Answer:
56.7 kg.
Step-by-step explanation:
Use the density formula to solve for the mass:
D = m/V.
Rearrange in terms of mass, or 'm':
DV = m.
Solve for the volume:
0.06 × 0.9 × 1.5 = 0.081 m³.
Plug this into the equation along with the density:
700 × 0.081 = 56.7 kg.
Point Q(-1,5) is reflected across the line x=-1. What are the coordinates of its image?
(15)
(1-5)
-1.5)
Answers
Answer:
(- 1, 5 )
Step-by-step explanation:
Since the x- coordinate of Q, x = - 1 lies on the line of reflection.
The point Q will remain unchanged, that is
coordinates of image are (- 1, 5 )
This graph shows how the length of time a canoe is rented is related to the rental cost. What is the rate of change shown in the graph? A. $3/hour B. 3 hours/dollar C. $6/hour D. 6 hours/dollar
Answers
Answer:
what is the answer?
Step-by-step explanation:
Answer:
C. $6/hour
Step-by-step explanation:
AP3X
I NEED HELP ASAP!!!! WILL MARK BRAINLIEST
Answers
Answer: 5x + 1
Step-by-step explanation:
f(x) - g(x)
(3x + 2) - (-2x + 1) Here you distribute the negative sign to (-2x + 1)
3x + 2 + 2x - 1 Here you combine like terms
5x + 1 This is the answer.
(Srry I need my points)
Please help me match these formulas . :)
Answers
Answer:
1. equilateral triangle
2. rectangle
3. circle area
4. trapezoid
5. circle circumference
6. parallelogram
7. regular polygon
8. triangle
Hope that helps.
I NEED HELP !!! If the probability of an event is StartFraction 2 over 7 EndFraction, what must be the probability of its complement?
StartFraction 1 over 7 EndFraction
StartFraction 2 over 7 EndFraction
StartFraction 4 over 7 EndFraction
StartFraction 5 over 7 EndFraction
Answers
Answer:
The answer is StartFraction 5 over 7 EndFraction
Answer:
The probability of the complement of the original event is 5/7.
Step-by-step explanation:
The probability of the complement of an event is 1 less the probability of the event, so
We get: 1 - 2/7, or 5/7
The probability of the complement of the original event is 5/7.
Note that 5/7 and 2/7 add up to 7/7, or 1.
Find the slope of a line parallel to the line
12x + 3y = 15.
A parallel line would have slope m =
The solution is
Answers
Answer:
The answer is - 4Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
12x + 3y = 15
Express it in the form y = mx + c
3y = -12x + 15
Divide all terms by 3
y = - 4x + 5
From the equation m = - 4
Since the lines are parallel their slope are also the same
So the slope of the parallel line is also - 4
Hope this helps you
Use the indicated x-values on the graph of y = f(x) to find the following.
Find intervals over which the graph is concave down. (Consider only the interval (a,h). Enter your answer using only interval notation.)
Answers
Answer:
(a,c) ∪ (f, g)
Step-by-step explanation:
The function is:
concave down in the intervals: (a,c) and (f, g)concave up in the intervals: (c, f) and (h, g)Draw the slope of the tangent lines of several points on the curve,
if the slope increases, the segment is concave upif the slope decreases, the segment is concave down.the rectangle below has an area of x^2-6x-7, square meters and a width of x-7 meters.What expression represents the length of the rectangle?
Answers
Answer:
Length = (x^2-6x-7)m²/ (x-7)m
Step-by-step explanation:
let L =length
let W= width
let A = area of the rectangle.
if A = L × W
making L the subject, divide both side by W
A/W= L×W/W
therefore, L =A/W
L= (x²-6x-7)m²/(x-7)m
Let f be defined as shown. Which statement is
true?
Answers
The inverse of f exists
The inverse of f does not exists
Answers
Answer:
[tex]\boxed{\sf \ \ \ the \ inverse \ of \ f \ does \ not\ exist \ \ \ }[/tex]
Step-by-step explanation:
hello,
for one x you cannot get several values of f(x), otherwise this is not a function
as 6 and 7 gives 0 it means that
f(6)=f(7)=0 which is fine for f
but then for [tex]f^{-1}[/tex] it would mean that 0 has two different images
and this is not possible
so the inverse of f does not exist
hope this helps
SOMEONE PLS HELP ME!!! The mean of a set of five different positive integers is 15. The median is 18. Find the maximum possible value of the largest of these five integers.
Answers
Answer:
35
Step-by-step explanation:
We know that the mean is 15 and the median is 18. In order to solve this problem, we can work backwards. First, image the scenario:
15, 15, 15, 15, 15.
We want the median to be 18, we we can add 3 to the middle number and then subtract three from the first number (in order to keep the mean constant). Thus, we have:
12, 15, 18, 15, 15.
Now, we can subtract and add in order to find the largest number. For instance, we can subtract 11 from 12 and add that 11 to the last number:
1, 15, 18, 15, 26
Next, we can subtract 13 (not 14 because each of the numbers should be different) from the second number and add that to 26:
1, 2, 18, 15, 39.
Finally, the most we an do is to add 4 to the fourth number and subtract 4 from 39 because we want to keep the median 18. Thus:
1, 2, 18, 19, 35.
Each value is distinct.
The largest possible value is 35.
Answer:
35.
Step-by-step explanation:
Since the mean of the five different positive integers is 15, you can assume that they all add up to be 5 * 15 = 75. The median is 18, which means that the rest of the four numbers add to be 75 - 18 = 57, with two numbers higher than 18 and two numbers lower.
You want to find the highest possible values for the maximum, you want to have very low minimums (so you can keep the maximum high). Since the question asks for different positive integers, the lowest numbers you can have are 1 and 2. So far, you have 1, 2, and 18 in your data set, so you have 57 - 3 = 54 to work with for your maximum.
You still want the highest value for the largest of the integers, so the fourth number will be 19. That is because that is the lowest you can go that is still higher than the median. Then, in your data set, you will have 1, 2, 18, and 19, which add up to be 40.
Since all five numbers add to be 75, the maximum will be 75 - 40 = 35.
To make sure this is correct, check your work. 1 + 2 + 18 + 19 + 35 = 75. 75 / 5 = 15. The mean is 15. The middle number is 18, so the median is 18. All five are different positive integers.
And there you have it! The maximum possible value of the largest of these five integers is 35.
Hope this helps!