Triangle ABC maps to triangle A′B′C′ by a 90∘ rotation counterclockwise about the origin.
If AB=61 units, BC=11 units, and AC=60 units, what is the length of A′C′?
11 units
61 units
90 units
60 units
Answer:
60 Units
Step-by-step explanation:
The length of AC does not change. Since the translation is a rotation, nothing about the size of the triangle should change. Meaning A'B'C' is still 60 units in length.
The length of the side A'C' of the triangle after rotation is A'C' =AC = 60 units
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 ΔABC
Now , the measures of the sides of the triangle are
The measure of side AB = 61 units
The measure of side BC = 11 units
The measure of side AC = 60 units
And , the triangle is rotated by 90° counterclockwise about the origin
The coordinates of the triangle after rotation is A'B'C'
And ,
The measure of side A'B' = 61 units
The measure of side B'C' = 11 units
The measure of side A'C' = 60 units
The length of the sides of the triangle does not change during a transformation of rotation by any degree
Hence , the measure of side A'C' of triangle is 60 units
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According to one study, the average monthly cell phone bill in the U.S. is $70. If a 20-year old student with an average bill gives up her cell phone and each month invests the $70 she would have spent on her phone bill in a savings plan that averages a 4% annual return, how much will she have saved by the time she is 65?
Answer:
$37,800
Step-by-step explanation:
If she put 70 dollars in every month for 45 years she would have $37,800
Victoria purchased 0.6lbs of deli ham for $4.71. What is the cost of ham per pound?
Answer:
$7.85
Step-by-step explanation:
Per pound = 1
Ratios:
[tex]\frac{4.71}{0.6} =\frac{x}{1} \\\\0.6x=4.71\\x=7.85[/tex]
Ana,beto y Carla son confeccionará de polos,por cada 12 polos que confecciona Ana,Beto confecciona 7,mientras que por cada 28 polos que confecciona Beto,Carla confecciona 15 si el fin de semana Carla confecciona 198 polos más que Carla,cuántos polos confecciono Beto ese día?
Resolviendo un sistema de ecuaciones veremos que polo hizo 170 polos.
¿Cuantos polos confecciono Beto ese día?Sabemos que por cada 12 polos que confecciona Ana, Beto hace 7.
Por cada 28 polos que confecciona Beto, Carla confecciona 15.
Y sabemos que Ana hizo 198 polos mas que Carla.
Definamos las variables:
C = polos que hizo Carla.
A = polos que hizo Ana
B = polos que hizo Beto.
Podemos escribir las ecuaciones:
A = C + 198
B = (7/19)*A
B = 28/(28 + 15)*C
Tenemos un sistema de ecuaciones, las segundas dos son las que obtenemos con los ratios que nos proporcionan.
Reemplazando la primer ecuacion en la segunda obtenemos el sistema:
B = (7/19)*(C + 198)
B = 28/(43)*C
De la segunda ecuacion podemos obtener:
C = B*(43/28)
Remplazando eso en la otra ecuacion obtenemos:
B = (7/19)*(B*(43/28)+ 198)
Ahora podemos encontrar el valor de B.
B = 0.57*B + 72.95
B - 0.57*B = 72.95
B*0.43 = 72.95
B = 72.95/0.43 = 169.6
Redondenado, B = 170, ese es el número de polos que Beto confecciono.
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Please Answer This question I will give you brainleist
Which of the following best describes an adaptation?
A characteristic that helps a living thing survive
A group of animals that behave in the same way
A trait that all animals have in common
A way that helps animals find shelter
WIll GIve 50 Points Very Easy Easy Plz Help
Answer:
Vertical Angles- 1 and 3
Corresponding Angles- 2 and 6
Alternate Interior Angles- 4 and 6
Alternate Exterior Angles- 2 and 8
Supplementary Angles- 1 and 2
WILL GIVE BRAINLIEST!!!
In a test of hypothesis for a mean, which statement is CORRECT?
The population must be normal because that is the only case when the sample mean is Normally distributed.
As long as the population distribution consists only of positive values, sample size does not matter.
The population distribution can be any distribution because the sample mean is always Normally distributed.
The test requires that the sample mean is normally distributed; this requires that either the population distribution is Normal or the sample size exceeds 30.
Answer:
As long as the population distribution consists only of positive values, sample size does not matter.
Step-by-step explanation:
As long as the population distribution consists only of positive values, sample size does not matter.
This is a hypothesis because a hypothesis is basically a prediction of what's gonna happen; the other choices are mostly facts that can be backed up, this can only be confirmed after it happens since it can end in different ways. This is a prediction where it says that if the population distribution continues to go on to positive value, then the sample size won't matter; this can come out in different ways, the sample size could matter or it would have to be negative values, e.t.c. This has different ways it could end up.
Does anyone know the answer to this one ???
What number divided by −3 gives 12 as the result
Answer: -36
Step-by-step explanation: a negative and a negative give a positive so -36/-3=12
(to check your answer you can also always just multiply the two numbers ex: 12 x -3= -36)
help me please asap
Please please i need help i will mark u brill
[tex] \bf\green{7.8 \times c + 3.4 = 19} \\ \\ \bf\red{7.8 \times 2 + 3.4 = 19} \\ \\ \blue{\bf{15.6 + 3.4 = 19}} \\ \\ \bf \red{\boxed{ \underline{\underline{\pink{ 19 = 19}}}}}[/tex]
Haha, very easy... :)
Factor this trinomial completely.
15x2 + 11x - 12
A. (x + 4)(15x - 3)
B. (3x + 3)(5x – 4)
C. (x+3)(15x - 4)
O D. (3x + 4)(5x – 3)
Answer:
D
Step-by-step explanation:
3x * 5x = 15x^2
3x * -3 = -9x
4*5x = 20x
4 *-3 = 12
so 15x^2 +(20x -9x) -12 or 15x^2 +11x -12
he point A has coordinates A(2, 4). What are the X-coordinates of A′ for the dilation D1.5(A)?
Answer:
(3,6)
Step-by-step explanation:
For dilation, you just multiply the coordinates by the scale factor (in this case 1.5) to get the answer! Hope that helps :)
standard normal distribution
Answer:
distribution form is like 12x6+24
Step-by-step explanation:
standard form is like 128
HELP ME FAST PLEASE!!!!!
the volume of a triangular prism is 32 cubic inches. The prism is 2 inches tall. What is the area of the base of the triangular prism?
A. 4 square inches
B. 12 square inches
C. 8 square inches
D. 16 square inches
Answer:
D. 16 in²Steps:
given:
V = 32 in³
h = 2
Ab = V/h
Ab = 32/2
Ab = 16 in²
Solve each equation.
1.5(n - 4) = -60
2.-3t+-8 = 25
3.7p - 8 = -22
4. (+40) = -4
5.4(w + 1) = -6
Answer:
1. n= -8
2. t= -11
3. p= -2
4. Not quite sure thats a proper equation.
5. w= -2.5 if thats the actual equation. if youre missing a 0 on 6 then its -15
Can someone please help me graph this I really need help and I’m really confused !!
Answer:
For example number 1 is A(-3,5), so on the graph you will go over -3 spaces to the left. Then for 5 you will go up on the graph. Your going up on the graph because it is a positive number. Then the A will be 3 spaces over from positive 5.
Step-by-step explanation:
Hope this helped :)
Irene is making bags of trail mix for hiking club. She will use 22 ounces of walnuts, 11.2 ounces of
almonds, and 12.3 ounces of cashews. This amount makes 25 bags of trail mix. How many
ounces are in each bag?
Please help :/ if i dont finish theses questions i will go to summer school & i dont wanna go there
Answer:
In each bag there will be 1.82 ounces of mixture.
Step-by-step explanation:
Since Irene is making bags of trail mix for hiking club, and she will use 22 ounces of walnuts, 11.2 ounces of almonds, and 12.3 ounces of cashews to make 25 bags of trail mix, to determine how many ounces are in each bag you must perform the following calculation:
(22 + 11.2 + 12.3) / 25 = X
45.5 / 25 = X
1.82 = X
Thus, in each bag there will be 1.82 ounces of mixture.
There are 6 squares and 9 circles. What is the simplest ratio of squares to
total shapes?
Answer:
2:5
Step-by-step explanation:
There are 9 students participating in a spelling bee. In how many ways can the students who go first, second, and third be
chosen?
B.504 ways
C.529 ways
a. 454 ways
d. 404 ways
Answer:
I'm pretty sure it is C
Step-by-step explanation:
Please help me im gonna fail.
Answer:
see below
Step-by-step explanation:
if the radius is 21, then the height is 24 (21 is 3 less than 24)
[tex]v=\pi r^{2} h\\v=\pi 21^{2} (24)\\v=\pi 441*24\\V=\pi 10.584\\v=3.14(10.584)\\V=33234[/tex]
the closest option would be the 33264
if you take 4 steps every 6 minutes, how long will 10 steps be?
Answer:
15
Step-by-step explanation:
divide 6 into 4 than what ever your answer is multi... by 10
The angle \theta_1θ
1
theta, start subscript, 1, end subscript is located in Quadrant \text{II}IIstart text, I, I, end text, and \sin(\theta_1)=\dfrac{9}{41}sin(θ
1
)=
41
9
sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 9, divided by, 41, end fraction .
What is the value of \cos(\theta_1)cos(θ
1
)cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Trig identity are written in term of cosine, sine and tangent, he value of cosθ if the value of sinθ is 9/41 is 40/41
Trigonometry ratioGiven the following parameters
sinθ = 9/41
According to the SOH CAH TOA identity
sinθ = opposite/hypotenuse
Determine the adjacent sides
a= √41² - 9²
a = √ 1600
a = 40
Determine the value of cosθ
cosθ = adjacent/hypotenuse
cosθ = 40/41
Hence the value of cosθ if the value of sinθ is 9/41 is 40/41
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Answer:
-40/41
Step-by-step explanation:
Enter the data to create a histogram. Then select the correct answer. hours 3 4 4 2 5 416 6 5 Faizah keeps track of the hours she practices. O The histogram is not symmetrical O The histogram is symmetrical. O The data are not evenly distributed O The left side of the graph is not the mirror image of the right side of the graph.
Through the use of the data given, the histogram can be classified as the histogram is not symmetrical.
When is histogram not symmetrical?The histogram is not symmetrical if it is or has skewed distribution.
This is said to be when a distribution is said to not have any mirror-imaging. and as such, through the use of the data given, the histogram can be classified as the histogram is not symmetrical.
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96 = 12d
A. 108 B. 84 C. 8 D. −1 8
Answer:
Step-by-step explanation:
Answer:
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5% of a number is 27.
1 %of the same number is 5.4
work out 14% of the number.
Answer:
75.6
Step-by-step explanation:
100*5.4=540
540/14=75.6
Sean Wrona is the fastest typist in the world and can type an average of about 500 words in three minutes.
What is Sean’s average typing speed in words per minute, WPM, to the nearest whole number?
Answer:
166.67 is answer of this question
Angle P and angle Q are supplementary angles. If m(angle)p is 21 degrees less than twice the measure of
Angle Q , find the measure of each angle.
Answer:
Angle Q: 67 degrees
Angle P: 113 degrees
Step-by-step explanation:
You can write an equation to solve this. We know that angle P + angle Q = 180. If we substitute angle Q into the second equation we get angle P = 2*angle Q -21.
Plugging that knowledge into the first equation, we get 2*angle Q-21 + angle Q =180. Simplifying, we get 3* angle Q -21 = 180. Adding 21 to both sides gives us 3*angle Q = 201, dividing by 3 gives us angle Q = 67. 180-67= 113 so angle P is 113.
Timothy took 2/3 hr to paint a portrait. This was 1/3 hr shorter than the time he took to paint scenery. How long did he take to paint scenery? I need help ASAP
Answer:
1 hour
Step-by-step explanation:
2/3+1/3
=3/3 or 1
that's my answer
i hope it helos
I need to find the answer to 3 questions. Which measure of central tendency is most representative of the data 6, 8, 3, 5, 32, 6, 5, 4, 28, 2, 2, 2. Which measure of central tendency is most representative of the data. 1, 3, 17, 20, 4, 3, 18, 1, 2, 19. and 15, 10, 13, 20, 152, 18, 8, 5, 13
Step-by-step explanation:
the first one is 2 that appears most while the second is 20 and 3
0) 9 deliveries in 3 hours deliveries in 1 hour Submit
Answer: 3 delivers an hour
Step-by-step explanation:
9/3=3