Answers
Answer: 180 degrees rotation, center (1.5, -0.5)
=====================================================
Explanation:
Notice how point (1,-1) on triangle A moves to (-2,0) and then that rotates to (2,0)
Form a line segment from (1,-1) to (2,0) to show the beginning and end states. The equation of the line through these two points is y = x-2
--------------
Similarly, the point (1,-4) moves to (-2,-3) after applying the translation vector, then it rotates to (2,3). Draw a line through (1,-4) and (2,3). The equation of this line is y = 7x-11
--------------
We have this system of equations
[tex]\begin{cases}y = x-2\\y = 7x-11\\\end{cases}[/tex]
Equate the right hand sides and solve for x
7x-11 = x-2
7x-x = -2+11
6x = 9
x = 9/6
x = 3/2
x = 1.5
which leads to
y = x-2 = 1.5-2 = -0.5
or
y = 7x-11 = 7(1.5)-11 = 10.5-11 = -0.5
Either way, x = 1.5 leads to y = -0.5
We get the ordered pair (x,y) = (1.5, -0.5)
This is the center of rotation when rotating figure A to have it match up with triangle C (the triangle in the upper right quadrant)
Notice in the diagram below point D is that center of rotation. Also, notice that if we use the distance formula, you should find that
AD = A''D
BD = B''D
CD = C''D
Related Questions
I am having a lot of difficulty in solving this question, so please help me..
Answers
Answer:
216
Step-by-step explanation:
=>log 36 = -2/3
m
=>36=(m)^-2/3
=>(root(-36))^3=m
=>m=(root(36))^3
=>m=6^3
=>m=216
Multiply 2x(5x+8y+3)
Answers
Answer:
10x² + 16xy + 6x
Step-by-step explanation:
2x(5x+8y+3)
10x² + 16xy + 6x
Answer:
[tex]10x^{2} + 16xy + 6x[/tex]
Hope this helped!
Help, please! With workings too!
I'm thinking of a 3-digit number.
When it is divided by 9, the remainder is 3
When it is divided by 2, the remainder is 1
When it is divided by 5, the remainder is 4
What is my number?
Answers
3-digit number is abc. ( just call it)
abc= 9d + 3, meaning abc = 3e
abc = 2k + 1, meaning abc is an odd number
abc = 5t + 4, meaning c = 9 ( because abc is an odd number so c can not be 4)
so a+b must be equal 3.
abc can be 309, 219, 129
8. Expand (2a – 3b + 4c)2
Helllpppp plz
Nowww it’s imp
Answers
Step-by-step explanation:
(2a–3b+4c)²=
4a²+9b²+16c²-12ab-24bc+8ac
which of the following does not describe a rigid motion transformation
Answers
Answer:
The answer to this question is dilating the figure by a scale factor of one half.
What’s the solution
Answers
Answer:
x ≥ 12
Step-by-step explanation:
-3/4x +2 ≤ -7
Subtract 2 from each side
-3/4x +2-2 ≤ -7-2
-3/4x ≤ -9
Multiply each side by -4/3, remembering to flip the inequality
-3/4x * -4/3 ≥ - 9 *(-4/3)
x ≥ 12
Answer:
x>=12
Step-by-step explanation:
-3/4x + 2<=-7
-3/4x <= -7 -2
-3/4x<=-9
cross multiply
-3x<=-36
dividing throughout by -3
x>=12
Find the missing angle x. Show your work.
Answers
x+55=90
x=90-55
x=35
The answer is 35 degrees.
Using the information in the Box-and-Whisker plot below, what is the minimum value?
A. 5
B. 12.5
C. 20
D. 27.5
Answers
Answer:
espero ayudarte ..............❤❤
Answer:
b
Step-by-step explanation:
The height of a triangle is 4 feet more than 3 times the base. If the area is 112 ft find the base and height of the triangle
Answers
Answer:
[tex]base = 8 ft\\height =28 ft\\[/tex]
Step-by-step explanation:
let base be x ft. then the height is 3x+4
[tex]Area=\frac{1}{2} \times x \times (3x+4)=112\\3x^{2} +4x=224\\3x^{2} +4x-224=0\\x=8, x=-9.33 (no sol. as length can not be negative)\\ x=8\\base = 8 ft\\height =3(8)+4=28 ft\\[/tex]
Answer:
base = 8 , height = 28
Step-by-step explanation:
Let base be = b
Given:
height is 3times base = 3b
Also 4 feet more than 3 times base = 3b + 4
Area = 112 square feet
[tex]area = \frac{1}{2} \times base \times height\\\\112 = \frac{1}{2} \times b \times (3b+ 4)\\\\224 = b(3b+4)\\\\224 = 3b^2 + 4b\\\\3b^2 + 4b - 224 = 0\\\\[/tex]
The quadratic equation with a = 3 , x = 4 , c = -224
Therefore ,
[tex]b = \frac{-x \pm \sqrt{x^2 - 4ac}}{2a}\\\\[/tex]
[tex]b= \frac{-4 \pm \sqrt{4^2 - (4 \times 3 \imes -224)}}{2 \times 3}\\\\b= \frac{-4 \pm \sqrt{16 + 2688}}{6}\\\\b= \frac{-4 \pm \sqrt{2704}}{6}\\\\b= \frac{-4 \pm52 }{6}\\\\b = \frac{-4 + 52}{6} , \ b = \frac{-4 -52}{6}\\\\b = \frac{48}{6} , \ b = -\frac{56}{6}[/tex]
Since base can't be negative base = 8 ft
Therefore , height = 3b + 4 = 3(8) + 4 = 24 + 4 = 28
Solve this math problem 20 points
Answers
Answer:
46
Step-by-step explanation:
Diagonals of square are equal, Therefore,
KM=161
JL=4x-23
4x-23=161
4x=161+23
4x=184
x=184/4
x=46
A road has a scale of 1:50 000 The length of a road on the map is 8.5cm.Work out the length of the real road in kilometres
Answers
The answer is 2.1 Km. Hope this helps!
What is the solution to the equation 3 + 4/4y = 4?
Answers
Answer:
B. y= ¼
Step-by-step explanation:
3 + ^4√4y = 4
^4√4y =4-3
^4√4y = 1
^4√4y =^4√1
so, 4y = 1
y = ¼
6.
40 x 6+ (9+21)
I need help ASAP please due tomorrow show work
Answers
A mother has 6 sons
Each has a sister
How many people are in the family?
A:13.
B)8.
D)7.
C:14.
Answers
A. 13
Explanation= 6 (sons) +6 (daughters) +1 (mother) = 13.
(notes: as a father is not within the problem, there is no reason to be in the answer)
Answer:
B)8
A mother has 6 sons. If there is only one sister, than each son has a sister. Don't forget to add the mother. 6 + 1 + 1
Step-by-step explanation:
What happens when the multiplicity of a real root is even?
Answers
Answer:
Step-by-step explanation:
The multiplicity of a root affects the shape of the graph of a polynomial. Specifically, If a root of a polynomial has odd multiplicity, the graph will cross the x-axis at the the root. If a root of a polynomial has even multiplicity, the graph will touch the x-axis at the root but will not cross the x-axis.
If an average-sized man with a parachute jumps from an airplane, he will fall
12.5(0.2t − 1) + 21t feet
in t seconds. How long will it take him to fall 150 feet? (Round your answer to two decimal places.)
Answers
Answer:
It will take him 5.85 seconds.
Step-by-step explanation:
12.5 (0.2t - 1) + 21t = 150
Use Distributive Property:
2.5t - 12.5 + 21t = 150
Combine like terms:
23.5t - 12.5 = 150
Subtract 12.5 from both sides:
23.5t = 137.5
Divide both sides by 23.5 to isolate variable t:
5.851063.....
Round to two decimal places (hundredths place):
5.85
2.What is 10:30 pm in the 24-hour clock?
3. How do you write 00:15 in the 12-hour clock?
4.How do you write 11:50 pm in the 24-hour clock?
11.How are the circumference and the diameter of any given circle related
12. The diameter of a circle is 22 cm long. What is its area?
13.What is the area of the largest circle that can be drawn on a square paper whose side is 20 cm? *
16. Two workers need to dig a rectangular pit that is 2 meters long, 1.5 meters wide, and 1 meter deep. How many cubic meters of soil must they remove? *
17.A cubical water tank has a 20 cm edge. How much water can it contain?
tulong
Answers
2. 22:30
just add 12 on the front
that is the formula
2 If 9:30pm is 21:30,then 10:30pm=22:30 pm
3 15 seconds
4. If 10:30 = 22:30 then 11:50pm = 23:50
16. 3*1.5*1=4.5m^3
I think this are the ones I can try ,I hope this helps.
tell whether or not the measurements below form a triangle:
1. 4, 5, 10
2. 12, 26, 20
3. 2, 3, 5
Answers
Answer:
Below.
Step-by-step explanation:
If the sum of any 2 sides are less than or equal to the third side then there's no triangle
1. N0 because 4 + 5 < 10
2. YES
3. NO because 2 + 3 = 5.
Answer:
Step-by-step explanation:
1 . 4,5,10 : this measurement does not form a triangle because the sum of two sides is not greater than the third side (longest side)
4 + 5 > 10
9 > 10 (this is not satisfied)
2. 12,26,20 :this measurement forms a triangle beacuse the sum of two sides is greater than the third side
12 + 26 > 20
38 > 20
3 .
2,3,4 : this measurement does not form a triangle because the sum of two sides is not greater than the third side.
2 + 3 > 5
5 > 5 (this is not satisfied)
During the worst periods of hyperinflation in a certain country, the price of the food increased at a rate of 20% per month. State whether this increase was linear or exponential. If your food bill was $130 in one month during this period, what was it three months later?
Answers
Answer:
After three months the value of the food bill will be $ 224.64.
Step-by-step explanation:
Given that during the worst periods of hyperinflation in a certain country, the price of the food increased at a rate of 20% per month, for state whether this increase was linear or exponential, and determine, if your food bill was $ 130 in one month during this period, what was it three months later, the following calculations must be performed:
A hyperinflation raises prices exponentially (the percentage is calculated based on the increase of the previous month). Thus, to calculate the price of the food bill, the following calculation must be performed:
130 x 1.20 ^ 3 = X
130 x 1.728 = X
224.64 = X
Therefore, after three months the value of the food bill will be $ 224.64.
Round the following as specified.
153.38519 to the nearest thousandth.
Answers
Answer:
153.3852
Step-by-step explanation:
After the decimal, you count the places. 3 is in the ones place, 8 in the tenths, 5 in the hundreths, and 1 in the thousandths. The thousandths place is what we are rounding, so we look at the next number, 9, which tells us to round the 1 up to 2
Answer:
153.385
Step-by-step explanation:
153.38519
153.38519
The digit to the right of the thousandth (the the one, which is bolded) is less than or equal to 4, which means we round down.
153.38519 ≈ 153.385
Hope this helps.
> Next question Get a similar question You this question below Find the distance between the points (-3,-3) and (-5,-1) Distance vo Х Submit Question
Answers
Answer:
The answer is the square root of 8, or 2root2.
Step-by-step explanation:
Use the distance formula.
d = sqrt((-3-(-5))^2 + (-3-(-1)))
d = sqrt(2^2 + 2^2)
d = sqrt(4 + 4)
d = sqrt8
d = sqrt4 * sqrt2
d = 2 * sqrt2
Show A and Show B are two of the most popular television shows of all time. The number of episodes of each show are consecutive even integers whose sum is 570. If there are more episodes of Show A, how many episodes of each were there?
Answers
Answer:
A = 286 episodes
B = 284 episodes
Step-by-step explanation:
Let n = the [tex]\text{number of episodes}[/tex] of show B
n + 2 = the [tex]\text{number of episodes}[/tex] of show A
Therefore, according to the question,
The sum of the number of the episodes of each show are consecutive even integers = 570
Therefore,
n + n + 2 = 570
2n + 2 = 570
2n = 568
n = 284
Therefore, the number of episodes for B = 284
The number of episodes for A = n + 2 = 284 + 2
= 286
What is the surface area of a rectangular prism with length 12 mm, width 3mm and height 5 mm
Answers
Answer:
The surface area of the rectangular prism is of 22 square millimeters.
Step-by-step explanation:
Surface area of rectangular prism:
The surface area of a rectangular prism with length l, width w and height h is given by:
[tex]S = 2(lw + lh + wh)[/tex]
Length 12 mm, width 3mm and height 5 mm
This means that [tex]l = 12, w = 3, h = 5[/tex]
Surface area:
[tex]S = 2(lw + lh + wh) = 2(12(3) + 12(5) + 3(5)) = 2(36 + 60 + 15) = 2(111) = 222[/tex]
The surface area of the rectangular prism is of 22 square millimeters.
Find(g-f)(x)
f(x)=1/x
g(x)=x^2+2x-5
a. 1/x-x^2-2x+5
b.1/x+x^2+2x-5
c.x^2+2x-5-1/x
d.1/x+x^2-5
Answers
Answer:
x^2+2x-5 - 1/x
Step-by-step explanation:
f(x)=1/x
g(x)=x^2+2x-5
(g-f)(x) = x^2+2x-5 - 1/x
Answer:
c. x² + 2x - 5 - 1 / x
Step-by-step explanation:
f ( x) = 1 / x.
g ( x) = x² + 2x - 5
so,
( g - f) ( x) = x² + 2x - 5 - 1 / x
What is the sum of the series 18 E n=4 (n+1) ^2? 1,239 2,415 2,440 2,469
Answers
9514 1404 393
Answer:
(c) 2440
Step-by-step explanation:
The sum of the squares of numbers 1 .. n is ...
s(n) = n(n +1)(2n +1)/6
You want the sum of squares from 5 to 19. We can compute that from ...
s(19) -s(4) = (19(20)(39) -4(5)(9))/6 = (14820 -180)/6 = 2440
Answer:
C. 2440Step-by-step explanation:
hope it helps u too
Figure ABCD is a rectangle find the value of x
Answers
Answer:
Espanol la vecsu
Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
The diagonals of a rectangle bisect each other , so
DE = EB , that is
7x - 1 = 2x + 4 ( subtract 2x from both sides )
5x - 1 = 4 ( add 1 to both sides )
5x = 5 ( divide both sides by 5 )
x = 1
HW HELP ASAP PLZZZZZ
Answers
Answer:
last step is (2x + 5)(2x + 1)
Step-by-step explanation:
4x^2 + 12x + 5
4x^2 + (10 + 2)x + 5
4x^2 + 10x + 2x + 5
2x(2x + 5) +1(2x + 5)
(2x + 5)(2x + 1)
In a mathematics each correct answer gains 5 marks - However, 1 mark is deducted for each incorrect answer. Mary answered 30 questions for a total of 78 marks Determine the number of correct and incorrect questions Mary answered.
Answers
Answer:
Correct answers= 18
Incorrect answers=30-18= 12 answers
Step-by-step explanation:
total questions=30
correct answers= x
incorrect answers= 30-x
given: 5 marks for each correct answer
therefore, marks for correct answers = 5*x = 5x
Given: 1 mark deducted for every incorrect answer
therefore, marks deducted = 1(30-x) = 30-x
Total marks scored= 78
★ The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78
5x- (30-x) =78
5x-30+x=78
5x+x=78+30
6x= 108
x=108/6 = 18
Correct answers= 18
Incorrect answers=30-18= 12 answers
find the equation of the line passing through points A(3,4) and B(1,10)
Answers
Answer:
y = -3x + 13
Step-by-step explanation:
First, find the slope:
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3[/tex]
Finally, find the equation:
[tex]y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13[/tex]
Antiderivative of Acceleration is???
Answers
Answer:
Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.
Step-by-step explanation:
Answer:
Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.
