ABC was dilated to create A' B' C'. What is the center of dilation? And what is the scale factor of the dilation?
Answers
Given:
In the given figure the vertices of triangle ABC are A(-2,2), B(4,2), C(-2,-2).
The vertices of triangle A'B'C' are A'(-4,4), B'(8,4), C'(-4,-4).
To find:
The center of dilation and the scale factor.
Solution:
In the given graph, draw the lines AA', BB' and CC'. The intersection point of these lines is the center of dilation.
From the below graph, it is clear that the lines AA', BB' and CC' intersect each other at (0,0).
Therefore, the center of dilation is (0,0).
If a figure is dilated by factor k and the center of dilation is origin, then
[tex](x,y)\to (kx,ky)[/tex]
[tex]A(-2,2)\to A'(k(-2),k(2))[/tex]
[tex]A(-2,2)\to A'(-2k,2k)[/tex]
It is given that A'(-4,4). So,
[tex](-2k,2k)=(-4,4)[/tex]
On comparing both sides, we get
[tex]-2k=-4[/tex]
[tex]2k=4[/tex]
[tex]k=\dfrac{4}{2}[/tex]
[tex]k=2[/tex]
Therefore, the scale factor is 2.
Related Questions
Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from T(2, –2) to W(–7, 3).
Answers
Answer:
10.3 units
Step-by-step explanation:
coordinate points are
T(2, -2) =(x1 , y1)
W(-7, 3) =(x2 , y2)
distance formula = [tex]\sqrt{(x2 -x1)^2 + (y2 -y1)^2}[/tex]
=[tex]\sqrt{(-7-2)^2 + {3-(-2)}^2[/tex]
=[tex]\sqrt{(-9)^2 + (3+2)^2[/tex]
=[tex]\sqrt{81 + 5^2[/tex]
=[tex]\sqrt{81 + 25[/tex]
=[tex]\sqrt{106[/tex]
=10.29563014
=10.3 (after converting it to the nearest tenth)
SOMEONE PLEASE PLEASE HELP ME WITH THIS THANK YOU
You can transform ⨀Z to ⨀Z' by translating it and then performing a dilation centered at Z'. Find the translation rule and the scale factor of the dilation.
Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number.
EXPLANATION = BRAINLIEST
Answers
Answer and Step-by-step explanation:
Scale factor of 4
x, y: (3, 10)
Translate 3 units right, up 10 units.
#teamtrese #PAW (Plant aNd Water)
Simplify fully
4x^2+ 4x
2x^2-2
Answers
Following are the simplification to the given equation:
Given:
[tex]\to \frac{4x^2+ 4x}{2x^2-2}[/tex]
To find:
simplify=?
Solution:
Using formula:
[tex]\to (a^2-b^2)= (a+b)(a-b)[/tex]
[tex]\to \frac{4x^2+ 4x}{2x^2-2}[/tex]
In the numerator part common the value 4x and in the denominator we common the value 2 then:
[tex]\to \frac{4x^2+ 4x}{2x^2-2}= \frac{4x(x+ 1)}{2(x^2-1)}\\[/tex]
[tex]= \frac{4x(x+ 1)}{2(x^2-1^2)}\\\\= \frac{4x(x+ 1)}{2(x-1)(x+1)}\\\\= \frac{4x}{2(x-1)}\\\\= \frac{2x}{(x-1)}\\\\[/tex]
Therefore, the final answer is "[tex]\frac{2x}{(x-1)}\\\\[/tex]"
Learn more about the Simplify:
brainly.com/question/24449175
The correct answer is (2 x)/(x - 1).
To simplify.
(4 x²+ 4 x)/(2 x²-2) = 4 x(x + 1)/2(x² - 1)
By this formula
(x² - 1²) = (x + 1)(x - 1).
4 x(x + 1)/2(x + 1)(x - 1) = (2 x)/(x - 1).
Therefore, simplification of (4 x²+ 4 x)/(2 x²-2) is (2 x)/(x - 1).
Learn more about simplification here:
https://brainly.com/question/23509407
#SPJ6
PLEASE HELP I'LL GIVE BRAINLIEST
Answers
Answer:
Step-by-step explanation:
3
Line A and Line B are
perpendicular lines.
If the slope of Line
A is 4/5, what is
the slope of Line B?
Answers
Answer:
C
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex] ← slope of line B
-5/4
this is dude to the slip being perpendicular which means that Line B will be the opposite reciprocal to Line A.
Line A=4/5
Line B=-5/4
Leo designs the skateboard ramp shown in the diagram. Type the height of the ramp (h), in inches. Round your answer to the nearest whole inch.
Answers
Answer:
h = 50 inches
Step-by-step explanation:
To find the value of h, we are to use the appropriate trigonometric ratio
The given angle faces the unknown length and that makes the unknown length the opposite side
The given side faces the right angle and that makes it the hypotenuse
The trigonometric ratio that connects the opposite and the hypotenuse is the sine
The sine of an angle is the ratio of the opposite side to the hypotenuse
Thus, we have it that;
sin 23 = h/129
h = 129 * sin 23
h = 50 inches
There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
Answers
Answer:
The probability of getting two of the same color is 61/121 or about 50.41%.
Step-by-step explanation:
The bag is filled with five blue marbles and six red marbles.
And we want to find the probability of getting two of the same color.
If we're getting two of the same color, this means that we are either getting Red - Red or Blue - Blue.
In other words, we can find the independent probability of each case and add the probabilities together*.
The probability of getting a red marble first is:
[tex]\displaystyle P\left(\text{Red}\right)=\frac{6}{11}[/tex]
Since the marble is replaced, the probability of getting another red is: [tex]\displaystyle P\left(\text{Red, Red}\right)=\frac{6}{11}\cdot \frac{6}{11}=\frac{36}{121}[/tex]
The probability of getting a blue marble first is:
[tex]\displaystyle P\left(\text{Blue}\right)=\frac{5}{11}[/tex]
And the probability of getting another blue is:
[tex]\displaystyle P\left(\text{Blue, Blue}\right)=\frac{5}{11}\cdot \frac{5}{11}=\frac{25}{121}[/tex]
So, the probability of getting two of the same color is:
[tex]\displaystyle P(\text{Same})=\frac{36}{121}+\frac{25}{121}=\frac{61}{121}\approx50.41\%[/tex]
*Note:
We can only add the probabilities together because the event is mutually exclusive. That is, a red marble is a red marble and a blue marble is a blue marble: a marble cannot be both red and blue simultaneously.
How to solve a+52/3=9
Answers
Answer:
-25/3
Step-by-step explanation:
Answer:
a+52/3=9
a + 52/3 - 52/3 = 9 - 53/3
a=[tex]\frac{27- 53}{3}[/tex]
a= [tex]\frac{26}{3}[/tex]
Step-by-step explanation:
PLEASE HELP ASAP IM TIMED!!
What is the standard form of y=2(x-3)(x+5) and show your work
Answers
Answer:
o really sis/bro hsgsmhsndjd
y=（2x-6）（x+5）
y= 2x^2 + 10x -6x -30
y= 2x^2 + 4x -30
evaluate h(0). What does this value represent?
Answers
Answer:
Step-by-step explanation:
Answer:
An equation is needed to evaluate h(0).
When you evaluate h(0), you find the y-intercept of the graph because the independent variable inside the brackets, probably x or t, equates to 0.
The problem is needed for its context to be explained.
Although in most math problems, when h(x) form is used, h usually represents height.
I assume h(0) is the initial height, maybe the height that the rocket was launched or the height that the person who threw the ball is.
Beth said the distance to school is 2.8 km. The actual distance is 3.5 km. What is the percent error
Answers
Answer:
20%
Step-by-step explanation: The percent of error formula is |(theoretical value-actual value)/actual value|=percent of error. Substitute the values in. |(2.8-3.5)/3.5|=|(-0.7)/3.5|=0.2. The percent equal to 0.2 is 20%.
Two Boys are building a skateboard ramp. They want the ramp to be 3 feet tall and 5 feet long. One of them thinks that they can use a piece of plywood that is 4 feet long to cover the top of the frame.
This is one of theirs work.
a2 + b2 = c2
32 + b2 = 52
9 + b2 = 25
b2 = 16
b = 16−−√
b = 4
Why is his reasoning incorrect? Explain.
How long does the piece of plywood have to be to cover the top of the frame of the skateboard ramp? Round your answer to the nearest tenth of a foot. Show your work.
Another boys parents bought a 10 foot piece of plywood for him and his friend to use to cover the top of the frame. Draw and label a ramp they could create. Justify your work using the Pythagorean Theorem.
Draw
Answers
Answer:
The answer is below
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are acute, obtuse, scalene, isosceles, equilateral and right angled triangle.
Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is equal to the sum of the square of the remaining two sides.
The ramp has the form of a triangle. The height of the ramp is the vertical side of a triangle, the top of the frame is the hypotenuse while the length of the ramp is the base side of the triangle.
Let the hypotenuse be b Hence:
b² = 3² + 5²
b² = 9 + 25
b² = 34
b = 5.83 feet
Answer:C
Step-by-step explanation:
Which symbol correctly completes the statement?
-7 + 2 ___ 3 + (-9)
>
<
=
?
Answers
Answer:
-7 + 2 ___ 3 + (-9)
lets break this up
-7+2=-5
3+(-9) or 3-9 = -6
so the correct one is...
B: <
Which of the following systems of inequalities has solutions represented by the graph shown below?
Answers
Answer:
y ≤ 1/2x - 1
y ≤ -2x + 4
If I = “-1” then i2 =
Answers
Answer:
-2
Step-by-step explanation:
negative times positive equal negative so
-1×2= -2
Answer:
[tex] \large{ \tt{✺ \: EXPLANATION}} : [/tex]
We're provided - i = -1 & we're asked to find out the value of i².Plug the value of ( i ) in ( i ²) , it would be ( - 1 ² ). Now , You must have known that when the two negative integers are multiplied , the result will be a positive integer i.e ( - 1 ) × ( - 1 ) = 1 .[tex] \large{ \boxed{ \boxed{ \tt{↝OUR \: FINAL \: ANSWER: \boxed{1}}}}}[/tex]
☂ Let me know if you have any questions regarding my answer :)▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
NUM ALDITORIO HA 224 CADEIRAS ORGANIZADAS EM 8 FILEIRAS COM A MESMA QUANTIDADE DE CADEIRAS QUANTAS CADEIRAS HA EM CADA FILEIRA
Answers
Answer:
The number of chains in each fileiras = 28.
Step-by-step explanation:
Total number of chains = 224
Number of fileiras = 8
Number of chains in each fileiras is given by the divison of total number of chains to the number filerias.
[tex]\frac{224}{8}\\\\=28[/tex]
solve using the quadratic formula 2x^2+9x=5
Answers
Answer:
x = -1/2, x = -5 OR x = -0.5 and x = -4
Step-by-step explanation:
I’ll just put a picture, I can’t fully explain digitally. ;D
If a randomly thrown dart hits the board below, what is the probability it will hit the shaded region?
Answers
What is the likely means of measurement for the data in the chart below?
a. 100-meter run data
b. seconds
c. stop watch
d. 7 observations
Answers
Answer:
C
Step-by-step explanation:
I might be wrong. I hope it helps:)
A regular octagon has a perimeter of 30 centimeters. Find the length of each side.
Answers
Step-by-step explanation:
Perimeter=8l
30cm=8l
l=30/8=3.75cm
Answer and Step-by-step explanation:
An octagon has 8 sides in total. The perimeter of a shape is the sum of all sides added together.
To find the length of each side, we divide the perimeter by the amount of sides.
30 ÷ 8 = 3.75
The answer is 3.75 centimeters.
#teamtrees #PAW (Plant And Water)
WILL GIVE BRAINLIEST AND 20 POINTS!
Find the slope of the line in the following graph using the points on the graph. Write the exact answer. Do not round. If the slope does not exist, write DNE for your answer.
(-5,2)(6,7)
Answers
Answer:
Step-by-step explanation:
Slope = (y2 - y1) / (x2 - x1)
y2 = 7
y1 = 2
x2 = 6
x1 = - 5
There is no particular reason for choosing which one is (x2,y2) and (x1,y1) The slope would turn out to be the same which ever way you tried it.
slope = (7 - 2)/(6 - - 5) Notice the double minus. One of the minus symbols belongs to the formula and the other belongs to the 5
slope = 5/(6 + 5)
slope = 5/11
Answer:
[tex]\frac{5}{11}[/tex]
Step-by-step explanation:
The slope of a line that passes through points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let:
[tex](x_1,y_1)=(-5,2),\\(x_2, y_2)=(6,7)[/tex]
The slope of the line, [tex]m[/tex], that passes through these points is equal to:
[tex]n=\frac{7-2}{6-(-5)}=\frac{5}{6+5}=\boxed{\frac{5}{11}}[/tex]
Help plz
1) __ × 4 = -20
2) __-7 = - 2
3) __ × - 5= 20
4) __- 9 = - 2
5) __+ 17 = 20
Answers
Answer:
1) -5
2) 5
3) -4
4) 7
5) 3
Step-by-step explanation:
1) -20 divided by -4
2) -2 plus 7
3) 20 divided by 5
4) -2 plus 9
5) 20 minus 17
2)5
3)-4
4)7
5)3
Self explanatory
Write the following as an inequality.
2 is less than w, and 7 is greater than or equal to w
Use w only once in your inequality.
Answers
Answer:
2 > w ≤ 7
Step-by-step explanation:
3. The total cost of 3 Nintendo Switch games is $89.97. If
each game costs the same amount, write an equation that
can be used to determine g, the cost of 1 game.
Answers
Answer:
3x=89.97
x=89.97/3
x=29.99 -- price of one
Step-by-step explanation:
On her vacation in Mexico Stephanie was Abel to drive 280 miles on 12 gallons of gas with us the average gas mileage for Stephanie car?
Answers
Answer:
0.0428 miles per gallon
Step-by-step explanation:
On her vacation in Mexico Stephanie was Abel to drive 280 miles on 12 gallons
Given data
Distance driven = 280miles
Fuel used= 12 gallons
Hence the gas per mile is expressed as
Gas per mile= 12/280
Gas per mile= 0.0428 miles per gallon
i need help with this plz
Answers
Answer:
-4 is the correct answer
Answer:
y=18
Step-by-step explanation:
equation:y=3x -7
x=7 then y =?
substitute the vale of x in the equation
y=3x-7
y=3*7-7
y=21-7
y=18
therefore the value of y corresponds to 7 is 18.
The distance around a circular park is 176 yards. What is the area of the park? Use 22/7 for π.
Answers
Answer:
2464 yd²
Step-by-step explanation:
Use the circle circumference formula: 2πr
2·[tex]\frac{22}{7}[/tex]·r=176
[tex]\frac{44}{7}[/tex]r=176
r=176·[tex]\frac{7}{44}[/tex]
r=28
Area of circle formula: πr²
[tex]\frac{22}{7}[/tex]·r²
[tex]\frac{22}{7}[/tex]·28²
[tex]\frac{22}{7}[/tex]·784
=2464 yd²
Help anybody please idem
Answers
Answer:
-64
Step-by-step explanation:
f(x)=-4^x
f(3)=-4^3=-64
Answer:
-64
Step-by-step explanation:
1) Substitute x with 3
-4^3
2) solve
-64
Which of the following is equivalent to 0.000001?
Answers
Find the value of x.
Answers
Answer:
Step-by-step explanation:
Vertically opposite angles are equal
8x + 2 = 7x + 11
Subtract 2 from both sides
8x = 7x + 11 - 2
8x = 7x + 9
Subtract 7x from both sides
8x - 7x = 9
x = 9
