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.
if f(x) = 3x+2 what is f(5)?
Answer:
just put 5 on the place of x
Step-by-step explanation:
3(5)+2
15+2
17
hope it helps
Answer:
lets say f equals 1
x-2 = 3x
-2 = 2x
x=-1
1(-1)
-1
i need help quick!! i need steps please. i dont understand it
will mark brainliest.
Answer:
Its just a slide 2 up and 3 to the right it seems. It can be a mirror because in never changes the shape. as of rules i dont understand want you need please comment and ill let you know
Step-by-step explanation:
It is not a rotation, a mirror a flip or anything like that i think its only slides.
I didnt se this before every slide counts as 2 so its 4 up and 6 to the right
when 2-(7g-3) =-9 is solved, the result is:
a. 2
b. -2
c. -4
d. none of these choices are correct
The answer is A. 2
Step-by-step explanation:
First let's simplify both sides of the equation
Now using the Subtraction Property of Equality subtract 5 from both sides
[tex]-7g+5-5=-9-5-7g=-14[/tex]
Now using the Division Property of Equality divide both sides by -7
Can some please help I don’t really know.
Answer: 1%
Step-by-step explanation:
Alternate angles add up to 180 degrees.
Is it true or false?
Please give real answers with an explaination. 80 points + I will give brainliest + 5-star rated. No Docs/No Files/No Links only answer with explaination.
Hellpp please and thank……………
Answer:
a1 = 2
a2 = 6 = 2.3 = a1.3
a3 = 18 = a1.3²
a4 = 54 = a1.3³
=> this is a geometric sequence with a1 = 2
q = 3
=> a11 = 2.3¹⁰ = 118098
4^2-2 X 3 + 6 = ?
SOLVE with PEMDAS
my son has had problems with algebra and tbh I don't know how to do it either i was hoping someone on here can help!
4^2 -2×3+6=16 is your answer
Answer:
Step-by-step explanation:
P means parenthesis, of which we have none. So we move to E, which is exponents, which we do have. So we start there:
[tex]4^2-2*3+6[/tex] becomes
16 - 2 * 3 + 6. Now we have to do multiplication/division in the order we come to it in the problem. That means multiplying 2*4 first:
16 - 6 + 6. Now we do addition/subtraction in the order we come to it in the problem:
16- 6 + 6 = 10 + 6 = 16
72. Linear Speed. A wheel with a 30-cm radius is rotat- ing at a rate of 3 radians / sec. What is the linear speed of a point on its rim, in meters per minute?
========================================================
Explanation:
Let's find the circumference
C = 2*pi*r
C = 2*pi*30
C = 60pi
This is the exact circumference in terms of pi.
In one revolution, the point on the wheel moves forward exactly 60pi cm.
In a sense, it's "speed" is 60pi cm per revolution.
----------------
Let's convert that speed to meters per minute as shown in the diagram below (I'm using the railroad tracks method to convert).
Note the color coding to see how the units cancel. The goal is to get meters on top and minutes down below. Also note how the "pi" terms cancel since we have on top and one down below.
After the canceled stuff goes away, we multiply straight across.
Multiplying the values across the top gives: 60*3*1*60*1 = 10800Multiplying across the bottom gives: 1*1*2*1*100 = 200Divide the results: 10800/200 = 54
The linear speed is 54 meters per minute
This speed is exact because the 60pi figure is the exact circumference
This is the speed the point on the wheel moves, and we can say that the car itself also moves at a linear speed of 54 meters per minute.
Side note: 54 meters per minute = 2.013 mph approximately, which is a fairly slow walking speed.
Nigel has 2 dogs one eats 21/2 pounds of food each week. The other eats 1 3/8 pounds a week together how much food do the dogs eat in a week?
Answer:The dogs eat 3 7/8 pounds of food together each week.
Step-by-step explanation:
First dog eats eats 21/2 pounds of food each week
The second eats eats 1 3/8 pounds of food each week
In total the two dogs eat
2 1/2 + 1 3/8 = 3 (4+3)/8
=3 7/8
The dogs eat 3 7/8 pounds of food together each week.
help me please: tan3x-tanx-1=0
Answer: [tex]x=0.30714\dots +\pi n[/tex]
Step-by-step explanation:
[tex]\Rightarrow \tan3x-\tan x-1=0\\\\\Rightarrow \dfrac{3\tan x-\tan ^3x}{1-3\tan ^2x}-\tan x-1=0\\\\\Rightarrow 3\tan x-\tan ^3x+( 1-3\tan ^2x)(-1-\tan x)=0\\\Rightarrow 3\tan x-\tan ^3x-1-\tan x+3\tan ^2x+3\tan ^3 x=0\\\Rightarrow 2\tan ^3x+3\tan ^2x+2\tan x-1=0\\\Rightarrow \tan \left(x\right)\approx \:0.31718[/tex]
Please help me. I feel really confused and I have no clue on what to do…
Answer:
i cant understand your questions. can you reply me? i will have better answer
Find the product of (2x-3)(x-1)
Answer:
Step-by-step explanation:
[tex](2x -3)(x-1) = 2x(x-1) -3(x-1)[/tex]
[tex]=2x^2 -2x -3x +3\\= 2x^2 - 5x + 3[/tex]
What is the basic unit of time? What is the relationship between time and sound in music? please help im desperate
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
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 equation describes the line graphed above?
Test question........................
You Have Passed Thy Test!!! BADAAAA (\•o•/)
A landscaper needs to rent tree-trimming equipment. The graph shows the rental costs for the equipment at two different stores. Choose the ordered pair that best estimates the time and cost at which the two stores charge the same amount.
Answer:
(105 | 35)
the x-component (how much to the side) is left, the y-component right (how high)
The ordered pair that best estimates the time and cost at which the two stores charge the same amount is (110,35).
What is a graph?A graph can be defined as a pictorial representation of statistical data in graphical form. The points on the graph often represents the relationship between two or more things. The points are plotted in x-axis and y-axis respectively.
For the given situation,
The graph shows the time in x-axis and cost in y-axis.
Ordered pairs are often used to represent two variables.
The number which corresponds to the value of x is called the x-coordinate and the number which corresponds to the value of y is called the y-coordinate.
From the graph, the point of intersection of x-axis and y-axis gives the the time and cost at which the two stores charge the same amount.
Thus the point of intersection is x at 110 and y at 35.
⇒ [tex](x,y)=(110,35)[/tex]
Hence we can conclude that the ordered pair that best estimates the time and cost at which the two stores charge the same amount is (110,35).
Learn more about graphs here
https://brainly.com/question/7563606
#SPJ2
What is sin(51°)?
A. 0.51
B. 1.23
C. 0.78
D. 0.63
Answer:
0.78
used a calculator
Find the optimized volume of a rectangular prism with a surface area of 864 m^2
Which choice is equivalent to 4 square root 3?
A. 12
B. 748
C. V12
D. 6
What are solutions to the equation x^2-34=864
Answer:
x=29.9
Step-by-step explanation:
x=29.9
Need honest and urgent help thank you
Answer:
(Top to bottom) The third and the fifth.
Step-by-step explanation:
I feel lazy typing this so I'll just take a pic if you're curious about the process.
can somebody help plz
Answer:
(3,2)
Step-by-step explanation:
the other three ordered pairs do not lie in the shaded region
factorise fully 3r+6r2
Answer:
3r(1 + 2r)
Step-by-step explanation:
3r + 6r^2
take common
3r(1 + 2r)
Answer:
3r(1+2r2)
Step-by-step explanation:
The diagram shows a man standing next to a dinosaur.
Estimate the height of the dinosaur.
Answer:
manz I think u would need like a ruler or something
Answer this for me thanks
Answer:
The value of x is 15 inch.
Step-by-step explanation:
Area, A = 81 square inch
Perimeter, P = 48 inch
let the side is y.
[tex]y^2 = 81\\\\y = 9 inch[/tex]
Let the other side is d.
P = 4 d = 48
d = 12 inch
the length x is given by
[tex]x^2 = 9^2 + 12^2\\\\x^2 =81 + 144 = 225\\\\x = 15 inch[/tex]
So, x = 15 inch.
Jeremy’s car travels 26 miles per gallon of gas (g). If the distance traveled (d) can be given by a function, what is the input of this function?
Find The Surface Area And Volume Of A Sphere Whose Radius Is 5.6ml
Answer:
surface area is A≈394.08
not so sure about volume
Step-by-step explanation:
The student enrollment of South High School was 1,350 students in 1995 and increased by15% per year until 2010. Approximately how many students were enrolled at South HighSchool in 2010?
Answer:
81
Step-by-step explanation:
1350 ×15 % by 100 = 81. 15 year = 1,215
Please help??? An explanation would help too and the answers
the first, (f+g)(x) is f(x) + g(x)
calculating it like:
x² + 7x + (8 -x²)
= x² + 7x + 8 -x²
= 7x + 8
you just writ it down as a calculation and calculate it. i hope that helps understanding the concept/basic idea. please let me know wich ones you need more help with.
edit1: the domain is the range of possibilities wich x we can plug into the new equation