Answer:
3
Step-by-step explanation:
We know that<span>
<span>Figures can be proven similar if one, or more,
similarity transformations (reflections, translations, rotations, dilations)
can be found that map one figure onto another.
In this problem to prove circle 1 and circle 2 are similar, a
translation and a scale factor (from a dilation) will be found to map one
circle onto another.
we have that</span>
<span> Circle 1 is centered at (5,8) and has a
radius of 8 centimeters
Circle 2 is centered at (1,-2) and has a radius of 4 centimeters
</span>
step 1
<span>Move the center of the circle 1 onto the
center of the circle 2
the transformation has the following rule</span>
(x,y)--------> (x-4,y-10)
so
(5,8)------> (5-4,8-10)-----> (1,-2)
so
center circle 1 is now equal to center circle 2
<span>The circles are now concentric (they have the
same center)
</span>
step 2
<span>A dilation is needed to decrease the size of
circle 1 to coincide with circle 2
</span>
scale factor=radius circle 2/radius circle
1-----> 4/8----> 0.5
radius circle 1 will be=8*scale factor-----> 8*0.5-----> 4 cm
radius circle 1 is now equal
to radius circle 2
<span>A
translation, followed by a dilation will map one circle onto the other,
thus proving that the circles are similar
the answer is
</span></span>The circles are similar because you can translate Circle 1 using the transformation rule (x-4,y-10) and then dilate it using a scale factor of (0.5)
Answer:
By rounding up of the constant and coefficient terms, we have;
The line of best, fit is y = 1.23 + 3.46 × 10⁻²·x
Step-by-step explanation:
The table for the data on the number of movie admissions each year is presented as follows;
Year, x
Admission, y
0
1.24
2
1.26
4
1.39
6
1.47
8
1.49
10
1.57
Using a graphing calculator, we have that the line of best fit is given by the following equation;
y = 1.23047619048 + 3.45714285714 × 10⁻²·x
Which is approximately, y = 1.23 + 3.46 × 10⁻²·x
Step-by-step explanation:
we can find the value of c by Pythagoras theorem
according to Pythagoras theorem
h² = a² + b²
where
h = hypotenuse (i.e. longest side of a right angled triangle)
a = side
b = base
so, we have to find h or hypotenuse here
h² = (24)² + (18)²
h = 576 + 324 = 900
h² = √900 = 30
c = 30
therefore, value of c is 30.
Hope this answer helps you dear!
Answer:
d(x) = √[(x - 2)² + (3x - 1)²]
Step-by-step explanation:
The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
So, the distance between point (2,0) and a point (x,y)
d = √[(x - 2)² + (y - 0)²]
d = √[(x - 2)² + (y)²]
But the point (x,y) is on the line y = 3x - 1
We can substitute for y in the distance between points equation.
d(x) = √[(x - 2)² + (3x - 1)²]
QED!