Answer:
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 2. and then rotating it about the origin by 180 degrees
Step-by-step explanation:
Step 1: Dilation by a scale factor of 1/2.
A point (x, y) is sent to (1/2 x, 1/2 y).
A(2, 2) ---> (1, 1)
B(2, 10) ---> (1, 5)
C(8, 12) ---> (4, 6)
Step 2: Rotate about the origin 180 degrees
A point (x, y) is sent to (-x, -y).
(1, 6) ---> A'(-1, -1)
(1, 5) ---> B'(-1, -5)
(4, 6) ---> C'(-4, -6)
Answer:
The translation would be
X = 40% + 5 + A
Step-by-step explanation:
First, translate the words, is, more than and 'the number'.
Is means equals (=).
More Than means plus (+).
'the number' can be x.
Now, put it together.
X(The Number) =(Is) 40% +(more than) 5 +(more than) A(a number)
I hope this helps!!
Answer:
6 weeks
Step-by-step explanation:
From the question:
Let us represent the number of weeks as x
Andre and Alina are each saving money.
For Andre:
Andre starts with $100 in a savings account and adds five dollars per week
$100 + $5 × x
= 100 + 5x
For Elena
Elena starts with $10 in her savings account and add $20 each week
$10 + $20 ×x
= 10 + 20x
The next step is to equate both algebraic expression for Andre and Elena together
Hence:
100 + 5x = 10 + 20x
Collect like terms
100 - 10 = 20x - 5x
90 = 15x
x = 90/15
x = 6 weeks
Hence, after 6 weeks Andre and Elena would have the same amount of money in their savings account.
Answer:
The equation of the parabola is (x-2)^2 =8(y-2)
Step-by-step explanation:
Given focus is (2,4) and the directrix is y=0 so the parabola axis is parallel to y- axis.
Focus is (α,β+a) and the directrix is of the form y = β-a
so given focus is (2,4) compare (α,β+a)
here β+a = 4 and a=2 and β=2
now given directrix y = β-a = 2-2 = 0
now the general parabola is (x-α)^2 =4a(y-β) ...(1)
now substitute α =2 ,β=2 and a=2 above equation
The equation of the parabola is (x-2)^2 =8(y-2)
