Answer: Y and Y'' are congruent after the translation, but not after the dilation.
Step-by-step explanation:
We know that we generally prefer rigid transformations if want to create congruent images.
There are three basic kinds of rigid transformations:
1) rotation 2) reflection 3) translation
So, they all create congruent images.
But a dilation does not create congruent images because it creates an image of similar same shape as the original but not the same size.
Given : Triangle XYZ is translated and then dilated by a scale factor of 4 centered at the origin.
Then, the correct option is "Y and Y'' are congruent after the translation, but not after the dilation."
Answer:
Step-by-step explanation:
so true bestie
Answer:
If the sign before the no. is same then they will get added and the resultant will have the same sign too.
Since before 28 and 12 , both of them have the negative sign , they will get added and the sign of their resultant will be negative too.
So , -28-12 = -40
Now, if the sign before the no.s are different then there will be subtraction, and the sign before the highest no. will be the sign of the resultant.
So,( -28)+38+(-12)
= -28+38-12
= -40+38
= -2
We know that 40> 38
sign before 40 is negative, therefore, their resultant i.e 2 will also get the negative sign
I hope this helps you...
Answer:
16.5 hours
Step-by-step explanation:
The bicycle costs $240. Eva already has $42. She is making $12 per hour.
240 = 12x + 42
Solve for x to find out how many hours Eva needs to work to buy the bicycle.
240 = 12x + 42
240 - 42 = (12x + 42) - 42
198 = 12x
198/12 = (12x)/12
16.5 = x
Eva needs to work 16.5 hours to be able to buy the bikw.
A)
y varies inversely as (x-1).
Implies y α 1/(x -1)
y = k/(x-1). Where k is constant of proportionality.
y*(x - 1) = k
when y = 12, x = 1/2
12*(1/2 - 1) = k
12*(0.5 - 1) = k
k = 12*(-0.5) = -6.
k = -6.
Equation connecting x and y
y*(x - 1) = k, recall k = -6
y*(x - 1) = -6
b)
when x = a.
y*(x - 1) = -6
y*(a - 1) = -6
y = -6 / (a -1)
when x = 2a.
y*(2a - 1) = -6
y = -6 / (2a -1)
Difference in y is 1.8
-6 / (2a -1) - -6/(a - 1) = 1.8
-6 / (2a -1) + 6/(a - 1) = 1.8
6 / (a -1) - 6 /(2a -1) = 1.8
6( 1/(a-1) - 1/(2a - 1)) = 1.8
1/(a-1) - 1/(2a - 1) = 1.8/6
1/(a-1) - 1/(2a - 1) = 0.3
((2a - 1) - (a - 1)) / ((a-1)(2a -1)) = 0.3
(2a - 1 -a + 1) /((a-1)(2a -1)) = 0.3
a / (2a² - 3a + 1) = 0.3
a/0.3 = 2a² - 3a + 1
10a/3 = 2a² - 3a + 1
2a² - 3a + 1 = 10a/3
2a² - 3a -10a/3 + 1 = 0
2a² - 19a/3 + 1 = 0
6a² - 19a + 3 = 0
This is a quadratic expression which can be factored.
6a² - 18a - a + 3 = 0
6a(a - 3) - 1(a - 3) = 0
(6a - 1)(a - 3) = 0
6a - 1 = 0 a = 1/6
a - 3 = 0 a = 3.
a = 3 or 1/6
Since a is positive integer, a = 3 only.
