Answer:
The corresponding lengths, from the point of rotation, between the pre-image and the image are preserved.
Step-by-step explanation:
As pre image is ΔQRS and image is ΔQ'R'S' . it shows that triangle is rorated at 360°. So that image is exactly same as pre image .
Answer:
19 blocks
Step-by-step explanation:
To amanda's house, it is 5 blocks (we count 1 to 6 = 5 units)
From amanda's to Karen's, is 6 units (we count from -1 to 5 = 6 units)
Now, to find Karen to own place, we have to use the Pythaogrean Theorem. It is applicable for right triangle (which is shown, Amanda's place is the right angle).
The two distance we found are the two legs of the triangle and the other side (what we need to find) is the hypotenuse (which is the side opposite of right angle). The theorem says:
Leg^2 + Another Leg^2 = Hypotenuse^2
We know the 2 legs' length, so we can solve for hypotenuse (Karen to Own place Distance). Shown below:

So, we have:
Hypotenuse^2 = 61
Hypotenuse = Sqrt(61) = 7.81
Rounded to nearest block, that is 8 blocks
So, total distance traveled is:
5 + 6 + 8 = 19 blocks
He had 40 pencils left after he gave away 8, so originally he had 40 + 8 pencils, which is 48.
Now, he bought 4 packages, which had a total of 48 pencils, so divide 48 by 4, which is 12. He had 12 pencils in each package.
To determine the solution arithmetically, first add 8 to 40, then divide 48 by 4.
To determine the solution algebraically, set up and solve the equation 40 = 4x - 8.
Each package contained 12 pencils.
Hope this helps
Answer:
x > -6/11
Step-by-step explanation:
4x - 10 > x/3 - 12
~Simplify
4x - 10 > 1/3x - 12
~Add 10 to both sides
4x > 1/3x - 2
~Subtract 1/3x to both sides
11/3x > -2
~Multiply 3/11 to both sides
x > -6/11
Best of Luck!