Answer:
n = -4
Step-by-step explanation:
2 - 1/2 n = 3n + 16
Combine the constants by subtracting 2 from both sides.
-1/2n = 3n + 14
Combine the variable by subtracting 3n from both sides.
-7/2n = 14
Multiply both sides by 2 to simplify the fraction.
-7n = 28
Isolate n by dividing by -7 on both sides.
n = -4
Check.
2 - 1/2(-4) = 3(-4) + 16
2 + 2 = -12 + 16
4 = 4
Your answer is correct.
Basically, you have two circles. You are asked to take circle 1 and "move it" so that it is on top of circle 2. This process of moving is called a translation and can be thought of as sliding. You do this by ensuring that the two have the same center. So, starting at (-4,5) how do you have to move to end up at (2,1)?
To do this we need to move right 6 as the x-coordinate goes from -4 to 2. We also need to move down 4 as the y-coordinate goes from 5 to 1. So we add 6 to the x-coordinate and subtract 4 from the y-coordinate. The transformation rule is (x+6, y-4).
Once you do this the circles have the same center. Next you wish to dilate circle 1 so it ends up being the same size at circle 2. That means you stretch it out in such a way that it keeps its shape. Circle 1 has a radius of 2 centimeters and circle 2 has a radius of 6 centimeters. That is 3x bigger. So we dilate by a factor of 3.
Translations and dilations (along with reflections and rotations) belong to a group known as transformations.
$25. 25 x 3 is 75. Plus the 100 is 175. 200 - 175 is $25
Answer:
length 60 feet
length 2=60 feet
width 1=30feet
width 2=30feet
those is because there is 4 sides to a rectangle
Step-by-step explanation:
because the length is twice the width, 2x 30=length
First write an equation system based on the problem
We can write "<span>Bread and sugar cost 110 together" as
</span>∴ b + s = 110
We can write "<span>bread cost 100 more than sugar" as
</span>∴ b = 100 + s
<span>
Second, solve the equation system by subtitution method
Subtitute b with (100+s) in the first equation, and we'll find the value of s
b + s = 110
(100 + s) + s = 110
100 + 2s = 110
2s = 110 - 100
2s = 10
s = 10/2
s = 5
The cost of the sugar is 5</span>
