Answer:
y
=
−
6
x
+
5
.
y
=
−
6
x
+
28
Step-by-step explanation:
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.
The number of buckets is directly proportional to the area and the thickness of the wall and inversely proportional to the amount of paint. Mathematically, we can write:
n = k · (a · t) / p
where k is the proportionality constant which we do not know.
We can calculate k with the given data: 5 2-gallon buckets, area of 100 square feet and thickness 3 inches:
k = (n · p) / (<span>a · t)
= (5 </span>· 2) / (100 · 3) = 0.0333
Now that we know the constant, we can calculate the area that can be painted with 8 2-gallon buckets if the thickness is 6 inches:
a = (n · p) / (k<span> · t)
= (8 </span>· 2) / (0.0333 · 6)
= 80 ft²
Please, note that we made sure to have the exact same units of measurements than the previous case.
Therefore, the correct answer is an area of 80 ft².
Answer:
Volume = 125 mm^3
Step-by-step explanation:
Here, we want to get the volume of the cube
What we have to do here is to substitute the value of the area
We have this as
:
V = 25^(3/2)
V = (√25)^3
V = 5 * 5 * 5 = 125 mm^3
<span>1. For the data in the table, does y vary directly with X? If it does write an equation for the direct variation.(X,y) (8,11) (16,22) (24,33)
</span><span>
Yes y=1.375x
</span><span>2.for the data in the table, does y vary directly with X? If it does write an equation for the direct variation. (X,y) (16,4) (32,16) (48,36)
</span>No y does not very directly with x*** <span>
</span><span>3. (Time/hour,distance/miles)(4,233) (6,348) (8,464) (10, 580)
Express the relationship between distance and time in a simplified form as a unit rate. Determine which statement correctly interprets this relationship.
</span><span>58/1 your car travels 58 miles in 1 hour
</span><span>4.what is the slope of the line that passes through the pair of points (2,5) and (8,3)
</span>-1/3
<span>4.what is the slope of the line that passes through the pair of points (-5.2,8.7) and (-3.2,2.7)
</span>
-3
<span>5. What is the slope of the line that passes through the pair of points (3/2,-2) and (-3,7/3)
-26/27
</span><span>6.write an equation in point slope from for the line through the given point with the given slope (5,2) m=3
Y-2=3(X-5)
7. Write an equation in point slope form for the line through the given point with the given slope (-3,-5) m=-2/5
Y+5=-2/5(X+3)
</span><span>8. Write an equation in point slope from for the line through the given point with the given slope. (4,-7) m=-0.54
Y+7=-0.54(x-4)
9. The table shows the height of a plant as it grows. Which equation in point slope from gives the plants height (time,plant height) (2,16)(4,32)(6,48)(8,64)
Y-16=8(X-2)***
</span>
<span>10. Write y=-2/3x+7 in standard form
2x+3y=21
11. Write y=-1/2x+1 in standard form using integers
X+2y=2
</span>
