Answer:
216 cm³
Step-by-step explanation:
1/3x + 63 = 5/8x
subtract 1/3x from each side; (1/3x = 8/24x and 5/8x = 15/24x)
63 = 7/24x
7x = 63(24)
7x = 1512
x = 216
Answer:
The dilation on any point of the rectangle is 
.
Step-by-step explanation:
From Linear Algebra, we define the dilation of a point by means of the following definition:
![G'(x,y) = O(x,y) +k\cdot [G(x,y)-O(x,y)]](https://tex.z-dn.net/?f=G%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2Bk%5Ccdot%20%5BG%28x%2Cy%29-O%28x%2Cy%29%5D)
(1)
Where:
- Coordinates of the point G, dimensionless.
- Center of dilation, dimensionless.
- Scale factor, dimensionless.
- Coordinates of the point G', dimensionless.
If we know that 
, 
and 
, then scale factor is:
![(5,-5) = (0,0) +k\cdot [(2,-2)-(0,0)]](https://tex.z-dn.net/?f=%285%2C-5%29%20%3D%20%280%2C0%29%20%2Bk%5Ccdot%20%5B%282%2C-2%29-%280%2C0%29%5D)
The dilation on any point of the rectangle is:
![P'(x,y) = (0,0) + \frac{5}{2}\cdot [P(x,y)-(0,0)]](https://tex.z-dn.net/?f=P%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%20%5Cfrac%7B5%7D%7B2%7D%5Ccdot%20%5BP%28x%2Cy%29-%280%2C0%29%5D)
(2)
The dilation on any point of the rectangle is .
1450 ft / 29.6 ft/s = 48.9864864865 seconds
Step-by-step explanation:
Is this even a question, it seems to be more of a statement..
Answer:
- Library 2 charges more for each book loaned.
- Library 1 has a cheaper subscription fee.
Step-by-step explanation:
Based on the table, we can write the equation for the cost of borrowing from Library 2 using the two-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
for (x1, y1) = (2, 15.50) and (x2, y2) = (8, 26) this equation becomes ...
y = (26 -15.50)/(8 -2)(x -2) +15.50 . . . . . fill in the values
y = (10.50/6)(x -2) +15.50 . . . . . . . . . . . . simplify a bit
y = 1.75x -3.50 +15.50 . . . . . . simplify more
In the above, we have x = number of books; y = cost. We can use "n" and "C" for those, respectively, as in the equation for Library 1. Then the monthly cost for Library 2 is ...
C = 12 + 1.75n . . . . . . . arranged to the same form as for Library 1
_____
Now, we can answer the questions.
Library 2 charges more for each book loaned. (1.75 vs 1.50 for Library 1)
Library 1 has a cheaper subscription fee. (10 vs 12 for Library 2)
_____
The numbers in the cost equations are ...
C = (subscription fee) + (cost per book loaned)·n
