Answer:
(x, y) = (-1, 6)
Step-by-step explanation:
y = 2x + 8
y = 5 - x
Substituting the second equation into the first equation, we get:
5 - x = 2x + 8
5 = 3x + 8
-3 = 3x
x = -1.
So, y = 5 - (-1).
Simplifying, we get:
y = 6.
What we know:
Circle A has a center at (2,0) and a radius of 8
Circle A' has a center at (-1,5) and a radius of 3
What we need to find:
we need to find the transformation from the center point of A to A' and the scale factor
Circle A can be mapped to Circle A'
center point translation (x,y)⇒[(x+a),(y+b)]⇒(x-3, y+5)
2+a=-1 0+b=5
-2+2+a=-1-2 b=5
a=-3
scale factor is 3/8
8x=3
8/8x=3/8
x=3/8
<span>A)(x, y) → (x - 3, y + 5); scale factor 3/8 </span>
Answer:
1 hour 56 minutes
Step-by-step explanation:
Given :
Time taken by Lucy = 3 hours 15 minutes = 3.25 hours
Time taken by brother = 4 hours 45 minutes = 4.75 hours
Rate = 1 / time taken
Lucy's rate = 1 / 3.25
Brother's rate = 1 / 4.75
Combined rate = Lucy's rate + brother's rate
Combined rate = 1/3.25 + 1/4.75
Combined rate = 0.5182186
Time taken if they work together = 1/ combined rate
= 1 / 0.5182186
= 1.9296 hours
= 1 hour (0.9296 * 60) minutes
= 1 hour 56 minutes (approximately)
4.4 km
100 cm = 1 m
440,000 cm = 4,400 m
1000 m = 1 km
4,400 m = 4.4 km
Answer: 1 27
2. 54
9 243
10. 270
Step-by-step explanation: for one batch, the total minutes will be 15 + 12, so 27. Multiply 27 times b, the number of batches.
There may be another solution IF he is starting to prepare the next batch while the preceding is in the oven. Since this is not stated, I won't offer that solution here.
