Answer:
it would be 45 total with the 20%
42=2*3*7
35=5*7
their GCF is 7, so the cats and dogs must be split into 7 groups
42/7=6, and 35/7=5, so there are 6 dogs and 5 cats in each group.
Answer:
(1, 9)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 
and (a, b) = (- 7, 5), hence
y - 5 = (x + 7)
y - 5 = x + 
y = x + 
← equation of line
To find another point on the line choose any value of x and substitute into the equation for the corresponding y- coordinate
x = 1 : y = + = 9
Thus (1, 9) is another point that the line passes through
Answer:
1.778 times more or 16/9 times more
Step-by-step explanation:
Given:
- Mirror 1: D_1 = 8''
- Mirror 2: D_2 = 6"
Find:
Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?
Solution:
- The light gathering power of a mirror (LGP) is proportional to the Area of the objects:
LGP ∝ A
- Whereas, Area is proportional to the squared of the diameter i.e an area of a circle:
A ∝ D^2
- Hence, LGP ∝ D^2
- Now compare the two diameters given:
LGP_1 ∝ (D_1)^2
LGP ∝ (D_2)^2
- Take a ratio of both:
LGP_1/LGP_2 ∝ (D_1)^2 / (D_2)^2
- Plug in the values:
LGP_1/LGP_2 ∝ (8)^2 / (6)^2
- Compute: LGP_1/LGP_2 ∝ 16/9 ≅ 1.778 times more
