Answer:
52:49
Step-by-step explanation:
pink:green
The ratio of pink to green marbles is
3k:4k
He removes 5 green marbles and adds 8 pink marbles.
Now the ratio of pink to green marbles is
(3k + 8):(4k - 5)
This rario is equal to 29:23.
(3k + 8)/(4k - 5) = 29/23
29(4k - 5) = 23(3k + 8)
116k - 145 = 69k + 184
47k = 329
k = 7
Original amounts:
3 * k = 3 * 7 = 21 pink
4 * k = 4 * 7 = 28 green
Original total = 21 + 28 = 49
Amounts after replacement:
3k + 8 = 3(7) + 8 = 29 pink
4k - 5 = 4(7) - 5 = 23 green
Total after replacement = 23 + 29 = 52
Answer: The ratio of the total number of marbles in the jar after replacement to the total number of marbles in the jar originally is 52:49.
3x = 9y
9y = 3x
y = 3x/9
y = 1/3x
The slope is 1/3
-16 + 5n = -7(-6 + 8n) + 3 Given
-16 + 5n = 42 - 56n + 3 Distribute
-16 + 5n = 45 - 56n Collect like terms
61n = 61 Add 56n to the left side and add 16 to the right side
n = 1 Divide 61 from both sides
The answer is n = 1. Remember that when you have a number beside two or more numbers in parentheses, you have to distribute, or multiply the number outside the parentheses by each number inside the parentheses.
Hope this helps!
W is 5 units
w=(P-2l)/2
w=(30-2(10))/2
w=(30-20)/2
w=(10)/2
w=10/2
w=5
we know that
1) scale factor is equal to 
2) The ratio of the perimeters of the triangles is equal to the ratio of the measures of the sides
3) the longest side of ∆ABC=[scale factor]*the longest side of ∆DEF
the longest side of ∆ABC=
the longest side of ∆ABC=
units
the answer part a) is
the longest side of ∆ABC is units
Part b)
The ratio of the area of ∆ABC to the area of ∆DEF is equal to the scale factor squared
so
![[scale factor]^{2} =(\frac{1}{10})^{2} \\ \\ =\frac{1}{100} \\ \\ =0.01](https://tex.z-dn.net/?f=%20%5Bscale%20factor%5D%5E%7B2%7D%20%3D%28%5Cfrac%7B1%7D%7B10%7D%29%5E%7B2%7D%20%5C%5C%20%5C%5C%20%3D%5Cfrac%7B1%7D%7B100%7D%20%5C%5C%20%5C%5C%20%3D0.01%20)
therefore
the answer part b) is
The ratio of the area of ∆ABC to the area of ∆DEF is 
