The estimate would be 1200.
We will set up a proportion for this. 10 out of 60 of the sample were tagged, so that is the first ratio. The 200 that were tagged would be in the numerator of the second ratio (10 was the portion tagged, and 200 is the portion tagged, so they both go on top). We do not know the total number so we use a variable:
10/60 = x/200
Cross multiply:
10*x = 60*200
10x = 12000
Divide both sides by 10:
10x/10 = 12000/10
x = 1200
Given:
The vertex of a triangle MNP are M(-4, 6), N(2, 6), and P(-1, 1).
The rule of dilation is:
The image of triangle MNP after dilation is M'N'P'.
To find:
The coordinates of the endpoints of segment M'N'.
Solution:
The end points of MN are M(-4, 6) and N(2, 6).
The rule of dilation is:
Using this rule, we get
And,
The endpoints of M'N' are M'(-6, 9) and N'(3, 9).
Therefore, the correct option is B.
Answer: -6
Step by step:
2x + 3(8) = 12
2x + 24 = 12
2x = -12
x = -6
I think ur homework sheet is wrong the difference is definitely 6
Answer: 11x
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Explanation:
Let L be the length of rectangle B
There are two copies of L (along the top and bottom of the rectangle). The vertical pairs of sides are both 7x each.
For the triangle, we have three sides of 12x since this is an equilateral triangle. All three sides are congruent for any equilateral triangle.
The perimeter of the triangle is
P = s1+s2+s3
P = 12x+12x+12x
P = 36x
The perimeter of the rectangle is
P = 2*L+2*W
P = 2L+2*7x
P = 2L+14x
Since both perimeters are the same, this means
perimeter of triangle = perimeter of rectangle
36x = 2L+14x
36x-14x = 2L+14x-14x
22x = 2L
2L = 22x
2L/2 = 22x/2
L = 11x
So the length of the rectangle, in terms of x, is 11x. This is the final answer.
Note: if we knew the value of x, then we could find the numeric value of the length for the rectangle. But since we don't know x, we leave it as 11x.
