Answer:
Step-by-step explanation:
Answer:
x = -5
Step-by-step explanation:
Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.
This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).
So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.
On the right side we are given 9 for AD, and 18 for DC.
9/18 = 0.5
This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:
If AD/DC = 0.5, then BE/EC will also = 0.5
BE = x+23
EC = x+41
Therefore:

Now we can solve by multiplying both sides by x+41 to eliminate the fraction:

Now we multiply out the brackets and move the terms to different sides:



And if we substitute the -5 into the equations:
-5+23 = 18
-5 + 41 = 36
We will see that -5 does indeed give us the same ratio between the lengths:
18/36 = 0.5
Hope this helped!
Answer:
a.Z(-2,1)
b.Z(1,1)
c.Z(-3,2)
Step-by-step explanation:
z(-2,3)
Imagine this point on a graph.
Translate it down two units :
the x stays -2, by going down the y decreases 2 so 3-2=1
Z(-2,1)
Translate Right three units : I'm assuming that we use the answer from the first translation
Z(-2,1)
The y doesn't change this time the x increases 3 since we're moving to the right.
Z(1,1)
Translate up 1 and left 4:
Z(1,1)
by moving up one we have Z(1,2) then by moving 4 to the left we get Z(-3,2)
Hope this helps :)
Answer:
ST = 12 units
Step-by-step explanation:
Δ RAS and Δ TES are similar triangles, thus the ratios of corresponding sides are equal, that is, noting that SR = 21 - ST, thus
=
substitute values
=
( cross- multiply )
6ST = 8(21 - ST)
6ST = 168 - 8ST ( add 8ST to both sides )
14ST = 168 ( divide both sides by 14 )
ST = 12
6.50x+2.50y = total
with x = # of movie tickets
with y= # of bags of popcorn