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:
Option <u>C. 13.3 in</u>.
Step-by-step explanation:
Here's the required formula to find the radius of the bike tire :

- C = circumference
- π = 3.14
- r = radius
Substituting all the given values in the formula to find the radius of the bike tire :

Hence, the radius of bike tire is 13.3 inches.

Answer: B
Step-by-step explanation:
A best describes the quality of symmetry, not specifically rotational symmetry.
C applies to that of A.
D applies to flipping an image across an axis.
B specifically outlines the symmetry of an object when rotated, thus B would be the most precise answer.
The fact that this triangle is a right angle triangle makes you now have 2 angles and the 1 side given, so it should be solvable.
First, You know that A=46 and C=90 as it is the right angle, and you know that the sum of any triangle's angles is 180. so now B=180-(90-46)=44
Now to the sides,
sin(B)=opp./hyp.=b/c=8/c=sin(44)
so, c=8/sin(44) which is approximately 11.52 unit length
now, use Pythagoras to find a,
a=√c²-b² =√11.52²-8² which is approximately 8.3 unit length.
Hope this helps.
Answer:
Option B.
Step-by-step explanation:
The given vertices of triangle ABC are (-1, -1), (-1, -5) and (0.5, -5).
We need to find the coordinates of triangle when it is translated two units left.
So, the rule of translation is
Using this rule, we get
The vertices of triangle A'B'C' are A'(-3,-1), B'(-3,-5) and C'(-1.5,-5).
Therefore, the correct option is B.