ABC
Solve for x
x + 30 + 2x - 4 + 4x = 180 All triangles have 180°. collect like terms.
7x + 26 = 180 subtract 26 to both sides.
7x = 154 Divide by 7
x = 154/7
x = 22
A = x + 30 = 22 + 30 = 52
B = 2x - 4 = 2(22) + 30 = 44 - 4 = 40
C = 4x = 4*22 = 88

Check
<A + <B + <C = 180
<52 + <40 + <88 = 180°
180 = 180

It checks and we are done with this triangle.

A'B'C'
2x + 8 + x + 18 + 5x - 22 = 180 Collect the like terms.
8x + 4 = 180 Subtract 4 from both sides.
8x = 180 - 4
8x = 176 Divide by 8
x = 176 / 8
x = 22

A' = 2x + 8
A' = 2(22) + 8 = 44 + 8 = 52
B' = x + 18 = 22 + 18 = 40
C' = 5x - 22 = 5*22 - 22 = 110 - 22 = 88

Conclusion
A = A'
B = B'
C = C'

All three angles of one triangle are equal to all three angles of the other. So by AA the two triangles are similar.

Comment
Note: the dilation of 12 has nothing to do with this answer. If you were asked about similarity of sides then the 12 would be something to do with the problem.

3 0

3 years ago

Which of the following phrases could be translated to the expression y + 5? the difference between a number and five

weqwewe [10]

Five more than a number, hope this helps!

3 0

3 years ago

Develop an explicit formula in terms of n for the nth term of the following sequence:

Pavel [41]

Answer:

$a_{n}=(n-1)n^{2}$

for the seventh term: $a_{n}=(7-1)7^{2}= (6)(49)=294$

Step-by-step explanation:

First, we need to observe the sequence, it is crescent, every term is bigger than the one before it. Now, if we put our numbers in a graph (added as an image) we'll notice we obtain an exponential function, this is another detail we'll consider to find our equation, from here it's trial an error.

Our formula is:

$a_{n}=(n-1)n^{2}$

where n is the number of term:

$a_{n}=(1-1)1^{2}= (0)(1)=0$
$a_{n}=(2-1)2^{2}= (1)(4)=4$
$a_{n}=(3-1)3^{2}= (2)(9)=18$
$a_{n}=(4-1)4^{2}= (3)(16)=48$
$a_{n}=(5-1)5^{2}= (4)(25)=100$
$a_{n}=(6-1)6^{2}= (5)(36)=180$ it works!
$a_{n}=(7-1)7^{2}= (6)(49)=294$

I hope you find this information useful! Good luck!

5 0

3 years ago