ABCSolve 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
ConclusionA = 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.
CommentNote: 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.
Answer:
See explanation below
Step-by-step explanation:
The calculations for this lottery <em>do not involve </em>the combinations rule because <em>the order of the numbers does matter</em>. For example, 1234 and 4321 are different although they have the same digits.
The calculations for this lottery <em>do involve</em> the permutations with replacement rule because any selected number can be used more than once.
By <em>the fundamental rule of counting</em>, there are 10*10*10*10 = 10,000 possible outcomes of the event with a probability 1/10,000 = 0.0001 each outcome.
<span>we are given the dimensions of a trapezoid: base lengths of 6 and 12 and a base angle of 45 degrees. In this case, we can identify the height of the trapezoid by: tan 45 = h/ (12-6)/2 ; h is equal to 2 units. The area of the trapezoid is A = (b1+ b2)*(h/2). Hence, A = 27 unit2 </span>
A and B are both quadratic functions
Answer:
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