When considering similar triangles, we need congruent angles and proportional sides.
Hence
"Angles B and B' are congruent, and angles C and C' are congruent." is sufficient to prove similarity of two triangles.
"Segments AC and A'C' are congruent, and segments BC and B'C' are congruent." does not prove anything because we know nothing about the angles.
"Angle C=C', angle B=B', and segments BC and B'C' are congruent." would prove ABC is congruent to A'B'C' if and only if AB is congruent to A'B' (not just proportional).
"<span>Segment BC=B'C', segment AC=A'C', and angles B and B' are congruent</span>" is not sufficient to prove similarity nor congruence because SSA is not generally sufficient.
To conclude, the first option is sufficient to prove similarity (AAA)
Part (i)
<h3>Answer:
x^2 + 5x + 6</h3>
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Work Shown:
(x+3)(x+2)
y(x+2) ..... Let y = x+3
y*x + y*2 ... distribute
x(y) + 2(y)
x(x+3) + 2(x+3) .... plug in y = x+3
x*x + x*3 + 2*x + 2*3 ... distribute
x^2 + 3x + 2x + 6
x^2 + 5x + 6
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Part (ii)
<h3>Answer:
4x^2 - 16x + 7</h3>
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Work Shown:
We could follow the same set of steps as shown back in part (i), but I'll show a different approach. Feel free to use the method I used back in part (i) if the visual approach doesn't make sense.
The diagram below is a visual way to organize all the terms. Many textbooks refer to it as "the box method" which helps multiply out any two algebraic expressions.
Each inner cell is found by multiplying the corresponding outer terms. For instance, in the upper left corner we have 2x*2x = 4x^2. The other cells are filled out the same way.
The terms in those four inner cells (gray boxes) are:
The like terms here are -14x and -2x which combine to -16x, since -14+(-2) = -16.
We end up with the answer 4x^2-16x+7
No, the question is stating the product of a number (the variable n represents the number) and 10 is 142. In other words, 10 times another number is 142. Hence, the answer would be A.
Answer:
32.5
Step-by-step explanation:
If CED is 65, then AEB is 65, therefore we can calculate that CEA is 115 because 180 - 65 = 115. Then we do 180 - 115 = 65 which is the sum of angles ACE and CAE so 65 / 2 = 32.5 which is CAE.
Hope this helped!
Job A pays better
there are roughly 52 weeks in a year so multiply that by 40 to get the total hours worked in a year. = 2,080
2,080 hours worked per year multiplied by the hourly pay 9.95 = 20,696
Job A pays $20,696 per year
Job B only pays $17,500
