Some parts are missing in the queston. Find attached the picture with the complete question
Answer:
Explanation:
Let's put the information in a table step-by step.
(number of remaining students)
Juniors Seniors
Condition
- Twice juniors as seniors 2(S - 15)
- 3/4 of the juniors left 1/4×2(S - 15)
- 1/3 of seniors left 2/3×(S - 15)
At the end, there were 8 more seniors than juniors:
- 2/3×(S - 15) - 1/4×2(S - 15) = 8
Now you have obtained one equation, which you can solve to find S, the number of senior students, and then the number of junior students.
Solve the equation:
- Addtion property of equalities:
- Division property of equalities:
That is the number of senior students that came out to the information meeting, but the number of students remaining to perform in the school musical is (from the table above):
Just substitute S with 153 fo find the number of students that remained to perfom in the musical:
0.33... (it goes on forever)
Answer:
(8a + 3)(a + b + c)
Step-by-step explanation:
8a^2 + 8ab + 8ac + 3a + 3b + 3c =
= 8a(a + b + c) + 3(a + b + c)
= (8a + 3)(a + b + c)
Let's go through the choices one by one
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Choice A
If all sides are congruent, then this figure is a rhombus (by definition). If all angles are congruent, then we have a rectangle. Combine the properties of a rhombus with the properties of a rectangle and we have a square.
In terms of "algebra", you can think
rhombus+rectangle = square
Or you can draw out a venn diagram. One circle represents the set of all rhombuses; another circle represents the set of all rectangles. The overlapping region is the set of all squares. The overlapping region is inside both circles at the same time.
So we can rule out choice A. This guarantees we have a square when we want something that isn't a guarantee.
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Choice B
If we had a parallelogram with perpendicular diagonals, then we can prove that we have a rhombus (all four sides congruent). However, we don't know anything about the four angles of this parallelogram. Are they congruent? We don't know. So we can't prove this figure is a rectangle. The best we can say is that it's a rhombus. It may or may not be a rectangle. There isn't enough info about the rectangle & square part.
This is why choice B is the answer. We have some info, but not enough to be guaranteed everytime.
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Choice C
This is a repeat of choice A. Having "all right angles" is the same as saying "all angles congruent". This is because "right angle" is the same as saying "90 degrees". So we can rule out choice C for identical reasons as we did with choice A.
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Choice D
As mentioned before in choice A, if we know that a quadrilateral is a rectangle and a rhombus at the same time, then the figure is also a square. This is always true, so we are guaranteed to have a square. We can cross choice D off the list.
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Once again, the final answer is choice B
