Answer:
(x/2) + 15 = 5 + 3x
Step-by-step explanation:
Follow the steps in the equation. X is your number. First you halve it, then you add 15. Next, set it equal to the other side. The second side is 5 + (because it is the sum) and 3x (the product of 3 and x means multiply them)
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
Answer:
{3,6,9,0}
Step-by-step explanation:
The range is the set of all second elements of ordered pairs (y-coordinates).
Answer:
Center: (-5,10)
Radius: 2
Step-by-step explanation:
The equation of the circle in center-radius form is:
Where the point (h,k) is the center of the circle and "r" is the radius.
Subtract 121 from both sides of the equation:
Add 10x to both sides:
Make two groups for variable "x" and variable "y":
Complete the square:
Add 
inside the parentheses of "x".
Add 
inside the parentheses of "y".
Add 
and 
to the right side of the equation.
Then:
Rewriting, you get that the equation of the circle in center-radius form is:
You can observe that the radius of the circle is:
And the center is:
More details need to be provided to answer this question
