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|---|---|---|
| Questions | 5 | 5 |
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If the area of this square is 1, what is the length of one of the diagonals?
| 6\( \sqrt{2} \) | |
| \( \sqrt{2} \) | |
| 9\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{1} \) = 1
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 12 + 12
c2 = 2
c = \( \sqrt{2} \)
Solve for y:
y2 - 1 = 0
| 8 or 1 | |
| 3 or -1 | |
| 1 or -1 | |
| 2 or -9 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
y2 - 1 = 0
(y - 1)(y + 1) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 1) or (y + 1) must equal zero:
If (y - 1) = 0, y must equal 1
If (y + 1) = 0, y must equal -1
So the solution is that y = 1 or -1
Solve for y:
y2 + 4y - 26 = 4y - 1
| 7 or -7 | |
| 2 or -5 | |
| 5 or -5 | |
| 6 or 4 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
y2 + 4y - 26 = 4y - 1
y2 + 4y - 26 + 1 = 4y
y2 + 4y - 4y - 25 = 0
y2 - 25 = 0
Next, factor the quadratic equation:
y2 - 25 = 0
(y - 5)(y + 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 5) or (y + 5) must equal zero:
If (y - 5) = 0, y must equal 5
If (y + 5) = 0, y must equal -5
So the solution is that y = 5 or -5
On this circle, line segment AB is the:
circumference |
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diameter |
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radius |
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chord |
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).
Which of the following is not true about both rectangles and squares?
all interior angles are right angles |
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the lengths of all sides are equal |
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the area is length x width |
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the perimeter is the sum of the lengths of all four sides |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).