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Questions and Answers
What is the simplified expression of $7 \sqrt{21} \sqrt{3}$?
What is the simplified expression of $7 \sqrt{21} \sqrt{3}$?
What do you call two binomial radical expressions that have the same number but only differ in the sign that connects the binomials?
What do you call two binomial radical expressions that have the same number but only differ in the sign that connects the binomials?
What is the simplified expression of $\frac{1}{5} (-32)$?
What is the simplified expression of $\frac{1}{5} (-32)$?
What is the conjugate of the radical expression $(3 - \sqrt{2})$?
What is the conjugate of the radical expression $(3 - \sqrt{2})$?
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What is the name of the quadrilateral that has four right angles and four congruent sides?
What is the name of the quadrilateral that has four right angles and four congruent sides?
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What is the simplified expression of $\frac{2}{3} (27)$?
What is the simplified expression of $\frac{2}{3} (27)$?
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What is the value of x in the expression 11x + 3 if YX = 13 and LK = 19?
What is the value of x in the expression 11x + 3 if YX = 13 and LK = 19?
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Which theorem states that 'The segment connecting the midpoint of two sides of a triangle is parallel to the third side and half as long'?
Which theorem states that 'The segment connecting the midpoint of two sides of a triangle is parallel to the third side and half as long'?
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In parallelogram BEST with diagonals BS and ET bisecting each other at O, if ES = 18 units, what is the length of segment BT?
In parallelogram BEST with diagonals BS and ET bisecting each other at O, if ES = 18 units, what is the length of segment BT?
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Which of the following is not a radical equation?
Which of the following is not a radical equation?
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Which statement about rhombuses is true?
Which statement about rhombuses is true?
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If ABCD is a rhombus and angle DAC measures 54 degrees, what is the measure of angle DAB?
If ABCD is a rhombus and angle DAC measures 54 degrees, what is the measure of angle DAB?
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What operation is needed to solve for x in the equation 2x - 3 = 5?
What operation is needed to solve for x in the equation 2x - 3 = 5?
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Which quadrilateral has exactly one pair of parallel sides?
Which quadrilateral has exactly one pair of parallel sides?
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What is the radical form of 3/4?
What is the radical form of 3/4?
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If YX = 13, LK = 19, and ZW = 11x + 3, what is the length of ZW?
If YX = 13, LK = 19, and ZW = 11x + 3, what is the length of ZW?
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What is the simplification of the radical expression $\sqrt{200}$?
What is the simplification of the radical expression $\sqrt{200}$?
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Which quadrilateral has no pair of parallel sides?
Which quadrilateral has no pair of parallel sides?
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What is the correct term for the power of a product when simplifying an expression like 3^3(y^2)?
What is the correct term for the power of a product when simplifying an expression like 3^3(y^2)?
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In mathematics, what is the special type of parallelogram that is considered the most unique?
In mathematics, what is the special type of parallelogram that is considered the most unique?
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What would be the simplest form of -1 exponent in 4x?
What would be the simplest form of -1 exponent in 4x?
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If a 10-meter ladder is placed 6 meters away from a building, how high up the building will the ladder reach?
If a 10-meter ladder is placed 6 meters away from a building, how high up the building will the ladder reach?
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What is the ideal power for the expression (3xy) to make it equal to 1?
What is the ideal power for the expression (3xy) to make it equal to 1?
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If the area of a kite is 98 cm^2 and EG = 7cm, what should be the length of FD in the given figure (diagram not shown)?
If the area of a kite is 98 cm^2 and EG = 7cm, what should be the length of FD in the given figure (diagram not shown)?
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Study Notes
Simplifying Expressions
-
(7/1) × (21/3) = 7/1 -
1/5 × (-32) = -2 -
2/3 × (27) = 9 -
1/4 × (-4) = undefined -
3200 = 10 × 2
Conjugates
- Two binomial radical expressions that have the same number but only differ in the sign that connects the binomials are called conjugates
- Example:
3 - √2and3 + √2are conjugates
Quadrilaterals
- A parallelogram with four right angles and four congruent sides is called a square
- A quadrilateral with two pairs of parallel and congruent sides is called a parallelogram
- A quadrilateral with exactly one pair of parallel sides is called a trapezoid
- A quadrilateral with no pairs of parallel sides is called a trapezium
- A quadrilateral with two distinct pairs of congruent sides is called a kite
Radical Equations
- An equation that contains radicals and a variable expression in the radicand is called a radical equation
- Example:
√(2x - 3) = 5
Theorems
- The Triangle Midline Theorem states that "The segment that connects the midpoint of the two sides of a triangle is parallel to the third side and half as long"
Laws of Exponents
- The Power of a Product states that
a^m × a^n = a^(m+n) - The Power of a Power states that
(a^m)^n = a^(mn) - The Power of a Quotient states that
(a/b)^m = a^m / b^m - The Product of a Power states that
(ab)^m = a^m × b^m
Miscellaneous
- Rationalization is the process of removing the radical sign in the denominator
- The index of an expression is another term for its order
- A convex quadrilateral is a quadrilateral where all angles are less than 180°
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Description
Test your mathematical knowledge with this quiz featuring true or false questions, fill in the blanks, and exponent laws. Prepared by JERWIN C.ORENCE, this quiz covers topics like basic arithmetic, geometry, and algebra.
