in order to find the value of a number, we have to translate the given mathematical phrases to an algebraic equation.
Algebraic equation refers to the statement of the equality of two algebraic expressions. Then, an algebraic expression is a combination of constant, variable and algebraic operation.
Translating Phrases to Algebraic Expressions
Let x be the number.
"square of a number" = x²
"nine times that number" = 9x
Algebraic Equation
"The square of a number equals nine times that number."
x² = 9x
Solution:
x² = 9x
x²/x = 9x/x
x = 9
Final Answer:
The number is 9.
Checking:
x² = 9x
(9)² = 9(9)
81 = 81 ✔
2. B
Since A = s², where s is a side of the square, then the answer is B.
3. B
If approximately forty-nine less than the square
of a number equals zero,
what is the number, ( -3 or 3 ), ( -7 or 7 ), ( -13 or 13 ), or ( 0 ) or ( 9 )?
Let us choose the number as ( X )
Therefore
( X )² - 49 = 0, Is “ X “ = -3, 3 or -7, 7 or -13, 13 or 0, or 9?
Let ( X )² - 49 = 0 ••••• Equation (1)
Rearrange Exchange (1)
( X )² = 49
Take the Square Root of both sides of the above Equation.
( X ) = sqrt( 49 ) = +/- ( 7 )
Therefore ( X ) has values of ( 7, -7 ).
4. D
A= 80
Let base be n
Height= n-6
A= 80 cm2
1/2×b×n =80
1/2×n×(n-6)= 80
x2- 6n= 80
---------
2
n2- 6n= 160
n2- 6n- 160= 0
n= 16, -10
n= 16
Base= 16 cm2
Height= n-6 = 16- 6
Height= 10 cm
5. B
Finding the Number
To find the number, we have to form the algebraic equation first by translating the given mathematical problem above to algebraic expression. The algebraic equation is a statement that shows the equality of two algebraic expressions.
Equation:
Let "x" be the number.
"four times the square of a number" = 4x²
"20 times that number" = 20x
"four times the square of a number equals 20 times that number"
Answers & Comments
Answer:
1. D
Step-by-step explanation:
Finding the Value of a Number
in order to find the value of a number, we have to translate the given mathematical phrases to an algebraic equation.
Algebraic equation refers to the statement of the equality of two algebraic expressions. Then, an algebraic expression is a combination of constant, variable and algebraic operation.
Translating Phrases to Algebraic Expressions
Let x be the number.
"square of a number" = x²
"nine times that number" = 9x
Algebraic Equation
"The square of a number equals nine times that number."
x² = 9x
Solution:
x² = 9x
x²/x = 9x/x
x = 9
Final Answer:
The number is 9.
Checking:
x² = 9x
(9)² = 9(9)
81 = 81 ✔
2. B
Since A = s², where s is a side of the square, then the answer is B.
3. B
If approximately forty-nine less than the square
of a number equals zero,
what is the number, ( -3 or 3 ), ( -7 or 7 ), ( -13 or 13 ), or ( 0 ) or ( 9 )?
Let us choose the number as ( X )
Therefore
( X )² - 49 = 0, Is “ X “ = -3, 3 or -7, 7 or -13, 13 or 0, or 9?
Let ( X )² - 49 = 0 ••••• Equation (1)
Rearrange Exchange (1)
( X )² = 49
Take the Square Root of both sides of the above Equation.
( X ) = sqrt( 49 ) = +/- ( 7 )
Therefore ( X ) has values of ( 7, -7 ).
4. D
A= 80
Let base be n
Height= n-6
A= 80 cm2
1/2×b×n =80
1/2×n×(n-6)= 80
x2- 6n= 80
---------
2
n2- 6n= 160
n2- 6n- 160= 0
n= 16, -10
n= 16
Base= 16 cm2
Height= n-6 = 16- 6
Height= 10 cm
5. B
Finding the Number
To find the number, we have to form the algebraic equation first by translating the given mathematical problem above to algebraic expression. The algebraic equation is a statement that shows the equality of two algebraic expressions.
Equation:
Let "x" be the number.
"four times the square of a number" = 4x²
"20 times that number" = 20x
"four times the square of a number equals 20 times that number"
4x² = 20x
Solution:
4x² = 20x
4x²/4x = 20x/4x
x = 5
Final Answer:
The number is 5.
Checking:
To check, substitute the number.
4x² = 20x
4(5²) = 20(5)
4(25) = 100
100 = 100 ✔
Done na po d^___^b