Sagot :
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INSTRUCTIONS :
- Write whether or not each of the following situations illustrates quadratic equations. Justify your answer by representing each situation by a mathematical sentence.
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EXAMPLE :
Quadratic
- 1. The length of a swimming pool is 8 m longer than its width and the area is 105 m²,
Mathematical Sentence :
- Ww+) = 105 - w2w 105 = 0 =
(medj. dko gets yung example dto nyahaha)
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Not Quadratic
- 2. Edna paid at least Php1,200 for a pair of pants and a blouse. The cost of the pair of pants is Php600 more than the cost of the blouse.
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ANSWER :
#1. The area of a rectangular plot is 528 m². The length of the plot (in meters) is one more than twice its width.
[tex]\red{\boxed{ \red{\boxed{ \rm Quadratic }}} }[/tex]
Mathematical sentence :
- [tex] \rm (2x+1) x=528 \: \implies \: \red{\underline{ 2x² + x - 528 = 0}}[/tex]
[tex] \\ [/tex]
#2. The product of two consecutive positive integers is 306.
[tex]\red{\boxed{ \red{\boxed{ \rm Quadratic }}} }[/tex]
Mathematical sentence :
- [tex]\rm{ x(x+1) =306 \: \implies \: \red{\underline{x²+x+306=0 }} }[/tex]
[tex] \\ [/tex]
#3. The length of a rectangular table is 6m more than its width and its area is 12 m2.
[tex]\red{\boxed{ \red{\boxed{ \rm Quadratic }}} }[/tex]
Mathematical sentence :
- [tex]\rm{ x(x+6) = 12 \: \implies \: \red{\underline{x² +6x -12 =0 }}}[/tex]
[tex] \\ [/tex]
#4. At 80 kilometers per hour it takes Anna 10 hours to travel from her house to their house in the province. How long will it take her if she travels at 80 kilometers an hour?
[tex]\red{\boxed{ \red{\boxed{ \rm Not\: Quadratic }}} }[/tex]
[tex] \\ [/tex]
#5. Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.
[tex]\red{\boxed{ \red{\boxed{ \rm Quadratic }}} }[/tex]
Mathematical sentence :
- [tex]\rm{ (x+3) (x+29) = 360 \: \implies \: \red{\underline{x²+32x-273=0}} }[/tex]
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#CarryOnLearning
[tex]\begin{gathered}\tiny\boxed{\begin{array} {} \red{\bowtie} \:\:\:\:\:\:\: \red{\bowtie}\\ ｡◕‿◕｡ \\ \end{array}}\end{gathered}[/tex]
ꨄ︎
✏️QUADRATIC EQUATIONS
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••} [/tex]
[tex] \underline{\mathbb{DIRECTIONS}:} [/tex]
- Write whether or not each of the following situations illustrates quadratic equations. Justify your answer by representing each situation by a mathematical sentence.
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••} [/tex]
[tex] \underline{\mathbb{PROBLEMS}:} [/tex]
- 1. The area of a rectangular plot is 528 m². The length of the plot in meters is one more than twice its width.
- 2. The product of two consecutive positive integers is 306.
- 3. The length of a rectangular table is 6 m more than its width and its area is 12 m².
- 4. At 80 kilometers per hour it takes Anna 10 hours to travel from her house to their house in the province. How long will it take her if she travels at 80 kilometers an hour?
- 5. Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••} [/tex]
[tex] \underline{\mathbb{ANSWERS}:} [/tex]
[tex] \qquad\large 1) \Large \tt\: \green{QUADRATIC} [/tex]
[tex] \qquad\large 2) \Large \tt\: \green{QUADRATIC} [/tex]
[tex] \qquad\large 3) \Large \tt\: \green{QUADRATIC} [/tex]
[tex] \qquad\large 4) \Large \tt\: \green{NOT \: QUADRATIC} [/tex]
[tex] \qquad\large 5) \Large \tt\: \green{QUADRATIC} [/tex]
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••} [/tex]
[tex] \underline{\mathbb{JUSTIFICATIONS}:} [/tex]
» We can classify an equation if it is quadratic when there is a variable that is raised by two or when its highest degree is two.
#1: Represent [tex] x [/tex] as the width of the rectangle, multiplied to the length which is 1 more than twice the width with a product of 528.
- [tex] (2x + 1)x = 528 [/tex]
- [tex] 2x^2 + x = 528 [/tex]
- [tex] \boxed{\boxed{2x^2 + x - 528 = 0}} [/tex]
» Since its highest degree is two, then we can say that this is a quadratic equation.
[tex] \: [/tex]
#2: Let [tex] x [/tex] be the positive integer and [tex] (x + 1) [/tex] as it is its positive consecutive integer. Make an equation in which their product is 306.
- [tex] x(x+1) = 306 [/tex]
- [tex] x^2 + x = 306 [/tex]
- [tex] \boxed{\boxed{x^2 + x - 306 = 0}} [/tex]
» Since its highest degree is two, then we can say that this is a quadratic equation.
[tex] \: [/tex]
#3: Represent [tex] x [/tex] as the width of the rectangle, multiplied to the length which is 6 more than the width with a product of 12.
- [tex] (x + 6)x = 12 [/tex]
- [tex] x^2 + 6x = 12 [/tex]
- [tex] \boxed{\boxed{x^2 + 6x - 12 = 0}} [/tex]
» Since its highest degree is two, then we can say that this is a quadratic equation.
[tex] \: [/tex]
#4: The ratio of the speed and the time taken to Anna to reach her house is proportional to the same speed to its time taken.
- [tex] \frac{80}{10} = \frac{80}{x} \\ [/tex]
- [tex] 8 = \frac{80}{x} \\ [/tex]
- [tex] 8x = 80 [/tex]
- [tex] \boxed{\boxed{x = 10}} [/tex]
» We can no longer find any variables that is squared. Thus, it doesn't show any equation that is quadratic.
[tex] \: [/tex]
#5: Represent [tex] x [/tex] as it is the age of Rohan added to 26 which is her mother's age. When their ages is added to 3, the product would be 360.
- [tex] (x + 3)(x + 26 + 3) = 360 [/tex]
- [tex] (x + 3)(x + 29) = 360 [/tex]
- [tex] x^2 + 29x + 3x + 87 = 360 [/tex]
- [tex] x^2 + 32x + 87 = 360 [/tex]
- [tex] x^2 + 32x + 87 - 360 = 0 [/tex]
- [tex] \boxed{\boxed{x^2 + 32x - 273 = 0}} [/tex]
» Since its highest degree is two, then we can say that this is a quadratic equation.
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••} [/tex]
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