sun shades are sold in the shape of right isosceles triangles. if the equation represents one shade that shields 64 square feet of area, which system can be used to find the lengths of the legs of the sun shade?
$\frac{1}{2}x^2 = 64$

$y = \frac{1}{2}x^2 + 64$ and $y = 0$
$y = \frac{1}{2}x^2$ and $y = 64$
$y = \frac{1}{2}x^2 + 64$ and $y = \frac{1}{2}x^2 - 64$

use the graphing calculator to graph the system. the solutions to the system are dropdown. since the side lengths of a triangle must be positive, the length of one leg of the sun shade is dropdown feet.

Question

sun shades are sold in the shape of right isosceles triangles. if the equation represents one shade that shields 64 square feet of area, which system can be used to find the lengths of the legs of the sun shade?
$\frac{1}{2}x^2 = 64$

$y = \frac{1}{2}x^2 + 64$ and $y = 0$
$y = \frac{1}{2}x^2$ and $y = 64$
$y = \frac{1}{2}x^2 + 64$ and $y = \frac{1}{2}x^2 - 64$

use the graphing calculator to graph the system. the solutions to the system are dropdown. since the side lengths of a triangle must be positive, the length of one leg of the sun shade is dropdown feet.

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Systems of Non-linear Equations", "Polynomial Word Problems" ], "new_concepts": [], "current_concepts": [ "Systems of Non-linear Equations", "Polynomial Word Problems", "Solving Equations Graphically" ] } ## Formulate the system of equations $$ \begin{aligned} &\frac{1}{2}x^2 = 64 \ &y = \frac{1}{2}x^2 \quad \text{and} \quad y = 64 \end{aligned} $$ ## Solve the system of equations $$ \begin{aligned} &\frac{1}{2}x^2 = 64 \ &x^2 = 128 \ &x = \pm \sqrt{128} \approx \pm 11.3 \end{aligned} $$ ## Determine the physical length $$ \begin{aligned} &x > 0 \ &x \approx 11.3 \end{aligned} $$ ## Question 1 Sun shades are sold in the shape of right isosceles triangles. If the equation represents one shade that shields 64 square feet of area, which system can be used to find the lengths of the legs of the sun shade? $\frac{1}{2}x^2 = 64$ $y = \frac{1}{2}x^2 + 64$ and $y = 0$

$y = \frac{1}{2}x^2$ and $y = 64$

$y = \frac{1}{2}x^2 + 64$ and $y = \frac{1}{2}x^2 - 64$ ## Question 2 Use the graphing calculator to graph the system. The solutions to the system are $-11.3\text{ or }11.3$. ## Question 3 Since the side lengths of a triangle must be positive, the length of one leg of the sun shade is $11.3$ feet. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Non-linear Equations" ] }

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Solve the system of equations

Determine the physical length

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