Answer:
The high school art teacher has 468 boxes in total and the elementary school art teacher has 1,664 boxes in total.
Step-by-step explanation:
1. Collect Information.
High School Teacher: 9 cases of crayons + 52 boxes per case
Elementary School Teacher: 16 cases of crayons with 104 boxes per case
2. Multiply the number of cases by the boxes per case to get the number of boxes that each teacher has in total.
High School: 9 cases × 52 boxes = 468 boxes in total
Elementary School: 16 cases × 104 boxes = 1,664 boxes in total
3. State your answer.
The high school art teacher has 468 boxes in total and the elementary school art teacher has 1,664 boxes in total.
4. Is my answer reasonable?
Yes, my answer is reasonable for multiple reasons:
- The elementary school art teacher had more cases and more boxes so it would only make sense that the total number of boxes which the elementary school art teacher has would be greater than the total number of boxes which the high school art teacher has.
- Using common knowledge of 50 × 9 being equal to 450 (If this isn't common knowledge then remember that 5×9=45 and that you could just bring down the 0 from the 50 and the answer would be 450) you could tell that the answer would be a little more than 450 and knowing that 50×10=500 you would know that it would also be less than 500. 468 falls in between of 450 and 500 so my answer here is reasonable.
- Using common knowledge of 16×100 being equal to 1,600 and 17×100=1,700 you could tell that the answer would be greater than 1,600 and less than 1,700. 1,664 falls in between of 1,600 and 1,700 so my answer here is reasonable.
By the law of sines, m∠<em>EFG</em> is such that
sin(m∠<em>EFG</em>) / (8 in.) = sin(m∠<em>G</em>) / (7.5 in)
so you need to find m∠<em>G</em>.
The interior angles to any triangle sum to 180°, so
m∠<em>DEG</em> = m∠<em>D</em> + m∠<em>G</em> + 43°
m∠<em>DEG</em> + m∠<em>D</em> + m∠<em>G </em>= 2 (m∠<em>D</em> + m∠<em>G</em>) + 43°
180° = 2 (m∠<em>D</em> + m∠<em>G</em>) + 43°
137° = 2 (m∠<em>D</em> + m∠<em>G</em>)
68.5° = m∠<em>D</em> + m∠<em>G</em>
But ∆<em>DEG</em> is isosceles, so m∠<em>D</em> = m∠<em>G</em>, which means
68.5° = 2 m∠<em>G</em>
34.25° = m∠<em>G</em>
<em />
Then
sin(m∠<em>EFG</em>) = (8 in.) sin(34.25°) / (7.5 in)
m∠<em>EFG</em> ≈ sin⁻¹(0.600325) ≈ 36.8932°
The value will be minimum, the coefficient of x is positive, so it will curve up causing a minimum vertex
