Answer:
• David
,
• 4 miles
Explanation:
In the graph:
The given locations are:
• Owen's House, A(11,3)
,
• David's House, B(15,13)
,
• School, C(3,18)
We determine both Owen's and David's distance from the school using the distance formula.
Owen's distance from school (AC)
![\begin{gathered} AC=\sqrt[]{(3-11)^2+(18-3)^2} \\ =\sqrt[]{(-8)^2+(15)^2} \\ =\sqrt[]{64+225} \\ =\sqrt[]{289} \\ AC=17\text{ miles} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20AC%3D%5Csqrt%5B%5D%7B%283-11%29%5E2%2B%2818-3%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B%28-8%29%5E2%2B%2815%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B64%2B225%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B289%7D%20%5C%5C%20AC%3D17%5Ctext%7B%20miles%7D%20%5Cend%7Bgathered%7D)
David's distance from school (BC)
![\begin{gathered} BC=\sqrt[]{(3-15)^2+(18-13)^2} \\ =\sqrt[]{(-12)^2+(5)^2} \\ =\sqrt[]{144+25} \\ =\sqrt[]{169} \\ BC=13\text{ miles} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20BC%3D%5Csqrt%5B%5D%7B%283-15%29%5E2%2B%2818-13%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B%28-12%29%5E2%2B%285%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B144%2B25%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B169%7D%20%5C%5C%20BC%3D13%5Ctext%7B%20miles%7D%20%5Cend%7Bgathered%7D)
We see from the calculations that David lives closer to the school, and by 4 miles.
The graph below is attached for further understanding:
Answer:
- length: 30 ft
- width: 10 ft
Step-by-step explanation:
The description of the garden fits that of 3 squares arranged side-by-side. The area of each of those would be 100 ft², so their side length would be ...
s = √A= √(100 ft²) = 10 ft
This dimension is the width of the garden, whose length is 3 times this amount.
The length and width of the garden are 30 ft and 10 ft, respectively.
Answer:
first option: Harulo is correct because the angle is coterminal with 3π / 4 and the reference angle is π / 4.
Explanation:
1) 19 π/4 = 4π + 3 π/4, which is 4 complete turns and 3/4 of turn.
2) 3 π/4 is in the third quadrant, so the reference angle is π - 3 π/4 = π/4
3) sin (π/4) = sin (3π/4) = (√2) / 2
4) csc (π/4) = 1 / [ sin (3π/4) ] = 1 / [ (√2) / 2 ] = 2 / (√2) = √2, which shows the validity of the statement and csc(19π/4) = √2.
Answer:
1/2.
Step-by-step explanation:
f(x) = (1/8)^x
when x = 1/3
f(x) = (1/8)^1/3
f(x) = ∛(1/8)
f(x) = 1 / ∛8
f(x) = 1/2.
16x³ - 54
= 2(8x³ - 27)
= 2(2x - 3)(4x² + 6x + 9) ← answer
