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:
1063 ft
Step-by-step explanation:
For shadow problems, we assume the sun's rays are parallel, so the triangles formed are similar. That means the ratio of height to shadow length is the same for each object.
h/(580 ft) = (5.5 ft)/(3 ft)
h = (5.5 ft)(580/3) ≈ 1063 ft
The height of the monument is about 1063 feet.
Answer:
$0.90
Step-by-step explanation:
A 10-minute call exceeds the 3-minute initial period by 7 minutes. The initial period charge is 37¢. The additional minute charge is 7·9¢ = 63¢. Then the regular charge for that call is ...
37¢ +63¢ = 100¢ = $1.00
The 10% discount reduces the charge by ...
10% × $1.00 = $0.10
so the final cost of the 10-minute call is ...
$1.00 -0.10 = $0.90 . . . . . cost of the call
Answer:
Step-by-step explanation:
The expression can be fully factored as ...
3·5·(x-3)
Equivalent expressions can be formed by eliminating parentheses to give ...
15x -45
or by combining different pairs of factors:
Of course any of the terms can be broken apart and/or combined in different ways:
= 15(x -2) -15
= (7x -7) + 2(4x -19)
