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VMariaS [17]
3 years ago
14

Ashley started the year with 45 comic books. Each month , she adds 5 more comic books to her collection. Which table correctly r

epresents y , the number of comic books in her collection, after x months

Mathematics
2 answers:
katen-ka-za [31]3 years ago
8 0
The rule for this situation would be y = 45 + 5x
the only table that gives you the correct output of y when you plug x into the equation is the second table


hope this helped!
dybincka [34]3 years ago
7 0
Ashley starts with 45 comics. 

So in the first box: 
x  = 0, y = 45
-------------------------------------------------------------------------------------------------------
Each month, she adds 5 comic books to her collection

x (+1), y (+5) (for each month).

First month. 

x = 0
y = 45

Second month

x = 1
y = 45 (+5) = 50

Third month

x = 2
y = 50 (+5) = 55

etc.

-------------------------------------------------------------------------------------------------------

B) is your best choice, as for every month add (+1), the comic books increase by 5 respectively.

-------------------------------------------------------------------------------------------------------

hope this helps

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Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list.
SOVA2 [1]

Answer:

23.92°, 78.503°, and 77.577°

Step-by-step explanation:

The coordinates of the vertices of the triangle are;

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The vectors are;

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y = \left \langle 6 - (-3), 3 - (-5)  \right \rangle = \left \langle 9, 8 \right \rangle

x = \left \langle 2 - 6, 6 - 3  \right \rangle = \left \langle -4, 3  \right \rangle

cos (\alpha ) = \dfrac{z \cdot y}{\left |  z \right | \times \left | y  \right |}

Therefore, we get;

cos (\alpha ) = \dfrac{5 \times 9  + 11 \times 8 }{\left |  \sqrt{5^2 + 11^2}  \right | \times \left | \sqrt{9^2 + 8^2}   \right |} = \dfrac{133}{\sqrt{146} \times \sqrt{145} } \approx 0.91409

α = arccos(0.91490) ≈ 23.92°

γ = The angle between -y and x

-y = \left \langle -9, -8 \right \rangle

We get;

cos (\gamma) = \dfrac{-y \cdot x}{\left |  -y \right | \times \left | x  \right |}

Therefore;

cos (\gamma) = \dfrac{-9 \times -4  + -8 \times 3 }{\left |  \sqrt{(-9)^2 + (-8)^2}  \right | \times \left | \sqrt{(-4)^2 + 3^2}   \right |} = \dfrac{12}{\sqrt{145} \times \sqrt{25} } \approx 0.199309

γ = arccos(0.199309) ≈ 78.503°

γ ≈ 78.503°

By angle sum property, β = 180° - (α + β)

β ≈ 180° - (23.92° + 78.503°) = 77.577°

β ≈ 77.577°

The interior angles are;

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