Zeroes are when f(x)=0
0=x^2+9x+20
factor
0=(x+4)(x+5)
set each to zero
x+4=0
x=-4
x+5=0
x=-5
zeroes are f(-5) and f(-4)
Answer:
Step-by-step explanation:
There is a point V with ration 6 to 2, therefore we must find the coordinates of point V and the distance from A to V
<u>According to the graph</u>
![c^{2}=x^{2}+y^{2}\\c^{2}=8^{2}+4^{2}\\c=\sqrt{64+16}=8.9.4\\sin\alpha =\frac{4}{8.94}](https://tex.z-dn.net/?f=c%5E%7B2%7D%3Dx%5E%7B2%7D%2By%5E%7B2%7D%5C%5Cc%5E%7B2%7D%3D8%5E%7B2%7D%2B4%5E%7B2%7D%5C%5Cc%3D%5Csqrt%7B64%2B16%7D%3D8.9.4%5C%5Csin%5Calpha%20%3D%5Cfrac%7B4%7D%7B8.94%7D)
α≅27°
V=2*8.94/6 (ratio 6:2)
V=2.98mile
![sin27=\frac{y}{2.98}\\y=sin27*2.98=1.35\\cos27=\frac{x}{2.98}\\x=cos27*2.98=2.65](https://tex.z-dn.net/?f=sin27%3D%5Cfrac%7By%7D%7B2.98%7D%5C%5Cy%3Dsin27%2A2.98%3D1.35%5C%5Ccos27%3D%5Cfrac%7Bx%7D%7B2.98%7D%5C%5Cx%3Dcos27%2A2.98%3D2.65)
coordinates of V = (2,65;1.35)
Distance from A to V
![d_{AV}=2.98 miles](https://tex.z-dn.net/?f=d_%7BAV%7D%3D2.98%20miles)
finally
Mary's mistake is to take the 6 to 2 ratio as the distance traveled from the globe only in the x direction
Answer:
I am guessing about 150 - 200 students did not buy a yearbook.
Step-by-step explanation:
First let's assume that there are 1,000 or so students in the school. 856 would be a little over 4/5 of 1,000 just as 8 would be 4/5 of 10.
Answer:
20.3
Step-by-step explanation:
Answer:
![x = 3 + 4\sqrt{3}](https://tex.z-dn.net/?f=x%20%3D%203%20%2B%204%5Csqrt%7B3%7D)
Step-by-step explanation:
OPQ is a right angle triangle.
<u>Using Pythagoras</u>
![x^{2} + (x+5)^{2} = (x+8)^{2}\\x^{2} + x^{2} + 10x +25 = x^{2} + 16x + 64\\x^{2} + x^{2} - x^{2} + 10x - 16x + 25 - 64 = 0\\x^{2} - 6x -39 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%20%28x%2B5%29%5E%7B2%7D%20%3D%20%28x%2B8%29%5E%7B2%7D%5C%5Cx%5E%7B2%7D%20%2B%20x%5E%7B2%7D%20%2B%2010x%20%2B25%20%3D%20x%5E%7B2%7D%20%2B%2016x%20%2B%2064%5C%5Cx%5E%7B2%7D%20%2B%20x%5E%7B2%7D%20-%20x%5E%7B2%7D%20%2B%2010x%20-%2016x%20%2B%2025%20-%2064%20%3D%200%5C%5Cx%5E%7B2%7D%20-%206x%20-39%20%3D%200)
<u>Using quadratic formula</u>
<u />![x = \frac{-b \± \sqrt{b^{2}-4ac}}{2a}\\x = \frac{-(-6) \± \sqrt{(-6)^{2}-4(1)(-39)}}{2(1)}\\x = \frac{6}{2} \± \frac{\sqrt{192}}{2}\\x = 3 \± \frac{8\sqrt{3}}{2}\\x = 3 \± 4\sqrt{3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%5C%C2%B1%20%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%5C%5Cx%20%3D%20%5Cfrac%7B-%28-6%29%20%5C%C2%B1%20%5Csqrt%7B%28-6%29%5E%7B2%7D-4%281%29%28-39%29%7D%7D%7B2%281%29%7D%5C%5Cx%20%3D%20%5Cfrac%7B6%7D%7B2%7D%20%5C%C2%B1%20%5Cfrac%7B%5Csqrt%7B192%7D%7D%7B2%7D%5C%5Cx%20%3D%203%20%5C%C2%B1%20%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B2%7D%5C%5Cx%20%3D%203%20%5C%C2%B1%204%5Csqrt%7B3%7D)
![x = 3 + 4\sqrt{3} = 9.928(4s.f.)](https://tex.z-dn.net/?f=x%20%3D%203%20%2B%204%5Csqrt%7B3%7D%20%3D%209.928%284s.f.%29)
OR
(Length can't be negative)
∴ ![x = 3 + 4\sqrt{3}](https://tex.z-dn.net/?f=x%20%3D%203%20%2B%204%5Csqrt%7B3%7D)