Step-by-step explanation:
5. Determine whether the
x
y
11
-2
-1
2.
0
-1
1
2
2
11
Is it a linear quadratic or exponential
A prime number can only be divided by one oritslef and a composite number can bedivided by other njmbers.
Answer:
![m\angle CDB=90\\m\angle CBD=90-\alpha\\m\angle BCD=\alpha\\\\m\angle CDA=90\\m\angle CAD=\alpha\\m\angle ACD=90-\alpha](https://tex.z-dn.net/?f=m%5Cangle%20CDB%3D90%5C%5Cm%5Cangle%20CBD%3D90-%5Calpha%5C%5Cm%5Cangle%20BCD%3D%5Calpha%5C%5C%5C%5Cm%5Cangle%20CDA%3D90%5C%5Cm%5Cangle%20CAD%3D%5Calpha%5C%5Cm%5Cangle%20ACD%3D90-%5Calpha)
Step-by-step explanation:
The triangles are drawn below.
CD is perpendicular to AB as CD is height to AB.
Therefore, angles
°
So, triangles ΔCBD and ΔCAD are right angled triangles.
Now, from the right angled triangle ΔABC,
![m\angle A+m\angle B =90\\\alpha+m\angle B=90\\m\angle B=90-\alpha](https://tex.z-dn.net/?f=m%5Cangle%20A%2Bm%5Cangle%20B%20%3D90%5C%5C%5Calpha%2Bm%5Cangle%20B%3D90%5C%5Cm%5Cangle%20B%3D90-%5Calpha)
From ΔCBD,
is same as
.
So, ![m\angle CBD=90-\alpha](https://tex.z-dn.net/?f=m%5Cangle%20CBD%3D90-%5Calpha)
![m\angle BCD+m\angle BDC =90\\m\angle BCD+90-\alpha=90\\m\angle BCD=\alpha](https://tex.z-dn.net/?f=m%5Cangle%20BCD%2Bm%5Cangle%20BDC%20%3D90%5C%5Cm%5Cangle%20BCD%2B90-%5Calpha%3D90%5C%5Cm%5Cangle%20BCD%3D%5Calpha)
Now, from ΔCAD,
is same as ![m\angle A](https://tex.z-dn.net/?f=m%5Cangle%20A)
So, ![m\angle CAD=\alpha](https://tex.z-dn.net/?f=m%5Cangle%20CAD%3D%5Calpha)
![m\angle CAD+m\angle ACD =90\\\alpha+m\angle ACD=90\\m\angle ACD=90-\alpha](https://tex.z-dn.net/?f=m%5Cangle%20CAD%2Bm%5Cangle%20ACD%20%3D90%5C%5C%5Calpha%2Bm%5Cangle%20ACD%3D90%5C%5Cm%5Cangle%20ACD%3D90-%5Calpha)
Hence, the unknown angles of both the triangles are:
![m\angle CDB=90\\m\angle CBD=90-\alpha\\m\angle BCD=\alpha\\\\m\angle CDA=90\\m\angle CAD=\alpha\\m\angle ACD=90-\alpha](https://tex.z-dn.net/?f=m%5Cangle%20CDB%3D90%5C%5Cm%5Cangle%20CBD%3D90-%5Calpha%5C%5Cm%5Cangle%20BCD%3D%5Calpha%5C%5C%5C%5Cm%5Cangle%20CDA%3D90%5C%5Cm%5Cangle%20CAD%3D%5Calpha%5C%5Cm%5Cangle%20ACD%3D90-%5Calpha)
Answer:
- f = -2/5a +14
- 12.4 ≈ 12 fish for 4 algae blooms
Step-by-step explanation:
The 2-point form of the equation for a line is useful when you are given two points to work with:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
The independent variable (x) is apparently "algae blooms" and is to be represented by "a". The dependent variable (y) is "number of fish" and is to be represented by "f". So, we have ...
f = (4 -10)/(25 -10)(a -10) +10
f = -6/15(a -10) +10
f = -2/5a +14 . . . an equation for the scenario
Four a=4, the fish population is predicted to be ...
f = -2/5(4) +14 = 12.4
There will be about 12 fish when there are 4 algae blooms.