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:
art class / all classes = 16 / (26 + 19 + 21 + 16 + 32) = 16/114 = 8/57Step-by-step explanation:
we know that
step 1
multiply
by ![\frac{10}{10}](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%7D%7B10%7D%20%20)
so
![0.6*\frac{10}{10} =\frac{6}{10}](https://tex.z-dn.net/?f=%200.6%2A%5Cfrac%7B10%7D%7B10%7D%20%3D%5Cfrac%7B6%7D%7B10%7D%20%20)
step 2
Divide numerator and denominator by ![2](https://tex.z-dn.net/?f=%202%20)
![\frac{\frac{6}{2}}{\frac{10}{2}} =\frac{3}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Cfrac%7B6%7D%7B2%7D%7D%7B%5Cfrac%7B10%7D%7B2%7D%7D%20%3D%5Cfrac%7B3%7D%7B5%7D%20%20)
therefore
the answer is
![\frac{3}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7D%20%20)
Answer: x = 31
Step-By-Step:
<u>To Find x:</u>
<u />
(Angle Sum Property Of Triangles)
(Remove the brackets)
<u />
<u />
(Group Accordingly)
<u />
<u />
= ![5x+20+10-5=180](https://tex.z-dn.net/?f=5x%2B20%2B10-5%3D180)
=
![=180](https://tex.z-dn.net/?f=%3D180)
= ![5x= 180 - 25](https://tex.z-dn.net/?f=5x%3D%20180%20-%2025)
= ![5x = 155](https://tex.z-dn.net/?f=5x%20%3D%20155)
= ![x=\frac{155}{5}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B155%7D%7B5%7D)
= ![31](https://tex.z-dn.net/?f=31)
<u>Therefore</u> x = 31
So,
Angle A = x + 10 = 31 + 10 = 41
Angle B = 2*x + 20 = 2*31 + 20 = 82
Angle C = 2*x - 5 = 62 - 5 = 57
Answer: It will one year (or 12 months) before Michael is able to ride the roller coaster.
Step-by-step explanation: Because he grows a half inch every month, this means that It takes him two months to grow one full inch. Because he has to grow six inches, you just multiply 2 by 6 to get 12 months or one year.