Answer:
Lines are parallel
Step-by-step explanation:
Given:
Right triangles:
To find:
The value of c and value of d
Solution:
<u>In the first right triangle:</u>
θ = 45°
Opposite side to θ = 5
Hypotenuse = c
![$\sin \theta=\frac{\text { Opposite side of } \theta}{\text { Hypotenuse }}](https://tex.z-dn.net/?f=%24%5Csin%20%5Ctheta%3D%5Cfrac%7B%5Ctext%20%7B%20Opposite%20side%20of%20%7D%20%5Ctheta%7D%7B%5Ctext%20%7B%20Hypotenuse%20%7D%7D)
![$\sin 45^\circ=\frac{5}{c}](https://tex.z-dn.net/?f=%24%5Csin%2045%5E%5Ccirc%3D%5Cfrac%7B5%7D%7Bc%7D)
The value of sin 45° = ![\frac{1}{\sqrt 2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%202%7D)
![$\frac{1}{\sqrt 2}=\frac{5}{c}](https://tex.z-dn.net/?f=%24%5Cfrac%7B1%7D%7B%5Csqrt%202%7D%3D%5Cfrac%7B5%7D%7Bc%7D)
Do cross multiplication, we get
![c=5\sqrt{2}](https://tex.z-dn.net/?f=c%3D5%5Csqrt%7B2%7D)
<u>In the second right triangle:</u>
θ = 60°
Opposite side to θ = 4
Adjacent side to θ = d
![$\tan \theta=\frac{\text { Opposite side of } \theta}{\text { Adjacent side of } \theta}](https://tex.z-dn.net/?f=%24%5Ctan%20%5Ctheta%3D%5Cfrac%7B%5Ctext%20%7B%20Opposite%20side%20of%20%7D%20%5Ctheta%7D%7B%5Ctext%20%20%7B%20Adjacent%20side%20of%20%7D%20%5Ctheta%7D)
![$\tan 60^\circ=\frac{4}{d}](https://tex.z-dn.net/?f=%24%5Ctan%2060%5E%5Ccirc%3D%5Cfrac%7B4%7D%7Bd%7D)
![$\sqrt{3} =\frac{4}{d}](https://tex.z-dn.net/?f=%24%5Csqrt%7B3%7D%20%3D%5Cfrac%7B4%7D%7Bd%7D)
Do cross multiplication, we get
![$d=\frac{4}{\sqrt{3} }](https://tex.z-dn.net/?f=%24d%3D%5Cfrac%7B4%7D%7B%5Csqrt%7B3%7D%20%7D)
The value of
and
.
Hmmmm I’ll have to calculate this
Answer:
Option D!
Step-by-step explanation:
Answer:
Jayden buys 4 pounds of coffee
Step-by-step explanation:
Let's say that p represents the number of pounds of coffee Jayden bought. She starts with $90, and for each pound she buys, she loses $7.26 dollars. Therefore, as she loses 7.26 dollars, we must subtract the amount she pays from $90. Then, as she loses 7.26 dollars for each pound, we multiply 7.26 by the number of pounds to find the money she spends.
We can thus write our equation as
90 - 7.26*p = final amount = 60.96
90-7.26p = 60.96
subtract 90 from both sides to isolate the p and its coefficient
-7.26p = -29.04
divide both sides by -7.26 to isolate the p
p = 4
Jayden buys 4 pounds of coffee