Determining whether two quantities are in a proportional relationship. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Answer: There are 41 dimes and 11 pennies in the cup.
Step-by-step explanation:
We know that 1 dime = 0.1 dollars
1 penny = 0.01 dollars
Let p be the number of pennies and d be the number of dimes.
Then we have the following equations :_
![d=4p-3..................(1)\\\\0.1d+0.01p=4.21...........(2)](https://tex.z-dn.net/?f=d%3D4p-3..................%281%29%5C%5C%5C%5C0.1d%2B0.01p%3D4.21...........%282%29)
Substitute the value of d from (1) in equation (2), we get
![0.1(4p-3)+0.01p=4.21\\\\\Rightarrow\ 0.4p-0.3+0.01p=4.21\\\\\Rightarrow\ 0.41p=4.21+0.3\\\\\Rightarrow\ 0.41p=4.51\\\\\Rightarrow\ p=\dfrac{4.51}{0.41}=11](https://tex.z-dn.net/?f=0.1%284p-3%29%2B0.01p%3D4.21%5C%5C%5C%5C%5CRightarrow%5C%200.4p-0.3%2B0.01p%3D4.21%5C%5C%5C%5C%5CRightarrow%5C%200.41p%3D4.21%2B0.3%5C%5C%5C%5C%5CRightarrow%5C%200.41p%3D4.51%5C%5C%5C%5C%5CRightarrow%5C%20p%3D%5Cdfrac%7B4.51%7D%7B0.41%7D%3D11)
Then , Put value of p in (1), we get
![d=4(11)-3=44-3=41](https://tex.z-dn.net/?f=d%3D4%2811%29-3%3D44-3%3D41)
Hence, there are 41 dimes and 11 pennies in the cup.
Answer:
Option A. <A and <B are complementary angles
Option D. ![Sin(C)=Cos(90\°-C)](https://tex.z-dn.net/?f=Sin%28C%29%3DCos%2890%5C%C2%B0-C%29)
Step-by-step explanation:
we know that
If ABC is a right triangle
then
------> by complementary angles
and
![Sin(C)=Cos(A)](https://tex.z-dn.net/?f=Sin%28C%29%3DCos%28A%29)
![Cos(C)=Sin(A)](https://tex.z-dn.net/?f=Cos%28C%29%3DSin%28A%29)
Remember that
![A=90\°-C](https://tex.z-dn.net/?f=A%3D90%5C%C2%B0-C)
so
![Sin(C)=Cos(90\°-C)](https://tex.z-dn.net/?f=Sin%28C%29%3DCos%2890%5C%C2%B0-C%29)
![Cos(C)=Sin(90\°-C)](https://tex.z-dn.net/?f=Cos%28C%29%3DSin%2890%5C%C2%B0-C%29)
Answer:
-29.1-(-71.3)=42.2
Step-by-step explanation: