Answer:
The number of nickels is 45 and the number of dimes is 72.
Step-by-step explanation:
Let
x ----> number of nickels
y ----> number of dimes
Remember that
![1\ nickel=\$0.05](https://tex.z-dn.net/?f=1%5C%20nickel%3D%5C%240.05)
![1\ dime=\$0.10](https://tex.z-dn.net/?f=1%5C%20dime%3D%5C%240.10)
so
------> equation A
![0.05x+0.10(2y)=16.65](https://tex.z-dn.net/?f=0.05x%2B0.10%282y%29%3D16.65)
------> equation B
<em>Solve the system by substitution</em>
we have
------> equation A
------> equation B
Multiply both equations by 100 both sides
---->
--> equation C
----> equation D
substitute equation C in equation D
![(945-10y)+20y=1,665](https://tex.z-dn.net/?f=%28945-10y%29%2B20y%3D1%2C665)
solve for y
![945+10y=1,665](https://tex.z-dn.net/?f=945%2B10y%3D1%2C665)
![10y=1,665-945](https://tex.z-dn.net/?f=10y%3D1%2C665-945)
![10y=720](https://tex.z-dn.net/?f=10y%3D720)
![y=72\ dimes](https://tex.z-dn.net/?f=y%3D72%5C%20dimes)
Find the value of x
![5x=945-10y](https://tex.z-dn.net/?f=5x%3D945-10y)
![5x=945-10(72)](https://tex.z-dn.net/?f=5x%3D945-10%2872%29)
![5x=225](https://tex.z-dn.net/?f=5x%3D225)
![x=45\ nickels](https://tex.z-dn.net/?f=x%3D45%5C%20nickels)
<em>Alternative Method</em>
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
the solution is the point (45,72)
therefore
The number of nickels is 45 and the number of dimes is 72.
Y = 3x + b
6 = 3(4) + b
6 = 12 + b, b = -6
Equation: y = 3x - 6
Answer:
?= 3
Step-by-step explanation:
let x = ?
18-2x=4x
6x=18x
x=3
Answer:
x = 18√3
Step-by-step explanation:
From the picture attached,
In a right triangle,
Measure of one angle = 30°
Measure of adjacent side of the angle = 9 units
We have to find the measure of Hypotenuse from the given properties.
By cosine rule,
cos(30°) = ![\frac{\text{Adjacent side}}{\text{Hypotenuse}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BAdjacent%20side%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D)
![\frac{\sqrt{3}}{2} =\frac{9}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%3D%5Cfrac%7B9%7D%7Bx%7D)
![x=18\sqrt{3}](https://tex.z-dn.net/?f=x%3D18%5Csqrt%7B3%7D)
Therefore, measure of Hypotenuse is 18√3 units.