Tangent Θ = opposite / adjacent
AB = short leg = opposite = 12
AC = long leg = adjacent = 5
BC = hypotenuse = 13
tangent Θ = 12/5 ⇒⇒⇒ this is in ratio form
tanΘ = 2.4 ⇒⇒⇒ this is in decimal form
Answer:
x = 56
Step-by-step explanation:
To start, distribute the 1/3 onto the x and the 4 in the parenthesis. That leaves you with
1/3x + 4/3 = 20
We want the x value by itself so we're going to subtract the 4/3 from the left and the right side, leaving us with
1/3x + 4/3 = 20 - 4/3
1/3x = 18 & 2/3 (since we're dealing with fractions, I'm going to change the 18 & 2/3 into an improper fraction just to make the next step easier.)
1/3x = 56/3
The last step is to divide the 1/3 off of the x, so x is by itself. To divide a fraction by a fraction, just flip the fraction you're dividing with and multiply.
56/3 x 3/1 = 56 (56 x 3 is 168, and 3 x 1 is 3, so when you reduce 168/3, you get 56)
So, 56 is our answer, because after dividing off the 1/3, we're left with x = 56
Answer:
Step-by-step explanation:
let the number of dimes=x
and number of quarters=y
x=2y
0.10 x+0.25 y=2.25
or 10x+25y=225
divide by 5
2x+5y=45
2 ×2y+5y=45
4y+5y=45
9y=45
y=45/9=5
x=2y=2×5=10
Hence dimes=10
quarters=5
M is the slope and b is the y-intercept in the form
.. y = mx +b
You have
.. y = -10x +1
Matching patterns, you see that
.. m = -10
.. b = 1
The slope is -10
The y-intercept is 1
