Answer:
x = 2
Step-by-step explanation:
Answer:
![cos^{-1} (\frac{8}{[tex]\sqrt{113}](https://tex.z-dn.net/?f=cos%5E%7B-1%7D%20%28%5Cfrac%7B8%7D%7B%5Btex%5D%5Csqrt%7B113%7D)
} )[/tex]
Step-by-step explanation:
Given two vectors a and b,we are rquired to find the angle between them.
a=(8,7);b=(7,0).
Angle between two vectors can be found by dot product of them.
If a and b are two vectors then the dot product of them is given by|a||b|cos(α).
Where α is the angle between the vectors a and b.
Now 
. and 
=56.
Now cosα=
so α= cosine inverse of that.
∴α=
} )[/tex]
Answer:
50 nickels, 20 quarters.
Step-by-step explanation:
System of equations (q = # of quarters, n = # of nickels):
<em>q + n = 70, 0.25q + 0.05n = 7.50</em>
the first equation can be changed to q = 70 - n, so we are able to <em>substitute q with 70 - n</em>.
So, it will look like <em>0.25*70 - 0.25n + 0.05n = 7.50</em>. This can be simplified to <em>0.2n = 10</em>, which means that n = 50.
Knowing that we can solve <em>q + 50 = 70</em>, which means that q = 20.
Answer:
18
Step-by-step explanation:
x + (x + 1) + (x + 2) = 57
x + x + 1 + x + 2 = 57
x + x + x + 1 + 2 = 57
3x + 3 = 57
3x = 57 - 3
3x = 54
x = 54/3
x = 18
1 mile is equal to 1.6 kilometers, so 8 miles (using a direct proportion) should be equal to 8 * 1.6 = 12.8 kilometers. The cyclist rides at 12.8 kilometers per hour. In four hours, the cyclist would have rode 12.8 * 4 = 48 + 3.2 = 51.2 kilometers.
