Line x is the mid point of both lines
so the triangle becomes base = 19.2/2 = 9.6
hypotenuse = 24/2 = 12
using Pythagorean theorem:
x^2 = 12^2 - 9.6^
x^2 = 144 - 92.16
x^2 = 51.84
x = sqrt(51.84) = 7.2
You have two types of terms here, two variables (terms with x attached to then) and a constant (a number by itself)
You just need to get the two different types of terms individually, on either side of the equal sign:
-4x=-2x+6
Add 2x on both sides to remove the variable from the right hand sign
-2x=6
Divide both sides by -2(the coefficient of x)
x= -3
x is on the LHS and -3 is on the RHS
The grade is the ratio of rise to run, i.e. the slope aka the tangent.
Answer: (a) 6 degrees
For part b, the road is the hypotenuse c of a right triangle whose tangent of the small angle is 1/10. The height h or rise is the side opposite the small angle.
We could just take the sine of the angle we got but let's get it from the tangent exactly.
Dividing by squared cosine
Answer: (b) Rise of 0.199 km
He can get 1 hot dog that is my smallest answer
There are two answers:
B) 5
C) 8
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Explanation:
If we had a triangle with sides a, b and c, then we can say
b-a < c < b+a
where b is larger than 'a'. This is the triangle inequality theorem
In this case, a = 5 and b = 9 so,
b-a < c < b+a
9-5 < c < 9+5
4 < c < 14
Telling us that c is some number between 4 and 14, not including either endpoint. If c is a whole number, then c could be any value from this set: {5,6,7,8,9,10,11,12,13}
We see that the numbers 5 and 8 are in this set. The values 3 and 15 are not in the set.