The angle between two vectors is given by:
cos (x) = (v1.v2) / (lv1l * lv2l)
We have then:
v1.v2 = (2, -5). (4, -3)
v1.v2 = (2 * 4) + (-5 * (- 3))
v1.v2 = 8 + 15
v1.v2 = 23
We look for the vector module:
lv1l = root ((2) ^ 2 + (-5) ^ 2)
lv1l = 5.385164807
lv2l = root ((4) ^ 2 + (-3) ^ 2)
lv2l = 5
Substituting values:
cos (x) = (23) / ((5.385164807) * (5))
x = acos ((23) / ((5.385164807) * (5)))
x = 31.33 degrees
Answer:
The angle between the two vectors is:
x = 31.33 degrees
Step-by-step explanation:

Solve b part yourself in the same way.
B. <span>She is correct. The remaining angle of the triangle measures less than 90 degrees.</span>
Answer:

Step-by-step explanation:
We have an extremely large equation and are asked to divide it, so let's solve it step-by-step :
Remove the parenthesis to make it easier to read :

Multiply the numerators :

Multiply the denominators :

Apply the negative rule :

Cancel the common factor which is 18 :

Apply the addition exponent rule :

Subtract :

Apply the rule for y :

Subtract :

Cancel the common factor of z^3 :

Answer:
24
Step-by-step explanation:
7x4