Take the dot product, if the dot product is zero, they are orthogonal
<span>the dot product here is 15(-5) + 45(12) so the vectors are not orthogonal </span>
<span>to see if they are parallel, take the dot product again, using the definition </span>
<span>u dot v = mag u x mag v cos (theta) where mag is the magnitude of the vector and theta is the angle between them </span>
<span>we know from above that u dot v = 465 </span>
<span>mag u = sqrt[15^2+45^2]=47.43 </span>
<span>mag v = sqrt[5^2+12^2]=13 </span>
<span>so we know: </span>
<span>cos(theta) = 465/(47.43x13) = 0.75 </span>
<span>
so theta = 41 deg</span>
Answer:
shop b
Step-by-step explanation:
We can find for example how much 100 grams of peanut butter cost in each shop using a proportion
shop A 100 : 250 = x : 325
x = (325 * 100) / 250 = $130
shop B 100 : 340 = x : 408
x = (408 * 100)/ 340 = $120
We discovered that shop B is cheaper
change 10 into a fraction and get 10/1 and then turn 2 1/2 into a fraction which is 5/2 and then multiply 10/1 by 2/5 because you need the reciprocal of 5/2 and get 20/5 which is 4.
8090kg-4854kg=decrease in kg ----- find the difference
3236=decrease in kg
3236kg/8090kg=percent decrease ----- decrease/original amount
0.4= percent decrease ------ percent decrease in decimal form
0.4*100=percent decrease ------ multiply by 100 to get percent form
40% decrease