We know that
If the scalar product of two vectors<span> is zero, both vectors are </span><span>orthogonal
</span><span>A. (-2,5)
</span>(-2,5)*(1,5)-------> -2*1+5*5=23-----------> <span>are not orthogonal
</span><span>B. (10,-2)
</span>(10,-2)*(1,5)-------> 10*1-2*5=0-----------> are orthogonal
<span>C. (-1,-5)
</span>(-1,-5)*(1,5)-------> -1*1-5*5=-26-----------> are not orthogonal
<span>D. (-5,1)
</span>(-5,1)*(1,5)-------> -5*1+1*5=0-----------> are orthogonal
the answer is
B. (10,-2) and D. (-5,1) are orthogonal to (1,5)
Answer:
67 people were still left waiting in line.
Step-by-step explanation:
If there are 65 plus 11 more, there'd be 76 people in line.
I guess the fact that it says "waiting in two lines" can be completely discarded because bottom line is 9 people got their drinks- which means that "waiting in two lines" means nothing.
76 - 9 = 67 people still left waiting in line.
For the red line, we have:
gradient (
) = 1/3
y-intercept = 3
Equation of straight line is given by
, where
is the gradient and
is where the line intercept the y-axis
So we have,
The shaded part is above the line, hence the first inequality is
The black line, we have
gradient,
= 3
y-intercept = -2
, rearranging gives
The shaded region is to the right of the line, hence the inequality is
Note: The first option should be the correct answer but the inequality sign for <span>y > 1/3x + 3 should be </span>
You would have to do 15 - 2 because according to PEMDAS you do parentheses first and you would do the multiplication and division
180 feet, cause you have already covered half the square