Answer:
Coordinates of the new library is (150, 70)
Step-by-step explanation:
To get the shortest possible distance means that line from point T to point R has to be perpendicular.
Now, the equation of R is given as;
y = x - 80 - - - (1)
For T to be perpendicular, it means it will have a slope equal to the negative reciprocal of line R.
Thus, slope of T is -1/1 = - 1
Thus, using line - slope intercept of y = mx + c, we can find equation of T as;
140 = -1(80) + c
140 = -80 + c
c = 140 + 80
c = 220
Thus, equation is;
y = -x + 220 - - - (eq 2)
Adding equation 1 to equation 2,we have;
y + y = 220 - 80
2y = 140
y = 140/2
y = 70
Putting 70 for y in eq 1 gives;
70 = x - 80
x = 70 + 80
x = 150
Thus;
Coordinate of the new library is (150, 70)
9514 1404 393
Answer:
√3
Step-by-step explanation:
The ratio of the short sides to the hypotenuse in an isosceles right triangle is ...
1 : 1 : √2
This means ...
p·√2 = √6
p = (√6)/(√2) = √(6/2)
p = √3
D because is the equal to the other side but added allá together
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)
Tangent Θ = opposite / adjacent
AB = short leg = opposite = 12
AC = long leg = adjacent = 5
BC = hypotenuse = 13
tangent Θ = 12/5 ⇒⇒⇒ this is in ratio form
tanΘ = 2.4 ⇒⇒⇒ this is in decimal form
is in the interval is 0.95 rather we are 95% confident that the true mean of the population will be in the stated interval.