The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:<span>

<span> $|PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2}}$ </span></span>

Using this formula we calculate the distances |PA|, |PB|, |PC|, |PD| and |PE| and compare to 5.

$|PA|= \sqrt{ (-2-2)^{2} + (-2-1)^{2}}= \sqrt{16+9}= \sqrt{25}=5$

$|PB|= \sqrt{ (-2-4)^{2} + (-2+1)^{2}}= \sqrt{36+1}= \sqrt{37} \approx 6$

$|PC|= \sqrt{ (-2-2)^{2} + (-2+3)^{2}}= \sqrt{16+1}= \sqrt{17}\approx4$

$|PD|= \sqrt{ (-2+6)^{2} + (-2+6)^{2}}= \sqrt{16+16}= \sqrt{32}\ \textgreater \ \sqrt{25}=5$

$|PE|= \sqrt{ (-2+5)^{2} + (-2-1)^{2}}= \sqrt{9+9}= \sqrt{16}=4$

Answer: B and D

3 0

3 years ago

Corn costs 99 cents per pound, and beans cost 45 cents per pound. If Shea buys 24 total pounds of corn and beans, and it costs $

viva [34]

Shea bought 13.5 pounds of corn

c = pounds of corn
b = pounds of beans

Here’s what we know:
c(0.99) + b(0.45) = 18.09
c + b = 24

Solve the second equation for c in terms of b

c = 24-b

Substitute that expression for c in our first equation to get a numerical solution for b:

0.99 (24-b) + 0.45b = 18.09
23.76 - 0.99b + 0.45b = 18.09
-0.54b = -5.67
b = 10.5

Substitute that value to get a numerical value for c:

c = 24 - b
c = 24 - 10.5
c = 13.5

Check the math:

0.99(13.5) + 0.45(10.5) =
13.365 + 4.725 = 18.09

4 0

3 years ago