If LaTeX: P\left(6,-2\right),\:Q\left(-2,\:8\ right),\:R\left(-4,\:3\right),\:P ( 6 , − 2 ) , Q ( − 2 , 8 ) , R ( − 4 , 3 ) ,and LaTeX: S\left(-9,\:y\right)\:S ( − 9 , y )find the value of LaTeX: yy so that LaTeX: PQ\bot RS.

Step-by-step explanation:

First let us get the slope of the line PQ and RS

For PQ;

Given P(6, -2) and Q(-2,8)

slope m = 8-(-2)/-2-6

slope of pQ = 10/-8

slope of PQ = -5/4

For RS

R ( − 4 , 3 ) and S(-9, y)

slope of RS = y-3/-9+4

slope of RS = y-3/-5

For PQ to be perpendicular to RS, the product of their slope must be -1

Hence -5/4 (y-3/-5) = -1

y-3/4 = -1

cross multiply

y-3 = -4

y = -4+3

y = -1

Hence the value of y for PQ to be perpendicular to RS is -1

d) 48

step-by-step explanation:

16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,272,288,304,320,336

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.