Ap 2 7 3 9 4 11 5 13 a farmer picked 3 more peaches than 2 times the apples. the table shows how the number of peaches, p, depends on the number of apples, a. choose the equation which represents the rule. a) p = 2a + 2 b) p = 3 − 2a c) p = 2a − 3 d) p = 2a + 3    plz

 The correct option is (D)

Step-by-step explanation:  Given that a farmer picked 3 more peaches than 2 times the apples. The following table shows how the number of peaches, p, depends on the number of apples, a.

a2     3     4      5

p     7      9     11      13

We are to choose the correct equation that represents the rule.

Since the relation between the number of apples and peaches is a linear one, so the resulting equation will be a linear equation in p and a.

And, the graph will be a straight line.

From the above table, we can see that the line passes through the points

(a, p) = (2, 7) and (3, 9).

So, the slope of the line will be

Since the line passes through (2, 7), so its equation will be

Thus, teh required equation is

Option (D) is CORRECT.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

20

step-by-step explanation: