Joachim bought a pair of shoes for $40, which was a 20% discount. what was the original price of the shoes?

ANSWER

The original price of the shoes was $50

EXPLANATION

The original price of the shoe corresponds to 100℅.

A discount of 20℅ means the reduced price of the shoe corresponds to 80℅.

Let the original price be .

If we find 80% of x, we should get the price at which he bought the shoes.

This means that;

We solve for x,

.

We multiply the numerator to obtain,

.

Therefore the original price was $50

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

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step-by-step explanation: