You wish to take flying lessons. the introductory course costs $125 per lesson and you want to take 12 lessons. smith flying academy also charged $50 registration fee. you currently have $700 saved for your flying lesson. how much more money do you need to pay for the class in full?

$850

Step-by-step explanation:

Multiply the $125 per lesson by 12 and that's $1500. Now add the $50 fee to make it a total of $1550. Subtract $1550 by $700 and you're left with $850 that you still need to pay.

First find the total amount you need to pay.

Since you need $125 for each lesson and you want to take twelve lessons, multiply.

125 * 12 = 1500

Then you need 50 dollars more.

1500 + 50 = 1550

That is the total amount you need to pay for the class.

You have 700 saved up so subtract that from the prices to find the answer.

1550 - 700 = 850.

You need 850 more dollars to pay for the class in full.

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

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15