Which method will NOT solve this equation completely?
-8 + 3y = 19

○Add 8 to both sides, then divide both sides by 3.
○Divide both sides by 3,then add 8/3 to both sides
○Add 8 to both sides, then multiply both sides by 1/3
○Subtract 8 from both sides, then divide both sides by
1/3

  ○  Subtract 8 from both sides, then divide both sides by 1/3

Step-by-step explanation:

Perhaps the usual sequence of steps is ...

  add 8:

     3y = 27

  divide by 3 (equivalently, multiply by 1/3)

     y = 9

___

If the division by 3 is done first, then the constant on the left becomes -8/3, so cancelling it requires adding 8/3 to both sides of the equation.

If you do the last suggestion, you get ...

  subtract 8 from both sides:

     -16 +3y = 11

  divide both sides by 1/3:

     -48 +9y = 33 . . . . . . . does not solve the equation completely

L(x)=-4x+9

L(2.1)=0.6

Step-by-step explanation:

It's asking us to find the tangent line to curve f(x) = 5−x^2 at x = 2.

Theb use this to estimate f(2.1).

To find slope of tangent line, we must differentiate and then plug in 2 for x.

f'(x)=0-2x by constant and power rule.

f'(x)=-2x

So the slope of the tangent line is -2(2)=-4.

A point on this tangent line shared by the curve is at x=2. We can find it's corresponding y-value using f(x)=5-x^2.

f(2)=5-(2)^2

f(2)=5-4

f(2)=1

So let's rephrase the question a little.

What's the equation for a line with slope -4 and goes through point (2,1).

Point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is a point on the line.

Plug in our information: y-1=-4(x-2).

Distribute: y-1=-4x+8

Add 1 on both sides: y=-4x+9

Let's call this equation L(x), an expression to approximate value for f near x=2.

L(x)=-4x+9

Now the appropriation at x=2.1:

L(2.1)=-4(2.1)+9

L(2.1)=-8.4+9

L(2.1)=0.6

If we did plug in 2.1 into given function we get 5-(2.1)^2=0.59 . This is pretty close to our approximation above.