For the equation y= x2+2 x2−1 , express x in terms of y and determine the values of y for which x is real.

y can take on values in:

Step-by-step explanation:

Hopefully this is the right equation:

.

Multiply both sides by :

Distribute:

Put x terms on one side together and non-x terms on opposite side.

Add y on both sides

and subtract x^2 on both sides:

Factor:

Divide both sides by (y-1):

Now square root both sides:

y cannot be 1 because we don't want to divide by 0.

Now we also need to find when (y+2)/(y-1) is positive or zero because we can't square root negative values if we intend to have just real solutions.

The fraction is zero when y=-2 because that will give us 0 on top.

I'm going to draw a number line and test which intervals gives us positive values for our expression under the square root.

--------(-2)-------(1)----------

Plugging in -3 gives us (-3+2)/(-3-1)=(-1)/(-4)=1/4 so anything before -2 works.

Let's try 0: (0+2)/(0-1)=-2 so nothing between -2 and 1 will work.

Let's try it for 2: (2+2)/(2-1)=4/1=4 so anything after 1 will work.

So y can take on values in:

3.4 pizzas

step-by-step explanation:

given is a scatter plot showing number of pizzas sold during weeks for different issues of coupon

y represents number of pizzas sold and x number of coupons issued

y is marked verticaly and x horizontally

the trend line is given as

y =3.4x+43

this says that even when no coupon is issued pizzas sold will be 43

and rate of change of pizza sold for 1 unit of coupon = slope = 3.4

i.e. when x increases by 1 unit y increases by 3.4 units

hence for each additional coupon issued 3.4 pizzas more will be sold

i think it might be a but you might want a second opinion