Answer:
Option C.
Step-by-step explanation:
Equation of the parent function graphed in the figure is,
G(x) = x²
By reflecting the parent function over the x-axis,
G'(x) = -x²
By shifting G'(x) by 2 units down over the y-axis,
f(x) = -x² - 2
Therefore, transformed form of the parent function will be
f(x) = -x² - 2
Therefore, Option C will be the answer.
Answer:
18. Commutative property of addition
19. Distributive property
20. Associative property of addition
Step-by-step explanation:
Lagrange multipliers:







(if

)

(if

)

(if

)
In the first octant, we assume

, so we can ignore the caveats above. Now,

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of

.
We also need to check the boundary of the region, i.e. the intersection of

with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force

, so the point we found is the only extremum.
Step-by-step explanation:
(1) Factor the GCF out of the trinomial on the left side of the equation. (2 points: 1 for the GCF, 1 for the trinomial) 2x²+6x-20=0
2x²+6x-20
2(x²+3x-10)
the factors are 2 and (x²+3x-10)
(2) Factor the polynomial completely. (4 points: 2 point for each factor)
2(x²+3x-10)
2(x²-2x+5x-10)
2(x(x-2) + 5(x-2)) group like terms
2(x+5)(x-2)
(3) If a product is equal to zero, we know at least one of the factors must be zero. And the constant factor cannot be zero. So set each binomial factor equal to 0 and solve for x, the width of your project. (2 points: 1 point for each factor)
constant = 2 cannot be zero
the other factors are (x+5) and (x-2)
(x+5)=0 => x= -5
or
(x-2)=0 => x=2
(4) What are the dimensions of your project? Remember that the width of your project is represented by x. (2 points: 1 point for each dimension)
thank you so much, sorry if it's a little confusing!!
(it is indeed confusing, because physical dimensions cannot be negative)
The dimensions of the project (assumed a rectangle) are +2 and -5
Solving Two- Step Equations:
First you have to add or subtract the number without the variable, x, then divide with the variable with x in it.
1.) -2 - 2=26
Answer: x= -14
Try some on your own, if you still need help comment back!