Are these expressions equivalent 20d - 16 and 4(5d - 4)

Yes they are equivalent

The reason why is because

4(5d - 4) = 4*(5d) + 4(-4) = 20d - 16

You multiply the outer term 4 by each term inside the parenthesis

4 times 5d = 4*5d = 20d

4 times -4 = 4*(-4) = -16

I'm using the distributive property.

Alternatively, you can start with 20d - 16 and factor out the GCF 4. Divide each term by 4 to get

20d/4 = 5d

-16/4 = -4

So after dividing each term of 20d-16 by 4, we get 5d-4 and the 4 will be pulled out to say 20d - 16 = 4(5d - 4)

As you can probably see, factoring is just thinking of distributing in reverse. Instead of multiplying each term by the same number, you divide each term by the same number. You can distribute the 4 back in to check your factorization.

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this

answer: a

step-by-step explanation: the answer is a due to the rule of symmetry; that a line of symmetry must divide a figure into 2 pieces that are the exact same, only reflected over a line of symmetry. b and c do not have lines of symmetry and would not divide the figure evenly, thus making the answer a.