Compute. show your work. (5 2/3)^2 -(4 1/3)^2

Step-by-step explanation:

First convert the mixed fractions to improper fractions.

We can use the identity a² - b² = (a +b)(a - b)

Here a = 17/3 and b = 13/3

We can add & subtract as they have common denominators.

Q1 - at the store before taking the product home, because "pre" in precycling stands for making environmentally sound decisions BEFORE buying a product.

Q2 -  in many household products, such as cleaning products, the ones that are used for doing laundry, medicine, etc.

Q3 - Environmental Protection Agency, which aims to protect and conservate the natural resources in the U.S.

Q4- the highest recycled content, because then you'd be contributing for the recycling cicle avoiding unnecessary waste of other materials.

Q5 - corrosive, since they destroy other materials (or cause corrosion).

Q6 - lower grade of recycling, because the result of this process are material that are less valuable than the former one.

Q7 - taking it to your local Household Hazardous waste station, since this place will dispose of your waste in a safe way, and give it a correct destination.

Q8- 100% recyclable and not expensive to do so, also it's very common to recycle it since this process is not complex or expensive.

Q9 - computer paper, because the wax in fast food wrapers make it difficult for it to be recycled, as well as the wax in juice boxes and the pet food bags that contain plastic and aluminium layers below the paper layer.

Q10-  waxed milk/juice cartons, plastic laminated packages, since the layers in those papers and the wax in it can't be removed properly in simple recycling processes.

Q11- reduce, reuse and recycle, to optimize and diminish the use of some materials and then reduce pollution and waste volume.

Q12 - fertilizer, as long as it has natural components. Industrial fertilizers are also very hazardous because they might contain toxic products in it that can pollute water and soil.

Q13- Letter R, for recycle! This is a strategy to stimulate recycling processes and the correct disposal of such materials.

Q14 - toxins, since they are toxic for an organism and might cause death after long exposure.

Q15 - recycle would be the most efficient way to eliminate waste, since we transform all the material used in other materials or in simpler compounds, therefore not letting waste accumulate.

Q16 - baking soda, lemon oil, and borax, since those household items can be decomposed naturally and won't pollute the environment.

Q17 - not poisionous to humans, since toxic products are considered to have the potential to harm human beings.

Q18 - toxins, because they are capable of harming living beings.

Q19 - all of the above, since they are all highly alkaline and can, therefore, cause corrosion.

Q20 - Ammonia, which causes an exothermic reaction liberating chemical fumes.

Q1 - at the store before taking the product home, because "pre" in precycling stands for making environmentally sound decisions BEFORE buying a product.

Q2 -  in many household products, such as cleaning products, the ones that are used for doing laundry, medicine, etc.

Q3 - Environmental Protection Agency, which aims to protect and conservate the natural resources in the U.S.

Q4- the highest recycled content, because then you'd be contributing for the recycling cicle avoiding unnecessary waste of other materials.

Q5 - corrosive, since they destroy other materials (or cause corrosion).

Q6 - lower grade of recycling, because the result of this process are material that are less valuable than the former one.

Q7 - taking it to your local Household Hazardous waste station, since this place will dispose of your waste in a safe way, and give it a correct destination.

Q8- 100% recyclable and not expensive to do so, also it's very common to recycle it since this process is not complex or expensive.

Q9 - computer paper, because the wax in fast food wrapers make it difficult for it to be recycled, as well as the wax in juice boxes and the pet food bags that contain plastic and aluminium layers below the paper layer.

Q10-  waxed milk/juice cartons, plastic laminated packages, since the layers in those papers and the wax in it can't be removed properly in simple recycling processes.

Q11- reduce, reuse and recycle, to optimize and diminish the use of some materials and then reduce pollution and waste volume.

Q12 - fertilizer, as long as it has natural components. Industrial fertilizers are also very hazardous because they might contain toxic products in it that can pollute water and soil.

Q13- Letter R, for recycle! This is a strategy to stimulate recycling processes and the correct disposal of such materials.

Q14 - toxins, since they are toxic for an organism and might cause death after long exposure.

Q15 - recycle would be the most efficient way to eliminate waste, since we transform all the material used in other materials or in simpler compounds, therefore not letting waste accumulate.

Q16 - baking soda, lemon oil, and borax, since those household items can be decomposed naturally and won't pollute the environment.

Q17 - not poisionous to humans, since toxic products are considered to have the potential to harm human beings.

Q18 - toxins, because they are capable of harming living beings.

Q19 - all of the above, since they are all highly alkaline and can, therefore, cause corrosion.

Q20 - Ammonia, which causes an exothermic reaction liberating chemical fumes.

In step 2, he confused the multiplication and addition signs.

Or C

In step 2, he confused the multiplication and addition signs.

Or C

Lets take

f(x) = a x +b

x= 3  ,f(3)=9

9 = 3 a + b                 ------------1

x=5   ,f(5) = 15

15 = 5 a + b                   ---------2

From equation 1 and 2

6 = -2 a

a = - 3

9 = 3 (-3)+ b  

b= 18

f(x) = -3 x + 18

f(8) = -3 x 8  + 18=-24 + 18 = -6

f(13) = -3 x 13+ 18 = - 39 + 18 =-11

f(12) = -3 x 12+ 18 = - 36 + 18 = -18

f(10) = -3 x 10 + 18 = -12

f(-3) = -3 x (-3)+ 18 =27

f(-5) = -3 x (-5)+ 18 = 33

f(0) = -3 x 0+ 18 = 18

Lets take

f(x) = a x +b

x= 3  ,f(3)=9

9 = 3 a + b                 ------------1

x=5   ,f(5) = 15

15 = 5 a + b                   ---------2

From equation 1 and 2

6 = -2 a

a = - 3

9 = 3 (-3)+ b  

b= 18

f(x) = -3 x + 18

f(8) = -3 x 8  + 18=-24 + 18 = -6

f(13) = -3 x 13+ 18 = - 39 + 18 =-11

f(12) = -3 x 12+ 18 = - 36 + 18 = -18

f(10) = -3 x 10 + 18 = -12

f(-3) = -3 x (-3)+ 18 =27

f(-5) = -3 x (-5)+ 18 = 33

f(0) = -3 x 0+ 18 = 18

The vector pointing from (2, 1) to (1, 3) points in the same direction as the vector . The derivative of at (2, 1) in the direction of is

We have

Then

The vector pointing from (2, 1) to (5, 5) has the same direction as the vector . The derivative of at (2, 1) in the direction of is

so that

Solving the remaining system gives and .

The vector pointing from (2, 1) to (1, 3) points in the same direction as the vector . The derivative of at (2, 1) in the direction of is

We have

Then

The vector pointing from (2, 1) to (5, 5) has the same direction as the vector . The derivative of at (2, 1) in the direction of is

so that

Solving the remaining system gives and .