Lesson 71 Adding And Subtracting Polynomials
Essential Question How can you add and subtract polynomials?
Work with a partner. Write the expression modeled by the algebra tiles in each step.
Work with a partner. Write the expression modeled by the algebra tiles in each step.
Communicate Your Answer
How can you add and subtract polynomials?Answer:
Use your methods in Question 3 to find each sum or difference.a. + b. + c. d. Answer:
Find the degree of the monomial.Question 1.
Question 41.MODELING WITH MATHEMATICSThe cost of making b bracelets is represented by 4 + 5b. The cost of making b necklaces is represented by 8b + 6. Write a polynomial that represents how much more it costs to make b necklaces than b bracelets.Answer:
Question 42.MODELING WITH MATHEMATICSThe number of individual memberships at a fitness center in m months is represented by 142 + 12m. The number of family memberships at the fitness center in m months is represented by 52 + 6m. Write a polynomial that represents the total number of memberships at the fitness center.Answer:
In Exercises 4346, find the sum or difference.Question 43. Answer:
REASONING In Exercises 4750, complete the statement with always, sometimes, or never. Explain your reasoning.Question 47.The terms of a polynomial are ________ monomials.Answer:
The difference of two trinomials is _________ a trinomial.Answer:
A binomial is ________ a polynomial of degree 2.Answer:
You bounce a tennis ball on a racket.Answer:
Pouring A Concrete Pad Specifically For An Above Ground Pool Versus Installing One On An Existing Slab
Deciding to pour a concrete slab for your future above ground pool is a nice decision. With a pool on concrete, you dont have to worry about nutgrass, moles, or any earth dynamics causing issues. There are a couple of drawbacks to it, but for the most part, its a solid way to go.
Most thinking about installing their pools on concrete are doing so because they have some kind of existing patio or slab in the yard. Using an existing concrete slab is often problematic though.
Unless youre a concrete person, you may not realize that most concrete patios or outdoor slabs of any kind are considerably off level. This is because any outdoor hard ground surface needs to have a gradual drop-off to allow rainwater to drain off of it.
When most people look at their existing concrete slab, it looks level. Ive had more than a few people call me out to build their above ground on an existing slab. When I talk to them, I explain how most slabs or patios are too off-level to install a pool on, but they will assure me that they checked and the concrete slab in their backyard is level.
When I get to their house to build the pool, Ill pull out my laser level and show them that the deck that they insisted was perfectly level, is off quite a bit.
Fiberglass Pool Coping Options
The coping is the transition from the pool to the pool deck.
The traditional method with fiberglass pools is to pour the concrete flush with the top of the pool, leaving the top of the fiberglass pool shell exposed.
Frankly, that’s an easy installation method…but it looks hideous!
Today, the most popular coping around fiberglass pools is what’s known as cantilevered concrete coping.
Cantilevered concrete coping is unique in that it is one continuous concrete pour.
Other coping types are set in place with mortar or industrial adhesive.
Paver, travertine, and bluestone are three popular coping upgrades. They will typically cost between $35 and $65 per linear foot.
Even though you cannot see it with alternative forms of coping, every fiberglass pool must have concrete poured around the perimeter of the shell.
This locks the pool in place and gives the coping a foundation to be laid upon.
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A Tuscan Stamped Concrete And Custom
This is an example of a Tuscan-style backyard featuring a custom-shaped pool and stamped concrete. The pool is large enough to accommodate all members of the family. There is also an outdoor seating area complete with a fire pit on one side of the pool.
If you are curious, the fire pit was built on-site. It is completed with an interior of fire brick and topped with Leuder limestone chopped stone that perfectly matches the house. There is a fire glass to fill around the gas burner as the medium.
The decking here is ivory travertine lined with a limestone banding. The tile used is HM140 from Master Tile. The plaster color here is a custom blend sunstone, which is 5 Turtle and 5 Mediterranean.
You may wonder whether such stone is perfect for a patio, whether it is slippery or not. For your information, travertine is not as porous as other stones usually used for a patio. Yes, it is more likely to be more slippery when wet. So it would be nice to add a sealer in a non-slippery material.
For a recommendation, you can use SolidStepCote. That is a special sealer that can turn your pool decking anti-slip. It is recommended to use SolidStepCote #4 or #3 for a travertine swimming pool deck
There is a spa area in this pool too. And at the far end of the pool, you can see a beautiful waterfall feature. The whole dimensions of this pool are 23 x 6 x 36, while the spa is 5 x 13. The wet deck is roughly 7 x 20.
Simple Ways To Enhance The Look Of Your Backyard Swimming Pool Oasis
Although there are certainly many ways to dress up an inground swimming pool, I wanted to write a brief list showing 11 things you may consider to dress up the overall appearance of your backyard poolscape.
Keep in mind that as you read the following ideas they are just thatideas, and by no means a requisite to having a beautiful pool in your backyard. As I always say, its better to have a pool in your backyard without all the options you wanted, than it is to have a beautiful pool with every option you ever dreamed of…in your headand not in your backyard.
Without further ado, here goes:
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Patios Budgets And The Principle Of Consolidation
When trying to adhere to a budget like everyone does, follow the principle of consolidation.
We simply mean that you want to put as much patio as possible in your congregating areas, and only enough everywhere else to be functional and aesthetically pleasing.
For example, let’s say your budget allows for 800 square ft. of patio around the pool.
The very worst use of that space would be to evenly distribute 8 ft. of patio around the entire pool. Why? Because you would be without any single place to congregate and have more area than you need around much of the pool.
The best use of that space would be to consolidate as much of that 800 ft. as possible into 1 or 2 areas.
You may have 12 ft. of patio along one side of the pool and have 8 ft. on the shallow end, and 3 or 4 ft. on the other two sides.
Or you could have 16 ft. on one end and 4 or 5 ft. around the rest of the pool…you get the idea. This is a much better use of your money and space.
Will You Need Fencing Where Will It Go
Fencing can be used for a variety of different purposes, but is most often put in to keep children or pets safely away from the pool. Safety fencing can go directly around the pool, or if you want to add a larger, permanent fence, you’ll need to consider how far out it will be going? Leave room for concrete to be poured for posts if needed.
Regardless of which type of fence you use, you will want to make sure you are including enough space to comfortably utilize the area between the fence and the pool. Remember, a fence will act in many ways like a wall, which means you won’t be able to as easily access the space outside the confines of the deck as you would without a fence. So plan the space accordingly.
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Lesson 73 Special Products Of Polynomials
Essential Question What are the patterns in the special products , 2, and 2?
Finding a Sum and Difference PatternWork with a partner. Write the product of two binomials modeled by each rectangular array of algebra tiles.
Finding the Square of a Binomial PatternWork with a partner. Draw the rectangular array of algebra tiles that models each product of two binomials. Write the product.
Communicate Your Answer
Question 3.What are the patterns in the special products , 2, and 2?Answer:
Question 4.Use the appropriate special product pattern to find each product. Check your answers using algebra tiles.a.
Describe how to use special product patterns to find 212.Answer:
Question 9.Each of two dogs has one black gene and one white gene . The Punnett square shows the possible gene combinations of an offspring and the resulting colors.a. What percent of the possible gene combinations result in black?b. Show how you could use a polynomial to model the possible gene combinations of the offspring.Answer:
Make Sure You Get Enough Patioor Plan To Add On In The Future
With that being said, it’s important to note that the most common mistake new pool owners make is that they don’t get enough patio when they initially get the pool.
So it’s important to make the best use of your patio through proper design, but it’s also important to make sure that you are getting enough patio to meet your needs.
Many clients find it beneficial to implement their total backyard design in phases.
If they plan this right, it allows them to have the pool installed so it meets their needs for a season.
Then they implement the next phase later, which adds more patio, outdoor kitchen, fire pit, etc.
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Mountain Style Backyard Area With Stamped And Stained Concrete Around A Pool
For a farmhouse-style house, adding a pool with a mountain and rustic design like this is highly recommended. This is a perfect example of a rustic backyard completed with a freeform pool, stone beach entry, rock flower beds, and stamped concrete deck.
The stamped concrete looks a lot like porcelain tile. The color is light brown with black streaks here and there. This concrete is also stained in a clear sealant. It is to make sure the natural color is still there, sure to match the natural stone of the spa and the rock weeping wall.
Next to the pool, there is a pergola for a sitting area. The pergola has a post and beam structure completed with stone walls and pillars. The stones are similar to the ones in the spa. Overall, this outdoor space looks stunning with a neutral color palette.
Polynomial Equations And Factoring Cumulative Assessment
Question 1.Classify each polynomial by the number of terms. Then order the polynomials by degree from least to greatest.a. -4×3
Which exponential function is increasing the fastest over the interval x = 0 to x = 2 ?Answer:
Find all solutions of the equation x3 + 6×2 4x = 24.Answer:
Question 4.The table shows the distances you travel over a 6-hour period. Create an equation that models the distance traveled as a function of the number of hours.Answer:
Consider the equation y = \x + 2.a. Graph the equation in a coordinate plane.b. Does the equation represent a linear or nonlinear function?c. Is the domain discrete or continuous?Answer:
Which expressions are equivalent to -2x + 15×2 8?Answer:
The graph shows the function f = 2x.a. Is the function increasing or decreasing for increasing values of x?b. Identify any x- and y-intercepts.Answer:
Which polynomial represents the product of 2x 4 and x2 + 6x 2?A. 2×3 + 8×2 4x + 8B. 2×3 + 8×2 28x + 8C. 2×3 + 8
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Things To Consider When Choosing Materials
Choosing deck material shouldn’t be just a matter of going with what you think is the most attractive. Important things to consider:
- The material must be safe and not become slippery when wet.
- Make sure the decking material isn’t coarse, bumpy, or uneven.
- Choose a heat-reflective material to keep the surface cooler on hot daysthink about bare feet!
- Select a material that blends well with other paved or hardscaped areas in your yard.
- If possible, find out if the material is resistant to algae, chemicals, acid, mold and mildew, and frost.
- A modern solution: for a seamless look, carry out the coping material to the surrounding deck or patio.
- Safety fences and barriers should be considered and integrated into the pool and deck design. Check city or local laws or guidelines regarding pool barriersmost should be at least 4 feet high and be positioned between the pool and areas of access.
Take a look at the variety of pool deck materials, along with their pros and cons.
Tips For Using An Existing Concrete Slab For And Above Ground Pool
Using an existing slab to put an above ground pool on seems like a better and easier idea than installing it on the earth, but its oftentimes very problematic. This is all because most existing slabs are off-level.
The following tips will mainly help you with info on installing on an off-level concrete slab.
1 MOST IMPORTANT Make sure the slab is level
I cannot stress to you how important this is. Every year, tons of people decide to put an above ground on their existing concrete patio and just think that it will be level enough.
They will go through the trouble of installing the pool and then at some point they realize that the pool will be too off-level. Some will install the pool completely and not know until they fill the pool up with water.
They will instantly notice how off-level the pool is by the water. Water has to be level because of its weight, its liquid form, and the gravitational pull of the planet. Duh! This is the main reason a swimming pool has to be level. Because its full of level water.
It sucks when people have to take their pool back down because they didnt check beforehand on the level of the concrete pad. So do that first.
To check the level of the slab, see above for directions.
If by some great luck, you find that your slab is level, then great. Read no further.
2 Make sure the concrete pad is big enough
Dont assume its big enough. Take out a tape measure and make sure it will fit the size pool you are wanting.
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Luxury Swimming Pool Designs
Welcome to our gallery of luxury swimming pool designs. An in-ground pool is a great way to add value to your home by enhancing your landscape with a water feature. It also provides you with a pleasant and cool outdoor space for entertaining, lounging and even for getting some exercise.
In the image shown above this beautiful above-ground rectangular pool gives the impression of an infinity design. The white wrought iron fence provides security without taking away from the stunning ocean view. Large blue and light blue tiles compliment the color of the ocean, and palm trees complete the tropical setting.
Installing An Above Ground Pool On A Concrete Slab
Commonly, above-ground swimming pools are installed on the earth or ground. Some will put them on concrete though and thats pretty nice. Well, its nice when its done right at least.
Installing an above ground swimming pool on concrete is nice as long as the slab is level. Most backyard patio concrete slabs are poured off- level to allow rainwater to drain off of them. This makes it difficult to install an above ground pool on them.
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Not All Existing Concrete Slabs Are Off Level But Most Of Them Are
You cant assume either that your existing slab is off level. Some are perfectly level. Last year, I build a pool on the basketball court that someone had in their backyard. It was perfectly level.
You cant accurately check to see if your slab is level by just laying down a four-foot level. Even the four-foot level will tell you its off, but many people dont really know how to read a level. The best way then is to either use a builders level that you can rent or borrow, or use a line level with a string.
Most dont have access to a builders or laser level, and renting one just to use for two minutes doesnt make much sense. So, using a two-dollar line level and some string is a good bet.
Use stakes in the ground beyond the slab or whatever you need to be able to have a nylon string running tightly across the slab and a few inches above it. Once the string is running across the concrete, attach the line-level onto the line in the middle of the run. The line-level is designed to attach to the string, so its easy to do.
Using the line level, adjust the level of the string by raising or lowering it at one or both ends. Do this until the line level shows the string to be perfectly level. Once you know that the string running across the slab is perfectly level, use a tape measure and measure down from the string, to the concrete on both ends of the slab. The difference in numbers is how off-level the slab is.
Installing An Oval Pool On Concrete Is Very Difficult
Almost all oval pool designs require some of their parts to be below the bottom track. This means they cannot be installed on just one plane or level. So, even if an existing concrete slab is perfectly level, an oval cannot be built on it.
In the case of an oval pool, I only recommend building a sandbox on the concrete slab for a proper installation. Making cuts in the concrete so an oval can rest on it level is too much work and too problematic. I did this once years ago and swore I would never do it again. And I havent.
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