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3 years ago

Use a geometric model to factor x + x - 2 by following these

Mathematics

2 answers:

Dima020 [189]3 years ago

8 0

Answer:

Mark Brainliest

Step-by-step explanation:

Factoring Trinomials using Algebra Tiles

Algebra tiles can be used as a model for factoring trinomials. When you multiply two binomials, your result is a trinomial. We used area models to multiply binomials. Therefore, to be able to factor a trinomial using algebra tiles, you must first rearrange the tiles into the shape of a rectangle.

1. Factor the expression x2 2x 1 .

a. This trinomial is made up of one x2 tile, two x tiles, and one unit tile.

b. Arrange these tiles to form a rectangle.

c. Use algebra tiles to identify the width and length of the rectangle.

d. The width has one x tile and one unit tile. The length has one x tile and one unit tile. Therefore, the factors of x2 2x 1 are x 1 and x 1. This means that:

x2 2x1x12

2. Factor the expression x2 8x 15.

a. This trinomial is made up of one x2 tile, eight x tiles, and fifteen unit tiles.

b. Arrange these tiles to form a rectangle. The key is to correctly arrange the unit tiles to match the number of x tiles.

c. Use algebra tiles to identify the width and length of the rectangle.

d. Write an equation to show the meaning of the model for this problem.

3. Special care must be taken when the c value in ax2  bx  c is negative. Let’s begin by factoring x2  x 6.

a. This trinomial is made up of one x2 tile, one x tile, and six negative unit tiles. It may be helpful to begin with the x2 tile and six negative unit tiles. Arrange these tiles to form a rectangle. (Note: There may be multiple ways to arrange the unit tiles so some trial and error may be necessary).

b. Since there are negative unit tiles, this means we will have to introduce some negative x tiles to create the rectangle. Just keep in mind – for every negative x tile you introduce, you must introduce a positive x tile. Otherwise, you are changing the value of the expression.

c. Identify the width and length of the rectangle and then write an equation to represent the model.

Practice: Factor each expression using algebra tiles.

1. x2 5x6 2. x2 5x4 3. x2 4x12

4. x2 7x8 5. 2x2 7x6 6. 2x2 5x12

Nikolay [14]3 years ago

6 0

Answer:

This should help

Step-by-step explanation:

Download pdf

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Solve for x: 1 1/5 x -2 1/3 < 1/7 x+ 1 1/2

Firlakuza [10]

Solving inequalities is similar to solving a regular equation. The only thing you need to worry about with inequalities is that when you are dividing or multiplying by a negative number, you must flip the inequality sign. You won't have to worry about that here if the coefficient in front of x is positive when you divide!

Also remember:
- To add/subtract fractions, you have to turn all mixed numbers into improper fractions (if needed), find a common denominator on both fractions (if needed), add/subtract the numerators, put the sum/difference over the common denominator, and simplify if needed.

- To multiply fractions, multiply the numerators and multiply the denominators. Put the product of the numerators over the product of the denominators.

- To divide fractions, remember that dividing by a fraction is the same as multiplying by the inverse of that fraction (aka fraction flipped).

- To turn mixed numbers into improper fractions, multiply the whole number by the denominator of the fraction. Add the numerator of the fraction to the product you get, and put that final sum over the original denominator.

Back to the problem:
You are told that $1 \frac{1}{5} x - 2 \frac{1}{3} \ \textless \ \frac{1}{7} x + 1 \frac{1}{2}$ and you have to solve for x.

1) Using the info for converting mixed numbers to improper fractions from above, you know that $1 \frac{1}{2} = \frac{3}{2}$ and $2 \frac{1}{3} = \frac{7}{3}$ and $1 \frac{1}{5} x = \frac{6}{5} x$ . Now add/subtract using the info above, isolating the variable x by adding $2 \frac{1}{3}$ to both sides and subtracting $\frac{1}{7} x$ from both sides.
$1 \frac{1}{5} x - 2 \frac{1}{3} \ \textless \ \frac{1}{7} x + 1 \frac{1}{2}\\
\frac{6}{5} x - \frac{7}{3} \ \textless \ \frac{1}{7} x + \frac{3}{2}\\
(\frac{6}{5} x - \frac{1}{7} x) \ \textless \ (\frac{3}{2} + \frac{7}{3})\\
(\frac{42}{35} x - \frac{5}{35} x) \ \textless \ (\frac{9}{6} + \frac{14}{6})\\
 \frac{37}{35} x \ \textless \ \frac{23}{6}$

2) Divide both sides by $\frac{37}{35}$ to get the inequality for x. Remember the info for dividing from above:
$\frac{37}{35} x \ \textless \ \frac{23}{6}\\
x \ \textless \ \frac{23}{6} \div \frac{37}{35} \\
x \ \textless \ \frac{23}{6} \times \frac{35}{37} \\
x \ \textless \ \frac{805}{222}$

Your final answer is x < $\frac{805}{222}$ or x < $3 \frac{139}{222}$ .

3 0

3 years ago

Please give me the correct answer!!!

Neko [114]

Answer:

Step-by-step explanation:

this one is tricky so b/c the lines are at 90 degees we know that the arcs are similar so set up the parts of the arcs equal to 360 degrees

360 = 130 + 130 + x + x

see each part of the circle ?

then use your mad algebra skilz

100 = 2x

50 = x

:) nice.. when I do the math , it seems easy , huh :DDD

7 0

3 years ago

Plz help... 6b - 49 =2(b - 3)

wel

You always start by simplifying.
6b-49=2(b-3) becomes 6b-49=2b-6
From there you can group the b's together by subtracting 2b from both sides, leaving you with 4b-49=-6
Now you can get the b's alone by adding 49 (to cancel out -49) to both sides, giving you 4b=43, You're still trying to get b by itself, so what you'll do is divide both sides by 4, giving you b=10.75

5 0

3 years ago

Read 2 more answers

Car A a can go 332 miles on 12.5 gallons of gasoline. Car B can go 304 miles on 10.5 gallons of gasoline. which car has a better

lidiya [134]

Answer:

B) car B

explanation :

I know that Car A can go at least 28 more miles than Car B. If you round 10.5 to the nearest ones place it would be 11; and if you round 12.5 to the nearest ones place it would be 13 so 13 - 11 = 2

I hope I can help you have a great day :)

4 0

4 years ago

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If a loan of 1,500 at 4% is paid off in 90 days what is the interest

slega [8]

Answer:

Compound interest =$14.58

Simple Interest=$14.79

Step-by-step explanation:

Let's assume the interest rate charged on the loan was simple in nature.

-Simple interest is calculated using the formula:

$I=PRT,\\\\=1500\times 0.04\times \frac{90}{365}\\\\=14.79$

Hence, the simple interest on the loan was $14.79

#If the interest is compound in nature with just one compounding per year:

$A=P(1+i)^n\\\\I=A-P\\\\I=1500(1.04)^{90/365}-1500\\\\=14.58$

Hence, the compound interest charged on the loan is $14.58

3 0

3 years ago