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Licemer1 [7]
3 years ago
8

Bobby's uncle gave him 300 baseball cards. Each week, Bobby purchases 40 baseball cards to add to his collection. Which inequali

ty can be used to find w, the number of weeks after starting his collection when Bobby will have more than 700 baseball cards in his collection?
Mathematics
2 answers:
QveST [7]3 years ago
8 0

Answer:

300+40w>700

Step-by-step explanation:

Bobby's uncle gave him 300 baseball cards. Each week, Bobby purchases 40 baseball cards to add to his collection.

Let the number of weeks he collects cards be w.

The inequality to get the number of weeks after starting his collection when Bobby will have more than 700 baseball cards in his collection is given by:

300+40w>700

If you want to find w;

40w>700-300

=> 40w>400

w > 10

Helga [31]3 years ago
4 0

Answer:

He already has 300 cards.

Take 700 and subtract that by 300

Then divide that by 40

Leaves you at

10 weeks

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Felix wrote several equations and determined that only one of the equations has no solution. Which of these equations has no sol
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If one table and two lamps cost $88, and two
Paul [167]

Answer:

One lamp is equal to 23 dollars

One table is equal to 42 dollars.

Step-by-step explanation:

We can solve this by first organizing what we have.

1 table (t) + 2 lamps (l) = 88.

2 tables (t) + 3 lamps (l) = 153.

_____________

===============

1t + 2l = 88

2t + 3l = 153

===============

-------------------------

If we multiply both sides by 2 on the first equation of

1t + 2l = 88

we could get

2t + 4l = 176.

If that is true, we can subtract the second equation of

2t + 3l = 153 from the new equation to get the price of a lamp.

    2t + 4l = 176

-    2t + 3l = 153

____________

= 0t + l = 23

One lamp is equal to 23.

We can check this by plugging it into an equation.

1 + 2(23) = 88

1t + 46 = 88

1t + 46 - 46 = 88 - 46

1t = 42

If one table equals 42, we can put this back into the second equation to check.

2 (42) + 3 (23) = 153

84 + 69 = 153

That is correct.

Another way to solve is to put this like a system of equations in a graph, by replacing "t" by "x" for example, and "l" by y.

Then you could put it into a graphing calculator and solve by looking for the place where the two lines converge or meet.

Since we put "x" for "t", that means that whatever the x-value is on the solution point, that is the cost of a table, and the y-value is the cost of the lamps.

Another way to solve, is to find the unit rate first by subtracting the first equation from the second equation.

    2t + 3l = 153

 -  1t + 2l = 88

____________

= t + l = 65

If t + l = 65, we can rearrange that equation to be something like t = 65 - l.

That means "t" is equal to 65 bucks minus a lamp.

We put this back into the first equation of

1t + 2l = 88

and replace "t" with the previous expression.

1(65 - l) + 2l = 88

Simplify/distributive property

65 - l + 2l = 88

65 - 65 - l + 2l = 88 - 65

-l + 2l = 23

l = 23

One lamp is equal to 23 bucks.

Confirmed :)

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Answer:

y=1/3x-2

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m=(y2-y1)/(x2-x1)

m=(0-(-2))/(6-0)

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What mathematical pattern can be seen in a perfect square trinomial and how is the
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Whenever you multiply a binomial by itself twice, the resulting trinomial is called a perfect square trinomial

For example, (x + 1) × (x + 1) = x2<span> + x + x + 1 = x</span>2<span> + 2x + 1 and x</span>2<span> + 2x + 1 is a perfect square trinomial</span>

Another example is (x − 5) × (x − 5)

(x − 5) × (x − 5) = x2<span> + -5x + -5x + 25 = x</span>2<span> + -10x + 25 and x</span>2<span> + -10x + 25 is a perfect square trinomial </span>

Now, we are ready to start factoring perfect square trinomials

The model to remember when factoring perfect square trinomials is the following:

a2<span> + 2ab + b</span>2<span> = (a + b)</span>2<span> and (a + b)</span>2<span> is the factorization form for a</span>2<span> + 2ab + b</span>2 

Notice that all you have to do is to use the base of the first term and the last term

In the model just described,

the first term is a2<span> and the base is a</span>

the last term is b2<span> and the base is b</span>

Put the bases inside parentheses with a plus between them    (a + b)

Raise everything to the second power   (a + b)2<span> and you are done </span>

<span>Notice that I put a plus between a and b. </span>You will put a minus if the second term is negative!

a2<span> + -2ab + b</span>2<span> = (a − b)</span>2

Remember that a2<span> − 2ab + b</span>2<span> = a</span>2<span> + -2ab + b</span>2<span> because a minus is the same thing as adding the negative ( − = + -) So, a</span>2<span> − 2ab + b</span>2<span> is also equal to (a − b)</span>2

Example #1:

Factor x2<span> + 2x + 1</span>

Notice that x2<span> + 2x + 1 = x</span>2<span> + 2x + 1</span>2

Using x2<span> + 2x + 1</span>2, we see that... the first term is x2<span> and the base is x</span>

the last term is 12<span> and the base is 1</span>

Put the bases inside parentheses with a plus between them    (x + 1)

Raise everything to the second power   (x + 1)2<span> and you are done </span>

Example #2:

Factor x2<span> + 24x + 144</span>

But wait before we continue, we need to establish something important when factoring perfect square trinomials.

<span>. How do we know when a trinomial is a perfect square trinomial? </span>

This is important to check this because if it is not, we cannot use the model described above

Think of checking this as part of the process when factoring perfect square trinomials

We will use example #2 to show you how to check this

Start the same way you started example #1:

Notice that x2<span> + 24x + 144 = x</span>2<span> + 24x + 12</span>2

Using x2<span> + 24x + 12</span>2, we see that...

the first term is x2<span> and the base is x</span>

the last term is 122<span> and the base is 12</span>

Now, this is how you check if x2<span> + 24x + 12</span>2<span> is a perfect square</span>

If 2 times (base of first term) times (base of last term) = second term, the trinomial is a perfect square

If the second term is negative, check using the following instead

-2 times (base of first term) times (base of last term) = second term

Since the second term is 24x and 2 × x × 12 = 24x, x2<span> + 24x + 12</span>2<span> is perfect and we factor like this</span>

Put the bases inside parentheses with a plus between them    (x + 12)

Raise everything to the second power   (x + 12)2<span> and you are done </span>

Example #3:

Factor p2<span> + -18p + 81</span>

Notice that p2<span> + -18p + 81 = p</span>2<span> + -18p + 9</span>2

Using p2<span> + -18p + 9</span>2, we see that...

the first term is p2<span> and the base is p</span>

the last term is 92<span> and the base is 9</span>

Since the second term is -18p and -2 × p × 9 = -18p, p2<span> + -18p + 9</span>2<span> is a perfect square and we factor like this</span>

Put the bases inside parentheses with a minus between them    (p − 9)

Raise everything to the second power   (p − 9)2<span> and you are done </span>

Example #4:

Factor 4y2<span> + 48y + 144</span>

Notice that 4y2<span> + 48y + 144 = (2y)</span>2<span> + 48y + 12</span>2

(2y)2<span> + 48y + 12</span>2, we see that...

the first term is (2y)2<span> and the base is 2y</span>

the last term is 122<span> and the base is 12</span>

Since the second term is 48y and 2 × 2y × 12 = 48y, (2y)2<span> + 48p + 12</span>2<span> is a perfect square and we factor like this</span>

Put the bases inside parentheses with a plus between them    (2y + 12)

Raise everything to the second power   (2y + 12)2<span> and you are done </span>
7 0
3 years ago
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