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muminat
3 years ago
13

Which number sentences show how to solve the problem? The bowling club donated 4 crates of orange juice for the neighborhood pic

nic. The soccer club donated 12 crates of mixed juices for the picnic. Each crate holds 32 juice boxes. How many juice boxes were donated altogether for the picnic? Choose all answers that are correct. 4 + 12 = 16 and 16 × 21 = 336 4 × 32 = 128 and 128 × 12 = 336 4 + 12 = 16 and 16 × 32 = 512 4 × 32 = 128, 12 × 32 = 384, and 128 + 384 = 512
Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
4 0

A and C are correct, you have to multiply 32 by 4 and by 12, then add the answers together to find how many juice boxes total.

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vovangra [49]

Answer:

(x - 8)(2x + 3)

Step-by-step explanation:

To factor a polynomial of the form

ax² + bx + c,

follow these steps:

1) Multiply ac together.

2) Find 2 factors of ac that add to b. Call these factors p and q.

3) Break up the middle term of the polynomial into px + qx.

4) Factor by grouping.

Now let's follow the steps above with your problem.

You are given the polynomial

2x² - 13x - 24,

so a = 2, b = -13, and c = -24

1) Find ac.ac is the product 2(-24) = -48

2) Now we need to find 2 factors of -48 that add to b, -13.

I know that 48 = 3 × 16, so if we use -16 and 3 for the two numbers, we have

-16 + 3 = -13

and -16 × 3 = -48.

3) Now we break up the middle term of the polynomial, -13x, into -16x + 3x.

The polynomial is now

2x² - 16x + 3x - 24

4) We factor the polynomial by grouping. To factor by grouping, you factor a common factor out of the first 2 terms and factor out a common factor out of the last two terms.

2x² - 16x + 3x - 24 =

= 2x(x - 8) + 3(x - 8)

We now see the common factor of x - 8, so we factor that out.

= (x - 8)(2x + 3)

Answer: (x - 8)(2x + 3)

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2 years ago
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