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3 years ago

The number sentence 4×7= (4×3) + (4×4) is an example of what property?

Mathematics

1 answer:

velikii [3]3 years ago

7 0

Associative Distributive Transitive Commutative

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Factorise 2x^2 - 3x -2 < 0

Galina-37 [17]

Step 1: Factor $2 x^{2} - 3x -2$
1. Multiply 2 by -2, which is -4.
2. Ask: Which two numbers add up to -3 and multiply to -4?
3. Answer: 1 and -4
4. Rewrite $-3x$ as the sum of $x$ and $-4x$

$2 x^{2} +x-4x-2\ \textless \ 0$

Step 2: Factor out common terms in the first two terms, then in the last two terms.

 $x(2x+1)-2(2x+1)\ \textless \ 0$

Step 3: Factor out the common term $2x+1$

$(2x+1)(x-2)\ \textless \ 0$

Step 4: Solve for $x$

1. Ask: When will $(2x+1)(x-2)$ equal zero?
2. Answer: When $2x + 1 = 0$ or $x-2=0$
3. Solve each of the 2 equations above:

 $x=- \frac{1}{2} ,2$

Step 5: From the values of $x$ above, we have these 3 intervals to test.
x = < -1/2
-1/2 < x < 2
x > 2

Step 6: Pick a test point for each interval

For the interval $x\ \textless \ - \frac{1}{2} 
$
Lets pick $x=-1.$ Then, $2(-1) ^{2} -3 * -1 -2 \ \textless \ 0$
After simplifying, we get $3\ \textless \ 0$ , Which is false.
Drop this interval.

For this interval $- \frac{1}{2} \ \textless \ x\ \textless \ 2$
Lets pick $x=0$ . Then, $2* 0^{2} - 3 * 0-2\ \textless \ 0$ . After simplifying, we get $-2\ \textless \ 0,$ which is true. Keep this interval.

For the interval $x\ \textgreater \ 2$

Lets pick $x = 3.$ Then, $2 * 3 ^{2} -3*3-2\ \textless \ 0.$ After simplifying, we get $7\ \textless \ 0$ , Which is false. Drop this interval.

.Step 7: Therefore,
$- \frac{1}{2} \ \textless \ x\ \textless \ 2$

Done! :)

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3 years ago

Chase works as a welder making $21.50 per hour. He works 40 hours.

m_a_m_a [10]

What is his net weekly pay?

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2 years ago

Read 2 more answers

If two or more polygons are congruent, which statement must be true about the polygons? Read all of the choices before deciding.

Lisa [10]

Pairs of corresponding angles have the same measure.

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3 years ago

2|x+1/4|=6 Can someone help me please, I'm so confused

aksik [14]

First divide by 2
|x+1/4|=3
Then you pick the possible answers
|x+1/4|=3
|x+1/4|=-3
2 3/4 or -3 1/4

5 0

3 years ago

The vertex form of the equation of a parabola is y=2(x+4)^2-7. What is the standard form of the equation.

Elan Coil [88]

Answer:

Step-by-step explanation:

To obtain the standard form of the equation of the parabola y=2(x+4)^2-7, first perform the indicated operations:

y = 2[x^2 + 8x + 16 - 7], or

y = 2[x^2 + 8x + 9],

or y = 2x^2 + 16x + 18

None of the given possible answers match. The fourth one, D, is closest to the above result, differing only in the constant term (25 versus 18).

6 0

3 years ago