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ExtremeBDS [4]
3 years ago
12

Solve |2x - 2| < 8

Mathematics
1 answer:
Alex777 [14]3 years ago
4 0

Answer:

C

Step-by-step explanation:

|2x - 2| < 8

it implies that

2x - 2 < 8

2x -2 + 2 < 8 + 2

2x < 10

x < 5

or

-(2x - 2) < 8

-2x + 2 < 8

-2x + 2 - 2 < 8 - 2

- 2x < 6

x > -3 ( the sense of the inequality reverse because I divided by minus)

The solution can be combine to

-3<x<5

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5 x 10^5 is how many times as large as 1 x 10^5?
Oxana [17]

Answer:

  5 times as large

Step-by-step explanation:

You can think of "10^5" as "green marbles" if you like. Then your question is ...

  5 green marbles is how many times as large as 1 green marble.

Hopefully, the answer is all too clear: it is 5 times as large.

_____

In math terms, when you want to know how many times as large y is as x, the answer is found by dividing y by x:

  y/x . . . . . tells you how many times as large as x is y.

Here, that looks like ...

  \dfrac{5\times 10^5}{1\times 10^5}\\\\=\dfrac{5}{1} \qquad\text{the factors of $10^5$ cancel}\\\\=5

4 0
3 years ago
Read 2 more answers
Find the nature of the root
GREYUIT [131]

Answer:

1) Real and same.

2) Real and distinct

3) Real and distinct

4) Real and distinct

5) Real and distinct

6) Real and distinct

7) Real and distinct

8) Real and distinct

Step-by-step explanation:

If a quadratic equation is in the form of ax² + bx + c = 0, then Discriminant of the equation D = b² - 4ac, which governs the nature of roots the equation has.

If D > 0, then there will be two different real roots.

If D = 0, then two same and real roots.

If D < 0, then two distinct but imaginary roots.

Now, 1) x² + 6x + 9 = 0 has D = 6² - 4 × 9 × 1 = 0. So, there will be two same and real roots.

2) 5x² - x = 4x² + 2

⇒ x² - x - 2 = 0

It has D = (-1)² - 4 × 1 × (-2) = 9. Therefore, the roots will be two distinct and real.

3) \frac{2}{x} + \frac{3}{x} = x - 4

⇒ 5 = x² - 4x

⇒ x² - 4x - 5 = 0.

So, D = (-4)² - 4 × (1) × (- 5) = 36. So, the equation has two real and distinct rools.

4) x(x - 5) = 4(5 - x)

⇒ x² - x - 20 = 0

Hence, D = (-1)² - 4 × 1 × (-20) = 81

So, the roots will be real and distinct.

5) x² + 7x + 1 = 0 has D = 7² - 4 × 1 × 1 = 45

So, the roots will be real and distinct.

6) 2x² + 9x + 3 = 0, has D = 9² - 4 × 2 × 3 = 57.

Hence, the roots will be real and distinct.

7) 5x² - 6 = 13x

⇒ 5x² - 13x - 6 = 0

So, D = (-13)² - 4 × 5 × (-6) = 289

So, the roots will be real and distinct.

8) x² - x = 3(x + 7)

⇒ x² - 4x - 21 = 0

It has D = (-4)² - 4 × 1 × (-21) = 100

So, the roots will be real and distinct. (Answer)

6 0
3 years ago
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Evgesh-ka [11]
The answers r online for that
4 0
2 years ago
A hockey goalie got shot on 18 times . She saved 10 of the shots . Which ratio represents the amount of shots that went in to th
vredina [299]
<h3>Answer is   4:5</h3>

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

Explanation:

She saved 10 shots out of 18 total, so that means 18-10 = 8 shots went in.

That forms the ratio 8:10 where we list the amount of shots that went in, followed by a colon, then the amount of shots that were saved. The order is important. From here, we divide both parts of the ratio by 2. The ratio 8:10 fully reduces to 4:5

Effectively, this means that for every 4 shots that went in, there were 5 shots that were blocked.

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3 years ago
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Raj used 4 3/4 cups of sugar for each batch of muffins. He made 3 1/2 batches. Raj used 16 5/8 cups of sugar altogether.
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Answer:

It is true!

Step-by-step explanation:

8 0
3 years ago
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