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1 year ago

Please help Linear equations

Mathematics

1 answer:

svlad2 [7]1 year ago

8 0

Answer:

2 and 4

Step-by-step explanation:

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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! :)

4 0

3 years ago

Solve the following equation for A. Be sure to take into account whether a letter is

Sati [7]

Answer:

4/a

Step-by-step explanation:

8 0

2 years ago

The range of 16,23,55,64,49

miskamm [114]

Answer: 48

Step-by-step explanation: To find the range of the data set shown here, remember that the range is the difference between the greatest number in the data set and the least number in the data set.

Greatest number → 64

Least number → 16

Now, we need to subtract 16 from 64.

64 - 16 = 48

Therefore, the range of the data set is 48.

7 0

3 years ago

An electric can opener is worth 36 dollars when it is new. After each year, it is worth half what it was the previous year. What

Likurg_2 [28]

So the equation is f(x)=36*(.5)^8, since your principal worth is 36 and it depreciates by 1/2 each year, which is 14 cents.

4 0

2 years ago

Anyone please help me anyone

NARA [144]

Answer:

The third answer: x+1

Step-by-step explanation:

Remember when writing roots, the signs are backwards. This is because you start with (x-__) and fill in the root.

So for x = -1, it'll be written as (x+1) [aka (x- -1)]

For x = -3, it'll be written as (x+3)

For x = 5, it'll be written as (x-5)

The only answer that is one of these is the the third answer

7 0

1 year ago