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LenaWriter [7]
3 years ago
5

Which situation is best represented by the following equation?

Mathematics
1 answer:
Maurinko [17]3 years ago
4 0

Answer:

The correct answers is B.

Step-by-step explanation:

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Solve the inequality and write down the solution in interval notation x(x-3)(x+1)<0
Ratling [72]
Since it's so nicely grouped, we can work with it! For the equation to equal 0, x=0, 3, or -1 (since x-3 and x+1 equal 0 when plugged in with 3 and -1 respectively). All we have to do is plug in numbers before, between, and after these numbers and apply it to the rest of them. Since -1 is the smallest number of the group, we can plug in a number below that (for this example, -5) and plug it in to get -8*-5*-4= something negative since it contains an odd number of negative numbers. Therefore, anything less than 1 is negative. For between -1 and 0, we get x=-0.5 equals -0.5*-3.5*0.5=something positive (since it has an even amount of negative numbers), proving that everything between -1 and 0 here is positive.  For something between 0 and 3, we can plug 1 in to get 1*-2*2= something negative. Do you see a pattern here? It's negative, then positive, etc.. Therefore, if the number is greater than 3 it is positive.  Reviewing a bit, we can see that (-inf, -1) is negative as well as (0,3), making the interval notation (-inf, -1) U (0, 3) since when you plug -1, 0, and 3 in it is 0, not less than 0!
8 0
3 years ago
If 2x• 3x +(2•3 )x +6x= 648, find x.
klasskru [66]

Answer:

x = -1 ± √109

Step-by-step explanation:

2x • 3x + (2 • 3)x + 6x = 648

According to PEMDAS (parentheses/exponents | multiplication/division | addition/subtraction), we should solve the parentheses first.

(2 • 3) = 6

Now we have:

2x • 3x + (6)x + 6x = 648

Now let's multiply.

2x • 3x = 6x²

6 • x = 6x

Now we have.

6x² + 6x + 6x = 648

Combine like terms.

6x² + 12x = 648

Let's factor out a 6.

6(x² + 2x) = 648

Divide both sides by 6.

x² + 2x = 108

Let's use completing the square.

Our equation is in a² + bx = c form.

Divide b by 2.

2/2 = 1

Then square it.

1² = 1

Add 1 to both sides.

x² + 2x + 1 = 108 + 1

Simplify.

x² + 2x + 1 = 109

Now we want to factor the left side. A shortcut is just to use b/2.

(x + 1)² = 109

Take the square root of both sides.

x + 1 = ±√109

The square root is as simplified as possible.

Subtract 1 from both sides.

x = -1 ± √109

Hope this helps!

4 0
3 years ago
Read 2 more answers
Find the volume of the cylinder
WARRIOR [948]

Answer:

C. 1,620 in^3

Step-by-step explanation:

Thank you!

6 0
3 years ago
A laboratory scale is known to have a standard deviation of Ï = 0.001 gram in repeated weighings. Scale readings in repeated wei
erica [24]

Answer:

the confidence interval for the true weight of the specimen is;

4.1593 ≤ μ ≤ 4.1611

Step-by-step explanation:

We are given;

Standard deviation; σ = 0.001

Sample size; n = 8

Average weight; x¯ = 4.1602

We are given a 99% confidence interval and the z-value at this interval is 2.576

Formula for confidence interval is;

CI = x¯ ± (zσ/√n)

Plugging in the relevant values, we have;

CI = 4.1602 ± (2.576 × 0.001/√8)

CI = 4.1602 ± 0.000911

CI = (4.1602 - 0.000911), (4.1602 + 0.000911)

CI ≈ (4.1593, 4.1611)

Thus, the confidence interval for the true weight will be expressed as;

4.1593 ≤ μ ≤ 4.1611

Where μ represents the true weight

4 0
3 years ago
Please help
MArishka [77]
2^4x-2^3x-3

2^3=2x2x2
Which equals 8
3 0
3 years ago
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