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Nady [450]
2 years ago
11

Identify The domain of the rational function, g(x)= 1/x+3

Mathematics
1 answer:
8_murik_8 [283]2 years ago
4 0

Answer:

The domain is (-∞ , -3) ∪ (-3, ∞) ⇒ D

Step-by-step explanation:

<em>The domain of the rational fraction is t</em><em>he values of x which make the fraction defined</em><em>. That means </em><em>the domain does not contain the values of x which make the denominator equal to 0</em><em>.</em>

∵ g(x) = \frac{1}{x+3}

∴ The denominator = x + 3

→ Equate the denominator by 0

∵ x + 3 = 0

→ Subtract 3 from both sides

∴ x + 3 - 3 = 0 - 3

∴ x = -3

→ That means the domain can not have -3 because it makes the denominator

   equal to 0

∴ The domain is all values of real numbers except x = -3

∴ The domain = {x : x ∈ R, x ≠ -3}

∴ The domain = (-∞ , -3) ∪ (-3, ∞)

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Taryn is shopping for a Christmas tree. At Home Depot the one she likes is $149.00 and she has a 15% off coupon. At Lowe's the o
Vitek1552 [10]

Answer:

Step-by-step explanation:

At home depot

Price of Christmas tree = $149.00

Discount = 15%

Amount discounted = 15% of $149

Amount discounted = 15/100 * $149

Amount discounted = 15 * 1.49

Amount discounted = $22.35

Amount she paid = $149-$22.35

Amount she paid = $126.65

At Lowe's:

Price of Christmas tree = $175.00

Discount = 260%

Amount discounted = 20% of $175

Amount discounted = 20/100 * $175

Amount discounted = 0.2 * 175

Amount discounted = $35

Amount she paid = $175-$35

Amount she paid at Lowe's = $140

<u><em>From the prices above, it can be seen that Home Depot has a better deal since the price after removing discount is lower than that of Lowe's.</em></u>

<u><em></em></u>

<u><em>Amount she will save will be $140 - $126.65 = $13.35</em></u>

6 0
3 years ago
sam's music teacher told him to practice his trombone for X amount of hours. he spent X amount of hours practicing did he practi
Crank
Yes if he practices X amount of hours and is told to practice X amount of hours than he practiced long enough
4 0
3 years ago
Explain in detail with at least two sentences how to represent the product of A and B geometrically given that A=15+56i and B =
Nookie1986 [14]

Basically each part of the first complex number gets multiplied by each part of the second complex number. You are multiplying 2 binomials.

(15 + 56i(7 + 4i)

= 105 + 60i + 392i + 224i^2

= 105 + 452i - 224 ( because i^2 = -1)

= - 119 + 452i


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3 years ago
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Marta_Voda [28]

Answer:

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3 years ago
Factor the trinomial f(x) = 2x² + 5x – 12 ?
gavmur [86]

Answer:

(x + 4)(2x - 3)

Step-by-step explanation:

Given

f(x) = 2x² + 5x - 12

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × -12 = - 24 and sum = + 5

The factors are + 8 and - 3

Use these factors to split the x- term

2x² + 8x - 3x - 12 ( factor the first/second and third/fourth terms )

2x(x + 4) - 3(x + 4) ← factor out (x + 4) from each term

(x + 4)(2x - 3)

Thus

f(x) = 2x² + 5x - 12 = (x + 4)(2x - 3) ← in factored form

5 0
3 years ago
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