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Olin [163]
3 years ago
5

Evaluate the expression if a = 9 and b = 2. 5(a 3b) 20 51 70 75

Mathematics
1 answer:
devlian [24]3 years ago
5 0
5(a + 3b) = 5(9 + 3(2)) = 5(9 + 6) = 5(15) = 75
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If georgina travels 355 km in 7 hours how far will she travel in 8.5 hours at the same rate
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She'll have traveled approximately 431.07 km in 8.5 hours, also, 267.85448 miles per hour.
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Find the product.
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3 years ago
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Exercise 3.5. For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ [x^2 − 25}.
masya89 [10]

a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

b. The inverse image of g(x) is g^{-1}(x) = e^{x}

c. The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

<h3 /><h3>The domain of T</h3>

Since T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

⇒ x ≥ ±5

⇒ -5 ≤ x ≤ 5.

<h3>Inverse image of f(x)</h3>

The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

f : R → R defined by f(x) = 3x³

Let f(x) = y.

So, y = 3x³

Dividing through by 3, we have

y/3 = x³

Taking cube root of both sides, we have

x = ∛(y/3)

Replacing y with x we have

y = ∛(x/3)

Replacing y with f⁻¹(x), we have

So,  the inverse image of f(x) is f⁻¹(x) = ∛(x/3)

<h3>Inverse image of g(x)</h3>

The inverse image of g(x) is g^{-1}(x) = e^{x}

g : R+ → R defined by g(x) = ln(x).

Let g(x) = y

y =  ln(x)

Taking exponents of both sides, we have

e^{y} = e^{lnx} \\e^{y} = x

Replacing x with y, we have

y = e^{x}

Replacing y with g⁻¹(x), we have

So, the inverse image of g(x) is g^{-1}(x) = e^{x}

<h3>Inverse image of h(x)</h3>

The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

h : R → R defined by h(x) = x − 9

Let y = h(x)

y = x - 9

Adding 9 to both sides, we have

y + 9 = x

Replacing x with y, we have

x + 9 = y

Replacing y with h⁻¹(x), we have

So, the inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

Learn more about inverse image of a function here:

brainly.com/question/9028678

5 0
2 years ago
Laura spent 78.5% of her paycheck on her mortgage payment. If her paycheck was $1562 how much was her mortgage?
torisob [31]

Answer:

$337.12

Step-by-step explanation:

Multiply $1562 by 78.5% (or 0.785) =1230.88

Then subtract the percent of her paycheck spent (1230.88) from the total of her paycheck(1562) to find out how much is missing(the mortgage payment)

1562-1230.88=337.12

5 0
2 years ago
(5m 3 + 3mn 2) + (-7m 2n + mn 2 - n 3) - (mn 2 + 2m 3)
lara [203]

Answer:

3m^{3}+3mn^{2}  -n^{3}- 14mn

Step-by-step explanation:

I assumed that the numbers after the spaces were powers. This question was rather unclear.

8 0
3 years ago
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