MATHEMATICS COLLEGE

brainiest and 50 points. Diana usually drives at an average rate of 30 mph. Today, she is going to drive 12 miles to her friend Tony's house. How many minutes will it take her to get there?

Answers

Answer 1

Answer:

Answer:

24 minutes

Step-by-step explanation:

Distance = speed x time

12 mi = 30 mi/h x time

time = 12/30 = 4/10 hours

since 1 hour has 60 minutes

4/10 hours x 60 = 24 minutes

Answer 2

Answer:

Answer:

It will take her 24 minutes to get there.

Hope This Helps! :) Plz Give Brainliest!

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Suppose that the functions g and h are defined for all real numbers x as follows. gx = x − 3x
hx = 5x + 2
Write the expressions for (g - h)(x) and (g * h)(x) and evaluate (g + h)(−2).

Answers

Answer:

Step-by-step explanation:

Given the functions g(x) = x − 3x and h(x) = 5x + 2, we are to calculatae for the expression;

a) (g - h)(x) an (g * h)(x)

(g - h)(x) = g(x) - h(x)

(g - h)(x) = x − 3x -(5x+2)

(g-h)(x) = x-3x-5x-2

(g-h)(x) =-7x-2

b) (g * h)(x) = g(x) * h(x)

(g * h)(x) = (x − 3x)(5x+2)

(g * h)(x) = 5x²+2x-15x²-6x

(g * h)(x) = 5x²-15x²+2x-6x

(g * h)(x) = -10x²-4x

c) To get (g + h)(−2), we need to first calculate (g + h)(x) as shown;

(g + h)(x) an (g * h)(x)

(g + h)(x) = g(x) +h(x)

(g + h)(x) = x − 3x + (5x+2)

(g+h)(x) = x-3x+5x+2

(g+h)(x) =3x+2

Substituting x = -2 into the resulting function;

(g+h)(-2) = 3(-2)+2

(g+h)(-2) = -6+2

(g+h)(-2) = -4

Solve for x. x+27=−12

Answers

x + 27 = -12
subtract 27 from both sides
x = -12-27
x = -39

-39 is the correct answer

Find the domain of f and f −1 and its domain. f(x) = ln(ex − 3). (a) Find the domain of f. (Enter your answer using interval notation.) (−2,[infinity]) (b) Find f −1. f −1(x) = x+ln(3)

Answers

Answer:

a.Domain of f=(1.099, $\infty)$

b. $f^(-1)(x)=ln(e^x+3)$

Step-by-step explanation:

Let $y=f(x)=ln(e^x-3)$

We know that domain of ln x is greater than zero

$e^x-3>0$

Adding 3 on both sides of inequality

$e^x-3+3>0+3$

$e^x>3$

Taking on both sides of inequality

$lne^x>ln 3$

$x>ln 3$ =1.099

By using $lne^x=x$

Domain of f=(1.099, $\infty)$

Let $y=f^(-1)(x)=ln(e^x-3)$

$e^y=e^x-3$

By using property $lnx=y\implies x=e^y$

$e^x=e^y+3$

Taking ln on both sides of equality '

$lne^x=ln(e^y+3)$

$x=ln(e^y+3)$

Replace x by y and y by x

$y=ln(e^x+3)$

Substitute y= $f^(-1)(x)$

$f^(-1)(x)=ln(e^x+3)$

Choose the expression that completes the equation 33 / 3 + 10=_______1. 2(10+1)

2. 10(1+1)

3. 3(6+1)

4 5(3+5)

Answers

Answer:

the answer is number 3. 3 ( 6+1 )

Number one would be your answer because 33/3+10 equals to 21 and 2(10+1) equals 21 as well.

Hope this helped

The Pacheco family has a monthly income of $ 7,300 . They have monthly fixed expenses of $ 3,280 . In July, they had monthly variable expenses of $ 2,620 . They have annual expenses totaling $ 14,000 . Assuming annual expenses are paid off at an equal rate monthly, what was the Pacheco’s cash flow for July?

Answers

Answer:

Positive 233

Step-by-step explanation:

7300-3280-2620-1167(14000/12)=233.

${x}^(2) + √(x) + \sqrt[5]{x}$
what is f'(3) of this equation?

Answers

Answer:

$3 + (1)/(2√(3) ) + \frac{1}{5\sqrt[5]{81} }$

Step-by-step explanation:

Just to make it easier to see, $√(x) = x^{(1)/(2) }$ and $\sqrt[5]{x} = x^{(1)/(5) }$ This way we could more easily use the power rule of derivatives.

So if f(x) = $x^(2) +x^{(1)/(2) } +x^{(1)/(5) }$ then f'(x) will be as follows.

f'(x) = $x^(1) +(1)/(2) x^{-(1)/(2) } +(1)/(5) x^{-(4)/(5) } = x +\frac{1}{2x^{(1)/(2) }} +\frac{1}{ 5x^{(4)/(5) }} = x +(1)/(2√(x)) +\frac{1}{ 5\sqrt[5]{x^4} }$

to find f'(3) just plug 3 into f'(x) so $3 + (1)/(2√(3) ) + \frac{1}{5\sqrt[5]{81} }$

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