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2 years ago

The function f(x) = In(x) has a domain of all real numbers greater than zero and a range of all real numbers. The

Mathematics

1 answer:

solniwko [45]2 years ago

4 0

Answer:

The domain of f–1(x) is all real numbers and the range is all real numbers greater than 0.

Step-by-step explanation:

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The base of a triangle is one third of its height. If the area of the triangle is 24 square inches, what are the base and height

Burka [1]

Answer:

D. 4in, 12in

Step-by-step explanation:

Area of triangle = 24in²

Unknown:

Base and height of the triangle = ?

Solution:

The area of a triangle = $\frac{1}{2}$ x base x height

From the problem,

base = $\frac{1}{3}$ x height

let the base = b

height = h

b = $\frac{1}{3}$ h

h = 3b

Input into the formula of area;

24 = $\frac{1}{2}$ x b x 3b

Mulitply through by 2;

48 = 3b²

b² = 16

b = √16 = 4

So, h = 3b= 3 x 4 = 12in

6 0

3 years ago

After distributing, which equation is equivalent to -4(3x + 2) = 10a.-12x -8 = 10b.-12x + 8 = 10c.-12x -6 = 10d.-12x + 6 = 1

rodikova [14]

Answer:

Option A: -12x-8=10 is the correct answer.

Step-by-step explanation:

Given equation is:

-4 (3x+2) = 10

We will distribute the equation by multiplying the terms inside the brackets with -4.

Therefore,

-4*3x + 2*-4 = 10

-12x +(-8) = 10

-12x - 8 = 10

The equation -4 (3x+2) = 10 will become -12x-8=10 after distributing.

Hence,

Option A: -12x-8=10 is the correct answer.

5 0

2 years ago

How is 7 (x + 2) different? Brainstorm how this problem could be simplified Help ples!!!!

Alborosie

answer:

distribute

step-by-step explanation:

7(x+2)

7(x)=7x

7(2)= 14

7x+14

6 0

2 years ago

Find the distance between points (-3,-4) and (1,-2)

Ludmilka [50]

Answer:

√20 or 4.47 ish

Step-by-step explanation:

√(1--3)²+(-2--4)²

√(1+3)²+(-2+4)²

√(4)²+(2)²

√16+4

√20

4.47 ish

(Hopefully this is correct, have a nice day!)

6 0

2 years ago

D Evaluate arcsin (6)] at x = 4. dx

sineoko [7]

Answer:

$\frac{1}{2\sqrt{5} }$

Step-by-step explanation:

Let, $\text{sin}^{-1}(\frac{x}{6})$ = y

sin(y) = $\frac{x}{6}$

$\frac{d}{dx}\text{sin(y)}=\frac{d}{dx}(\frac{x}{6})$

$\frac{d}{dx}\text{sin(y)}=\frac{1}{6}$

$\frac{d}{dx}\text{sin(y)}=\text{cos}(y)\frac{dy}{dx}$ ---------(1)

$\frac{1}{6}=\text{cos}(y)\frac{dy}{dx}$

$\frac{dy}{dx}=\frac{1}{6\text{cos(y)}}$

cos(y) = $\sqrt{1-\text{sin}^{2}(y) }$

= $\sqrt{1-(\frac{x}{6})^2}$

= $\sqrt{1-(\frac{x^2}{36})}$

Therefore, from equation (1),

$\frac{dy}{dx}=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}$

Or $\frac{d}{dx}[\text{sin}^{-1}(\frac{x}{6})]=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}$

At x = 4,

$\frac{d}{dx}[\text{sin}^{-1}(\frac{4}{6})]=\frac{1}{6\sqrt{1-\frac{4^2}{36}}}$

$\frac{d}{dx}[\text{sin}^{-1}(\frac{2}{3})]=\frac{1}{6\sqrt{1-\frac{16}{36}}}$

$=\frac{1}{6\sqrt{\frac{36-16}{36}}}$

$=\frac{1}{6\sqrt{\frac{20}{36} }}$

$=\frac{1}{\sqrt{20}}$

$=\frac{1}{2\sqrt{5}}$

4 0

2 years ago