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4 years ago

What is the domain of the function y = sqrt x + 4?

Mathematics

2 answers:

SOVA2 [1]4 years ago

8 0

Answer:

$[-4,\infty)$

Step-by-step explanation:

We are asked to find the domain of of the function $y=\sqrt{x+4}$ .

We know that domain of a square root function is not defined for negative values, so we can set an inequality to find the domain of our given function as:

$x+4\geq 0$

$x+4-4\geq 0-4$

$x\geq -4$

Therefore, the domain of our given function is values of x greater than or equal to $-4$ , that is $[-4,\infty)$

LekaFEV [45]4 years ago

5 0

The domain is the set of numbers that the x value can be.
In an equation like $y=x$ the domain is all real numbers because x can be any number.

In the case of $y = \sqrt{x+4}$ , any x value that is less than or equal to -4 will not work because you would be taking the square root of a negative number, which doesn't work unless you're graphing on a complex plane, which I assume you aren't.

Thus, the domain is $x \geq -4$
I hope that helps!

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Solve for all complex roots (2x^10)+(3x^9)-(5x^8)-(9x^7)-(x^6)+(3x^5)+(7x^4)+(9x^3)-(x^2)-(6x)-2

fomenos

Solve for x by completing the square:

2 x^10 + 3 x^9 - 5 x^8 - 9 x^7 - x^6 + 3 x^5 + 7 x^4 + 9 x^3 - x^2 - 6 x - 2 = 0

The left hand side factors into a product with five terms:

(x - 1)^2 (x + 1)^3 (2 x + 1) (x^2 - 2) (x^2 + 1) = 0

Split into five equations:

(x - 1)^2 = 0 or (x + 1)^3 = 0 or 2 x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0

Take the square root of both sides:

x - 1 = 0 or (x + 1)^3 = 0 or 2 x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0

Add 1 to both sides:

x = 1 or (x + 1)^3 = 0 or 2 x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0

Taking cube roots gives 0 times the third roots of unity:

x = 1 or x + 1 = 0 or x + 1 = 0 or x + 1 = 0 or 2 x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0

Subtract 1 from both sides:

x = 1 or x = -1 or x + 1 = 0 or x + 1 = 0 or 2 x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0

Subtract 1 from both sides:

x = 1 or x = -1 or x = -1 or x + 1 = 0 or 2 x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0

Subtract 1 from both sides:

x = 1 or x = -1 or x = -1 or x = -1 or 2 x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0

Subtract 1 from both sides:

x = 1 or x = -1 or x = -1 or x = -1 or 2 x = -1 or x^2 - 2 = 0 or x^2 + 1 = 0

Divide both sides by 2:

x = 1 or x = -1 or x = -1 or x = -1 or x = -1/2 or x^2 - 2 = 0 or x^2 + 1 = 0

Add 2 to both sides:

x = 1 or x = -1 or x = -1 or x = -1 or x = -1/2 or x^2 = 2 or x^2 + 1 = 0

Take the square root of both sides:

x = 1 or x = -1 or x = -1 or x = -1 or x = -1/2 or x = sqrt(2) or x = -sqrt(2) or x^2 + 1 = 0

Subtract 1 from both sides:

x = 1 or x = -1 or x = -1 or x = -1 or x = -1/2 or x = sqrt(2) or x = -sqrt(2) or x^2 = -1

Take the square root of both sides:

x = 1 or x = -1 or x = -1 or x = -1 or x = -1/2 or x = sqrt(2) or x = -sqrt(2) or x = i or x = -i

There are {2} duplicate solutions:

Answer: x = -1 or x = 1 or x = -1/2 or x = -i or x = i or x = sqrt(2) or x = -sqrt(2)

3 0

4 years ago

Read 2 more answers

The area of a circular table is 22511 in2.

zzz [600]

Answer:

1. Radius = 84.65 in

2. Circumference = 531.65 in

3. Diameter = 169.3 in

Step-by-step explanation:

1] In order to find the area of a circle, we use the formula

Area of a circle = πr²

Where r is the radius. So substitute the value of the area of the circle in the formula, to find the radius r.

22511 = π r²

r² = 22511 ÷ π

r = $\sqrt{22511 / \pi }$

r = 84.65 in

2] Now that we found the radius, we can easily find the circumference using the formula:

Circumference of a circle = 2πr

Substitute the value of r in the formula.

Circumference = 2 × π × 84.65

Circumference = 531.87 in

3] The diameter is twice the radius, so:

diameter = r × 2

diameter = 84.65 × 2

diameter = 169.3 in

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3 years ago

A jacket with an original price of $50.70 is discounted 30%. What is the sale price?

fgiga [73]

Answer:

$35.49

Step-by-step explanation:

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3 years ago

An adult human heart beats an average pf 72 per minute. With each beat, it pumps 70 milliliters of blood. How many milliliters o

myrzilka [38]

Please do take the time to read my explanation, it will only help you if you do...

Solution

if the heart beats 72 beats per minute and 1 beat pumps 70 MLs of blood:

70ml*72=5040

Hence, on average the human heart beats about 5040 mililiters in one minute.

6 0

3 years ago

What is the surface area of the composite figure?

Bingel [31]

A1 = 6 × 6 = 36 mm²

A2 = 4 × 6 × 7 = 168 mm²

A3 = 4 × 6 × 4 / 2 = 48 mm²

A1 + A2 + A3 = 36 + 168 + 48 = 252 mm²

7 0

3 years ago