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Don't have to state your income? Taxes are all based on gross income you earn!!

Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.)

f(x) = x + 4 / sqrt(x)

\(f(x) = x +\frac{ 4 }{ \sqrt{x}}\\ \)

You cannot divide by 0 so x cannot be zero

You cannot find the sqrt of a negative number so x >  =0

Put thses together and we get x>0

Since x>0 y must be > 0 too

Anyway, only the x value is of interest so

(0,infinity)  

I'll check with a graph.

Yes that is correct

ok I have been away and had a think

a and b are positive  integers but  they are not square numbers

so sqrt(a) and sqrt(b) are irrational numbers.

When will     \(\sqrt{a}+\sqrt{b}=Q\)      where Q is a  rational number.

To me the answer seems to be an obvious 'never' but here is a 'proof' by contradiction.

Lets assume that such a number Q exists then

\(\sqrt{a}+\sqrt{b}=Q\\ \sqrt{a}=Q-\sqrt{b}\\ \mbox{Square both sides}\\ a=Q^2+b-2Q\sqrt{b}\\ a-b=Q^2-2Q\sqrt{b}\\ \mbox{Now } R^2 \mbox{ is rational and } 2b\sqrt{b}\mbox{ is irational }\\ \mbox{A rational - an irrational = an irational}\\ \mbox{therefore a-b is irrational}\\ \mbox{but a and b are integers so a-b is rational}\\ \mbox{Contradiction!! }\\ \mbox{Therefore there are no values of a and b such that }\sqrt a +\sqrt{b} \mbox{ is equal to a rational number!}\)

The y-axis is not in dollars, it is in 10^4 dollars. Look at the x10^4 in brackets after the word Dollars.

So the y- intercept  isn't $10 it's $10*10^4 or $100000

Sorry, I added the post twice by mistake

1 week =7 days

2 x 7 =14 days in 2 weeks

14 days x 24 hours x 60 minutes x 60 seconds =1,209,600 seconds in 2 weeks.

10-(1/2)^4 *48 i know the answer is 7 but how to work it out is what i need

10 - (1/16) * 48 =

10 - (48/16) =

10 - 3 = 7

Divide: 1 / 4 = 1⁄4

Power: 1 ^ 0.25 = 1

z = -1^(1/4)
z = -1

tim gave 50,50$ to lunch with 20% tips how much money gave he together

$50.50 + 20% =

$50.50 + $10.10 =$60.60 Total bill.

       what is 26 to the 340th power?=1.232929687e+481

(5/6) / (1/2) =5/6 x 2 =10/6=1 2/3 of an hour.

Solve for x:
sqrt(3 x+4)-sqrt(x+5) = 1

(sqrt(3 x+4)-sqrt(x+5))^2 = 9+4 x-2 sqrt(x+5) sqrt(3 x+4) = 9+4 x-2 sqrt((x+5) (3 x+4)) = 1:
9+4 x-2 sqrt((x+5) (3 x+4)) = 1

Subtract 4 x+9 from both sides:
-2 sqrt((x+5) (3 x+4)) = -8-4 x

Raise both sides to the power of two:
4 (x+5) (3 x+4) = (-8-4 x)^2

Expand out terms of the left hand side:
12 x^2+76 x+80 = (-8-4 x)^2

Expand out terms of the right hand side:
12 x^2+76 x+80 = 16 x^2+64 x+64

Subtract 16 x^2+64 x+64 from both sides:
-4 x^2+12 x+16 = 0

The left hand side factors into a product with three terms:
-4 (x-4) (x+1) = 0

Divide both sides by -4:
(x-4) (x+1) = 0

Split into two equations:
x-4 = 0 or x+1 = 0

Add 4 to both sides:
x = 4 or x+1 = 0

Subtract 1 from both sides:
x = 4 or x = -1

sqrt(3 x+4)-sqrt(x+5) => sqrt(4+3 (-1))-sqrt(5-1)  =  -1:
So this solution is incorrect

sqrt(3 x+4)-sqrt(x+5) => sqrt(4+3 4)-sqrt(5+4)  =  1:
So this solution is correct

The solution is:
Answer: | x = 4

The square root of 4 is +2 not -2.

The roots of x^2 = 4 are +sqrt(4)and -sqrt(4), but sqrt(4) = +2.

Thanks Alan,
I'm going to do immediately.

how to solve the equation
((3x+4)^(1/2))-((x+5)^(1/2))=1

x = -1 ??

(3x + 4)^(1/2) - (x + 5)^(1/2) = 1

(3*(-1) + 4)^(1/2) - (-1 + 5)^(1/2) = 1

√1 - √4 = 1

-1 - (-2) = 1  q.e.d.

But is that a "knotless" proof ??

Greeting asinus :- )

  !

These are presumably hexadecimal numbers, as indicated by the H at the end.

   F000H

 +3000H

 12000H

In decimal:   F000H → 15*16^3 = 61440

                    3000H →    3*16^3 = 12288

                        sum →                   73728

73728/16^4 = 1.125

0.125*16^4/16^3 = 2

Hence 73728 = 1*16^4  + 2*16^3 + 0*16^2 +0*16^1 + 0*16^0  or 73728 decimal → 12000 hexadecimal

4 is certainly a solution asinus, but put x = -1 back into the original equation and see what you get.

Good morning Guest!

how to solve the equation
((3x+4)^(1/2))-((x+5)^(1/2))=1

(3x + 4)^(1/2) - (x + 5)^(1/2) = 1
(3x + 4)^(1/2) = (x + 5)^(1/2) + 1        [I squaring

3x + 4 = (x + 5) + 2(x + 5)^(1/2) + 1

2x - 2 = 2(x + 5)^(1/2)

x - 1 = (x + 5)^(1/2)                            [I squaring

x² - 2x + 1 = x + 5

x² - 3x - 4 = 0

x_1,2 = 1.5 ±√(2,25 + 4)

x₁ = 4

x₂ = -1

Greeting asinus :- )

  !

50/544

50 / 544 = (2 * 5²) / (2⁵ * 17) = 5² / (2⁴ * 17) = 0.0919117647059

\(5xyz=xyz\)

Solve for x.

\(5xyz=xyz\)

\(\frac{5xyz}{yz}=\frac{xyz}{yz}\)

\(5x=x\)

\(5x-x=x-x\)

\(4x=0\)

\(\frac{4x}{4}=\frac{0}{4}\)

\(x=0\)

Solve for y.

\(5xyz=xyz\)

\(\frac{5xyz}{xz}=\frac{xyz}{xz}\)

\(5y=y\)

\(5y-y=y-y\)

\(4y=0\)

\(\frac{4y}{4}=\frac{0}{4}\)

\(y=0\)

Solve for z.

\(5xyz=xyz\)

\(\frac{5xyz}{xy}=\frac{xyz}{xy}\)

\(5z=z\)

\(5z-z=z-z\)

\(4z=0\)

\(\frac{4z}{4}=\frac{0}{4}\)

\(z=0\)

\(x=0\)

\(y=0\)

\(z=0\)

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

a = 19

A = 43°

B = 26°

I know the problem says to find the length of c; however, angle C and length b can also be found using the Law of Sines and that a traingle is equal to 180°.

\(\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}\)

To find angle C, subtract angles A and B from 180°.

\(C=180°-43°-26°\)

\(C=137°-26°\)

\(C=111°\)

Now I will find length b.

\(\frac{sin(43°)}{19}=\frac{sin(26°)}{b}\)

\(19b\times\frac{sin(43°)}{19}=19b\times\frac{sin(26°)}{b}\)

\(sin(43°)b=19sin(26°)\)

\(\frac{sin(43°)b}{sin(43°)}=\frac{19sin(26°)}{sin(43°)}\)

\(b=\frac{19sin(26°)}{sin(43°)}\)

\(b≈\frac{19\times0.438371146789}{sin(43°)}\)

\(b≈\frac{8.329051788991}{sin(43°)}\)

\(b≈\frac{8.329051788991}{0.681998360062}\)

\(b≈12.2127152743209113\)

\(b≈12.2\)

Now I will length c.

\(\frac{sin(43°)}{19}=\frac{sin(111°)}{c}\)

\(19c\times\frac{sin(43°)}{19}=19c\times\frac{sin(111°)}{c}\)

\(sin(43°)c=19sin(111°)\)

\(\frac{sin(43°)c}{sin(43°)}=\frac{19sin(111°)}{sin(43°)}\)

\(c=\frac{19sin(111°)}{sin(43°)}\)

\(c≈\frac{19\times0.933580426497}{sin(43°)}\)

\(c≈\frac{17.738028103443}{sin(43°)}\)

\(c≈\frac{17.738028103443}{0.681998360062}\)

\(c≈ 26.0089014023881936\)

\(c≈26.0\)

A = 43°

B = 26°

C = 111°

a = 19

b ≈ 12.2

c ≈ 26.0

the answer is 4

To find out how many seconds are in two weeks, first you have to find out how many seconds are in a minute.  1 minute equals 60 seconds.

Next, you have to find out how many minutes equal 1 hour.  1 hour equals 60 minutes.

Since 1 minute equals 60 seconds and 1 hour equals 60 minutes, you can calculate the number of seconds in an hour by multiplying 60 by 60 and when you do that you get 3600 seconds.

Next, you have to find out how many hours are in a day.  1 day equals 24 hours.

Since 1 hour equals 3600 seconds and 1 day equals 24 hours, you can calculate the number of seconds in one day by multiplying 3600 by 24 and when you do that you get 86400 seconds.

Next, you have to find out how many days are in a week,  1 week equals 7 days.

Since 1 day equals 86400 seconds and 1 week equals 7 days, you can calculate the number of seconds in one week by multiplying 86400 by 7 and when you do that you get 604800 seconds.

Next, you have to figure out how many seconds are in 2 weeks.  Since 1 week is equal to 604800 seconds, multiply 804800 by 2 and when you do that you get 1209600 seconds.

2 weeks is equal to 1209600 seconds.

No because it becomes other types of energy