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3 years ago

Find the product of (4x - 3 ()2x^2 - 7x + 1)

Mathematics

1 answer:

Paul [167]3 years ago

4 0

Asked and answered at brainly.com/question/8532103

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When Sarah turned 18, she took $500 from her savings and opened a

Montano1993 [528]

The worth of Sarah's investment when she is 68 is $14,728.51.

<h3>What is the worth of the investment?</h3>

The formula that can be used to determine the worth of the investment is:

FV = P (1 + r)^n

FV = Future value

P = Present value

R = interest rate

N = number of years = 68 - 18 = 50

$500 x (1.07)^50 = $14,728.51

To learn more about future value, please check: brainly.com/question/18760477

6 0

2 years ago

What is the derivative of x times squaareo rot of x+ 6?

Dafna1 [17]

Hey there, hope I can help!

$\mathrm{Apply\:the\:Product\:Rule}: \left(f\cdot g\right)^'=f^'\cdot g+f\cdot g^'$
$f=x,\:g=\sqrt{x+6} \ \textgreater \ \frac{d}{dx}\left(x\right)\sqrt{x+6}+\frac{d}{dx}\left(\sqrt{x+6}\right)x \ \textgreater \ \frac{d}{dx}\left(x\right) \ \textgreater \ 1$

$\frac{d}{dx}\left(\sqrt{x+6}\right) \ \textgreater \ \mathrm{Apply\:the\:chain\:rule}: \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx} \ \textgreater \ =\sqrt{u},\:\:u=x+6$
$\frac{d}{du}\left(\sqrt{u}\right)\frac{d}{dx}\left(x+6\right)$

$\frac{d}{du}\left(\sqrt{u}\right) \ \textgreater \ \mathrm{Apply\:radical\:rule}: \sqrt{a}=a^{\frac{1}{2}} \ \textgreater \ \frac{d}{du}\left(u^{\frac{1}{2}}\right)$
$\mathrm{Apply\:the\:Power\:Rule}: \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1} \ \textgreater \ \frac{1}{2}u^{\frac{1}{2}-1} \ \textgreater \ Simplify \ \textgreater \ \frac{1}{2\sqrt{u}}$

$\frac{d}{dx}\left(x+6\right) \ \textgreater \ \mathrm{Apply\:the\:Sum/Difference\:Rule}: \left(f\pm g\right)^'=f^'\pm g^'$
$\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(6\right)$

$\frac{d}{dx}\left(x\right) \ \textgreater \ 1$
$\frac{d}{dx}\left(6\right) \ \textgreater \ 0$

$\frac{1}{2\sqrt{u}}\cdot \:1 \ \textgreater \ \mathrm{Substitute\:back}\:u=x+6 \ \textgreater \ \frac{1}{2\sqrt{x+6}}\cdot \:1 \ \textgreater \ Simplify \ \textgreater \ \frac{1}{2\sqrt{x+6}}$

$1\cdot \sqrt{x+6}+\frac{1}{2\sqrt{x+6}}x \ \textgreater \ Simplify$

$1\cdot \sqrt{x+6} \ \textgreater \ \sqrt{x+6}$
$\frac{1}{2\sqrt{x+6}}x \ \textgreater \ \frac{x}{2\sqrt{x+6}}$
$\sqrt{x+6}+\frac{x}{2\sqrt{x+6}}$

$\mathrm{Convert\:element\:to\:fraction}: \sqrt{x+6}=\frac{\sqrt{x+6}}{1} \ \textgreater \ \frac{x}{2\sqrt{x+6}}+\frac{\sqrt{x+6}}{1}$

Find the LCD
$2\sqrt{x+6} \ \textgreater \ \mathrm{Adjust\:Fractions\:based\:on\:the\:LCD} \ \textgreater \ \frac{x}{2\sqrt{x+6}}+\frac{\sqrt{x+6}\cdot \:2\sqrt{x+6}}{2\sqrt{x+6}}$

$Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions$
$\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \ \frac{x+2\sqrt{x+6}\sqrt{x+6}}{2\sqrt{x+6}}$

$x+2\sqrt{x+6}\sqrt{x+6} \ \textgreater \ \mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c}$
$\sqrt{x+6}\sqrt{x+6}=\:\left(x+6\right)^{\frac{1}{2}+\frac{1}{2}}=\:\left(x+6\right)^1=\:x+6 \ \textgreater \ x+2\left(x+6\right)$
$\frac{x+2\left(x+6\right)}{2\sqrt{x+6}}$

$x+2\left(x+6\right) \ \textgreater \ 2\left(x+6\right) \ \textgreater \ 2\cdot \:x+2\cdot \:6 \ \textgreater \ 2x+12 \ \textgreater \ x+2x+12$
$3x+12$

Therefore the derivative of the given equation is
$\frac{3x+12}{2\sqrt{x+6}}$

Hope this helps!

8 0

3 years ago

Use a system of equations to solve this problem.Bronze is a mix, or alloy, of tin and copper. A metal worker needs 100 g of bron

d1i1m1o1n [39]

Answer:

x = 50 grs

y = 50 grs

Step-by-step explanation:

" x " is quantity of bronze of 5% tin

" y " is quantity of bronze of 45% tin

The worker needs 100 grs of bronze and this bronze must be 25% tin

The mathematical expression for the 100 grs condition is:

x + y = 100

And the The mathematical expression for the % condition is:

0,05*x + 0.45*y = 0,25 * ( x + y )

The system is:

x + y = 100

0,05*x + 0,45*y = 0,25* ( x + y )

Solving this system we get values of x and y

y = 100 - x

0,05*x + 0,45* ( 100 - x ) = 0,25 * ( x + 100 - x )

0,05*x + 45 - 0,45*x = 0,25*( 100 )

0,05*x + 45 - 0,45*x = 25

- 0,4*x = -45 + 25

x = 20/0,4 x = 50 grs

and y = 50 grs

8 0

3 years ago

I have 30 ones 2thousands 4hundred thousands , 60 tens and 100 hundreds what number am I ?

viva [34]

Answer:

Step-by-step explanation:

Units = 30

Thousands = 2,000

Hundreds of Thousands = 400,000

Tens = 60

Hundreds = 100

HTHHTU

400,000

2,000

100

7 0

3 years ago

Read 2 more answers

Identify the property used in each step of solving the inequality 7x+4 <46.

ELEN [110]

Answer:

2.Addition Property

3.Multiplication Property

Step-by-step explanation:

3 0

3 years ago