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3 years ago

Let f(x) = x - 2 and g(x) = x2 - 7x - 9. Find f(g(-1))

1 answer:

Montano1993 [528]3 years ago

4 0

$f(x)=x-2 \\
g(x)=x^2-7x-9 \\ \\
g(-1)=(-1)^2-7 \times (-1)-9 = 1+7-9=-1 \\
f(g(-1))=f(-1)=-1-2=-3 \\ \\
\boxed{f(g(-1))=-3}$

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Step-by-step explanation:

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3 years ago

A bank advertises that it compounds money quarterly and that it will take Double your money in 10 years. what is the interest-ra

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The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

Step-by-step explanation:

The given is,

Compounds money quarterly

Double your money in 10 years

Step:1

Formula to calculate future investment with compounded quarterly,

$A =P(1+\frac{r}{n} )^{nt}$ ...............................(1)

Where, A - Future amount

P - Initial investment\

r - Rate of interest

n - No. of compounding in a year

t - No. of years

Step:2

Let, P = X

A = 2X ( Double your money )

From given, n - 4 ( for compounding quarterly )

t - 10 years

From equation (1)

$2X =X(1+\frac{r}{4} )^{(4)(10)}$

$\frac{2X}{X} =(1+\frac{r}{4} )^{(4)(10)}$

$2 =(1+\frac{r}{4} )^{40}$

Take root $40^{th}$ root on both side,

$\sqrt[40]{2} = (1+\frac{r}{4} )$

$1.017479692 = (\frac{4+r}{4} )$

$(1.017479692)(4) = (r+4)$

$4.06992=(r+4)$

$r = 4.06992 -4$

$r =( 0.06992)(100)$

r = 6.992 %

Result:

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

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3 years ago