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Lera25 [3.4K]
3 years ago
5

Find the graphed solution to the inequality. 3(x-9) < -18

Mathematics
1 answer:
Ket [755]3 years ago
6 0

Answer:

x

Step-by-step explanation:

3\left(x-9\right)

<u>Divide both sides by 3</u>

\frac{3\left(x-9\right)}{3}

x-9

<u>Add -9 to both sides:</u>

x-9+9

x

_______________________

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Dave is considering two loans. Loan U has a nominal interest rate of 9. 97%, and Loan V has a nominal interest rate of 10. 16%.
Vsevolod [243]

Loan U  will have a lower effective interest rate, and 0.0713 lower percentage points lower than Loan V and it can be determined by using the rate of interest formula.

Given that,

Dave is considering two loans.

Loan U has a nominal interest rate of 9.97%, and Loan V has a nominal interest rate of 10.16%.

If Loan U is compounded daily and Loan V is compounded quarterly.

We have to determine,

Which loan will have the lower effective interest rate, and how much lower will it be?

According to the question,

<h2>Effective Interest Rate;</h2>

The effective interest rate is determined by the formula;

= \left(1+\dfrac{r}{t} \right )^t

Loan U has a nominal interest rate of 9.97%,

Loan U is compounded daily,

Then,

The effective annual multiplier for loan U is,

= \left(1+\dfrac{0.997}{365}\right)^{365}\\\\= (1+0.0027)^{365}\\\\= (1.0027)^{365}\\\\= 1.104824

And Loan V has a nominal interest rate of 10.16%,

and Loan V is compounded quarterly.

Then,

= \left(1+\dfrac{0.1016}{4}\right)^{4}\\\\= (1+0.0254)^{365}\\\\= (1.0254)^{365}\\\\= 1.105537

Therefore,

Loan V has a higher effective rate by,

=1.105537 -1.104824 \\\\= 0.000713 \\\\= 0.0713%

Hence, Loan U  will have a lower effective interest rate, and 0.0713 lower percentage points lower than Loan V.

For more details about Interest rate refer to the link given below.

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The polynomial equation for the given roots is x³-7x²+20x-24=0.

Given that, the polynomial equation of the smallest degree whose roots are 3, 2+2i and 2-2i.

Now, we need to write the polynomial equation.

<h3>What is a polynomial equation? </h3>

A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation. For an equation to be a polynomial equation, the variable in it should have only non-negative integer exponents. i.e., the exponents of variables should be only non-negative and they should neither be negative nor be fractions.

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