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3 years ago

If √6 is the geometric mean between 4 and another number, then the number is 1.5 9 24

1 answer:

4 0

Correct answer is A.

g - geometric mean
$g= \sqrt{ab} 
\\
\\g= \sqrt{6} ,a=4,b=?
\\ \sqrt{6}= \sqrt{4b} 
\\ (\sqrt{6})^2= (\sqrt{4b} )^2
\\6=4b
\\
\\b= \frac{6}{4} = \frac{3}{2}=1.5$

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Determine the number of real solutions of -2x2 + 5x - 3 = 0.

andrew11 [14]

-2x^2 + 5x -3 =0

Find the discriminate:

In the given formula a = -2, b = 5 and c = -3

The discriminate is found using the formula b^2 - 4(ac)

Replace the letters with their values:

5^2 - 4(-2*-3)

25 - 4*6

25-24 = 1

When the discriminate is greater than or equal to 0, there are two real solutions.

The answer is c) 2

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3 years ago

Find the savings plan balance after 2 years with an APR of 4% and monthly payments of $250. The balance is $ (Do not round until

alexdok [17]

Answer:

$6,506.51

Step-by-step explanation:

Recall that increasing an amount C in x% is equivalent to multiply it by (1+x/100)

As we have 4% APR, the monthly interest would be (4/12)% = 0.04/12

Month 0 (first payment)

$250

Month 1

$250 + 250 \frac{0.04}{12}= 250(\frac{12.04}{12})$

Month 2

$250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2)$

Month 3

$250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3)$

Month 24 (2 years)

$250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3+...+(\frac{12.04}{12})^{24})$

The sum

$1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3+...+(\frac{12.04}{12})^{24}$

is the sum of the first 24 terms of a geometric sequence with common ratio $\frac{12.04}{12}$ which is

$\frac{1-(12.04/12)^{25}}{1-(12.04/12)}=26.02603071$

so, after 2 years the saving balance is

250*26.02603071 = 6,506.50767= $6,506.51 rounded to the nearest cent.

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