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Multiple choice Math Questions?

0 votes
Find the Product of (3+6i)(4-7i)
a.12-42i b. -30+45i c.-44-45i d.54+3i

Find the quotient 4+6i/2-3i
a. -5/26 - 6/13i b. -10/13+24/13i c.2-2i d. none of these

Population of Starke company is 72,000 and is growing at 4.8%. What expression fits for population after n decades?
a. 72,000(1.48) b. 72,000(1.048) c.72,000(4.8) d. 72,000+(4.8)

Kim invests $3000 at 7.8 annual interest. Amount after 15 years?
a. $9557.74 b. $9593.62 c. $9629.45 d. $9665.98

Jamie invests $800 at 8.2 interest compounded contiously. Amount of investment after 20 years?
a. $3869.32 b. $4124.14 c. $4356.63 d. $4409.87

Approximate value of the expression log16 of 160?

Another way to write 4log 3 of a + 3 log 3 of 2b - log3 of m?

Solution to the the equation 2log a of 3 + log a (x-4) = log a (x+8)

Find the solution to the equation ln (x^2 + 3x) - ln10 = 0?

(2x^2 - 3x^4 - 6) - (5x^4 - 2x^2 + 4) in standard form?

vertex in equation y = x^2 + 6x - 7?

Factor 8x^3 - 125?

Remainder when 3x^3 - 9x^2 + 7x + 4 is divided by x - 3?

Quotient wheen 4x^3 + 12x^2 - 14x + 8 is divided by x + 4?
asked Jun 11, 2014 in ALGEBRA 1 by anonymous

10 Answers

0 votes

a) (3 + 6i)(4 - 7i)

General rule of multiplying complex numbrs (a + bi)(c + di) = (ac - bd) + (ad + bc)i

a = 3, b = 6, c = 4, d = -7

(ac - bd) + (ad + bc)i = [3*4 - 6*-7] + [3*-7 + 6*4]i

= [12 + 42] + [-21 + 24]i

= 54 + 3i

(3 + 6i)(4 - 7i) = 54 + 3i

Option d is correct answer.

b)image

Step - 1) determine conjugate of the denominator

Conjugate of the denominator  2 - 3i = 2 + 3i

Step - 2) Multiply the numarator and denominator by the conjugate.

image  image

image

image

image

Since i 2 = -1

image

image

image

image

Option b is correct answer.

answered Jun 11, 2014 by david Expert
0 votes

9) The equation image

Quotient rule in natural logarithm : ln(x / y) = ln(x) - ln(y)

image

image

Since the bases of the lns are same then the insides must be equal.

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image

image

image

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Solution

image

answered Jun 11, 2014 by david Expert
0 votes

10) (2x2 - 3x4 - 6) - (5x4 - 2x2 + 4)

= 2x2 - 3x4 - 6  - 5x4+ 2x2 - 4

= 4x2 - 8x4- 10

Writng the polynomial 4x2 - 8x4- 10 in standard form.

The highest exponent is 4, so that entire term must be written first - 8x4

The next highest exponent is 2, so the term comes next, so far we have - 8x4+ 4x2

The constant term always comes last so the final answer is - 8x4 + 4x-10

Standard form of the above polynomial is  - 8x4 + 4x-10.

11) The equation y = x2 + 6x - 7

Compare it to standard form of parabola y = ax2 + bx + c.

a = 1 , b = 6, c = -7.

Coordinates of vertex [-b/2a, f(-b/2a)] = (x , y)

x = axis of symmetry = -b/2a

x = -6/2(1) = -3

To find y coodinate of vertex substitute x value in y = x2 + 6x - 7

y = (-3)2 + 6(-3) - 7 = 9 - 18 - 7 = -16

Vertex in equation y = x2 + 6x - 7 is (-3, -16).

answered Jun 11, 2014 by david Expert
0 votes

12) The binomial 8x3 - 125

= 23 x3  - 53

From properties of exponents

Product to a power ; am * bm = (ab)m

= (2x)3 - 53

The factored form of a 3 - b 3 is (a - b)(a 2 + ab + b 2)

Similarly the factored fom of (2x)3 - 53

a = 2x , b = 5

(a - b)(a 2 + ab + b 2) = (2x - 5)[ (2x)2 + (2x)(5) + 52 ]

= (2x - 5)(4x2 + 10x + 25)

Factoing of 8x3 - 125 = (2x - 5)(4x2 + 10x + 25).

13) 

image

By division algorithm

image

Remainder is 25.

answered Jun 11, 2014 by david Expert
0 votes

14)

image

By division algorithm

image

Quotient image

 

answered Jun 12, 2014 by david Expert
0 votes

5) James invest $800 at 8.2 interest compounded contiously.

Find amount of investment after 20 years

To calculate continuously compounded interest use the formula below.

Where = amount , P  = principal, r  = rate of intrest, t = time in years and e  = mathematical constant .

In this case t = 20 years , r = 8.2/100 = 0.082, P = $800

image

image

A = 4124.135609

A = $ 4124.14

Option b is correct answer.
 

answered Jun 12, 2014 by david Expert
edited Jun 12, 2014 by david
0 votes

Approximate value of the expression log16 of 160

image

Change of base formula : image

image

image

image

 

answered Jun 12, 2014 by david Expert
0 votes

Kims invest $300 at 7.8 annual interest.

To calculate continuously compounded interest use the formula below.

Where = amount , P  = principal, r  = rate of intrest, t = time in years and e  = mathematical constant .

In this case = $3000, r  = 7.8/100 = 0.078, t  = 15 years.

image

image

image

image

A = 9665.9779

A = $ 9665.98

Option d is correct answer.

 

answered Jun 12, 2014 by david Expert
0 votes

image

 logb(m n ) = n · logb(m )

image

From the log properties product rule: logb(mn ) = logb(m ) + logb(n )

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From the log properties quotient rule: logb(m/n) = logb(m ) – logb(n)

image

imageimage.

 

answered Jun 12, 2014 by david Expert
0 votes

The logarthimic equation image

logb(m n ) = n · logb(m )

image

image

From the log properties product rule: logb(m ) + logb(n ) = logb(mn )

image

Since the bases of the logs are same then the insides must be equal.

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Solution image.

 

answered Jun 12, 2014 by david Expert

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