Multiple choice Math Questions?

Question

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?

Answer 1

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)

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.

 

Since i ² = -1

Option b is correct answer.

Answer 2

9) The equation

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

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

Solution

Answer 3

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 + 4x²  -10

Standard form of the above polynomial is  - 8x⁴ + 4x²  -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).

Answer 4

12) The binomial 8x³ - 125

= 2³ x³  - 5³

From properties of exponents

Product to a power ; a^m * b^m = (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) 

By division algorithm

Remainder is 25.

Answer 5

14)

By division algorithm

Quotient

 

Answer 6

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 A  = 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

A = 4124.135609

A = $ 4124.14

Option b is correct answer.
 

Answer 7

Approximate value of the expression log16 of 160

Change of base formula :

 

Answer 8

Kims invest $300 at 7.8 annual interest.

To calculate continuously compounded interest use the formula below.

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

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

A = 9665.9779

A = $ 9665.98

Option d is correct answer.

 

Answer 9

 log_b(m ⁿ ) = n · log_b(m )

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

From the log properties quotient rule: log_b(^m/_n) = log_b(m ) – log_b(n)

.

 

Answer 10

The logarthimic equation

log_b(m ⁿ ) = n · log_b(m )

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

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

Solution .