Algebra II Midterm

simplify: (7-2i)/(3+7i)

(14-55i)/58

solve using square root: -5/2x^2 - 12/7= 0

(2i Times Square root of 6)/(square root of 35)

suppose p(x)=3x-4. Find a binomial B(X) such that (P[x])(B[x]) is a quartic binomial.

(3x-4)x= 3x^2 - 4x (quartic binomial) P(x)=3x-4 B(X)= x

factor: 27x^5 + 125x^2=0

(3x-5)(3x^2-15x+25)

What polynomial completes the equation (x-5)/(4x^2-9) times (________)/(x-5)= 2x+1

(4x^2-9)(2x+1)

State when the x-value is undefined: 3x/(2x^2-5x+7)

(5+/- i times the square root of 31)/4

solve with quadratic formula: 7x^2 - 12x = -9

(6 +/- 3i Times Square root of 3)/7

simplify: (7k^2 + 4k -3/ 14k^2 +29k - 15)/(3k - 27/2k + 5)

(k+1)/[3(k-9)]

Use completing the square to write the quadratic in vertex form: n^2 + 36= -20n

(n + 10)^2 - 64

Use completing the square to write the quadratic in vertex form: 7x^2 = 56 + 14x

(x - 1)^2 - 9=0

use rational root theorem: f(x)=5x^3+x^2-5x-1

+/- 1, +/- 1/5

evaluate using mental math or changing the base: log*(64) 1/4

-.33

simplify: (-2 - 8i) - (2i) + (1 - 7i)

-1 - 17i

simplify: log*3 (1/243)

-10/9

Evaluate: p(t)= -45 + 3t; Find p(-4x^2 - 2x - 1)

-12x^2 - 6x - 48

Find discrimination: -4k^2 - 10=k

-159<0 two complex solutions

simplify: (5n-n^3+n^2) - (3n^2+8n^3-5n) + (7n^3-4n)

-2n^3-2n^2+6n

simplify: (5 - 3i)(-7+6i)(8+6i)

-442 + 306i

A van de Graaff generator is a machine that produces very high voltages by using small, safe levels of electric current. One machine has a current that can be modeled by I(t)= t+10, where t represents time in seconds. The power of the system can be modeled by P(t)=.5t^3+16t^2+18t. Write an expression that represents the voltage pf the system if the equation for voltage is V=P/I

.5t^2+11t-92+(920/t+10)

solve by factoring: f(x) = 81a^6 b^4 - 100a^8 b^2

27a^6 b^2 (3b^2 - 37/10a^2

Given the formula E=IZ where E is voltage, I is current, and Z is impedance, find the voltage if you know the current is -9-5i amps and the impedance is 8-6i ohms.

E= -102+14i

Solve by factoring: 4x^2 + 8x + 3=0

X=-1/2 X=-3/2

find values of X and y that make each equation true: 5(X-1) + (3y)i = -15i - 20

X=-3 y=-5

solve by completing the square: f(x)=x^2 - 16x + 77

X=8 +/- i Times Square root of 13

simplify: [(x^5 - 4x^3 - x^2 + 4)/(2x^3 - 4x^2 + 2x - 4)]/[(3x^3 + 3x^2 + 3x)/(4x^2 - 4)]

[2(x-1)^2(x+1)(x+2)]/[3x(x^2+1)]

find the inverse: h(x) = cubic root of (x-3)/2

h^-1(x)=2x^3+3

solve by using algebra: -2x^2 + 2x + 24 < or equal to 0

in photo library

solve by using algebra: 2x^2 < or equal to 7x - 5

in photo library

write in logarithmic form: 6^-3=1/216

log6^(1/216)= -3

find the maximum or minimum: y=-3/4x^2 - 3x - 4

maximum: -1 aos: -2

solve equation by taking square root: 3n^2 + 10=283

n= +/- square root of 91

evaluate using mental math or changing the base: log*(5) -3.7

no solution

use synthetic substitution: f(x)= -3x^2 - 3/2x + 11/2 at 7/6

p(7/6)= -1/3?

solve by completing the square: 6p^2 - 90 = 12p

p= +/- 4 +1

Use table to graph: f(X) = x^2 + 2x

picture in library

graph each number in complexity plan: -3 + i

picture in library

Graph: the line through (-3,1) that is parallel to the line with equation -X-4y=2

picture in photo library; y= -1/4x + 1/4

Graph the line through (4,1) that is perpendicular to the line with equation 4x - 3y=4

picture in photo library; y= -3/4 + 4

Graph: -2x + 1/3y=-2

picture in photo library; y=6x - 6

State the shifts and graph 1) f(x)=-e^(x-3) + 1 2) f(x)= -ln (x+3)-3 3) y= (1/4)^(x+2) + 1

pictures in library

given the quadratic ax^2 + bx + c = o derive the quadratic formula formula using completing the square

quadratic formula

find all roots: -5x^3-9x^2-x=0

solutions: x=0 and x=(9+/- square root of 61)/-10

find all roots: 2x^4 + x^3 - 9x^2-4x +4=0

solutions: x=2, x=-2, and x=1/2

How long would Jack's money have been in the bank if his final amount was $2848.72, his initial amount was $1410, and it was compounded continuously at 5.26%?

t= 13.4

write a polynomial function of least degree with integral coefficients that has the given zeros: 2, 5, -2, 5/3

x^4-20/3x^3+13/3x^2+80/3x-100/3

Write an equation for the line that passes through (-2,-1) and is perpendicular to 7x-3y + 1=0

y=-3/7x - 1 6/7

Write an equation that passes through (3,4) and is parallel to the line that passes through (2,-4) and(-1,6)

y=10/-3x + 14

Is 2i a zero of the polynomial x^3-2ix^2-4x+8i

yes

determine if the binomial is a factor: (-29b+25b^3+40b^2-36)/(4+5b)

yes

write a quartic trinomial with a leading coefficient of 5

5x^4+x^2+7

Solve: 1) -3.8e^(8x+8) - 4 = -101 2) ln (x-4)- ln x = 2

1) (ln 25.5-8)/8 2) x= -4/(e^2 - 1)

solve: 1) log*3 (x+1)- log*3 x=2 2) log*5 (x-7) + log*5 2= log*5 3

1) 1/8 2) 17/2

write in standard form. Then identify the leading coefficient, degree, and number of terms. Name the polynomial. 1) 7n^2 - 4n + 10n^3 2) 4n^5 + 9n^3

1) 10^3 + 7n^2 -4n LC= 10 D= 3 number of terms= 3 cubic trinomial 2) 4n^5 + 9n^3 LC= 4 D= 5 number of terms= 2 quadratic binomial

solve: 1) (9x^2-49)/(3x-7)=11 2) (x^2+3x-4)/(2x+1)=-2

1) 4/3 2) (-7 +/- the square root of 57)/2?

solve: 1) (1/216)^2n=36^-3n-1 2) -9 times 9^(-8v-2.3) + 10 = -88

1) no solution 2)

find product: (1/2u - 3/8v)(2/5u^2 + 1/2uv + 3/8v^2)

1/5u^3 + 1/10u^(2)v - 9/16v^3?

write in exponential form: log k=-17

10^-17=k

divide using long division: (70x^3-11x^2-24x+3)/(7x + 1)

10x^2-3x-3+(6/7x+1)

given zeros, find original quadratic: X= -1/3 and X=2/5

15x^2 - X - 2

find absolute value: |-2 + 8i|

2 Times Square root of 17

A soccer ball is kicked from ground level with an initial velocity of 48 ft/s. After how many seconds will the ball hit the ground?

3

The power p in horsepower (hp) generated by a high performance speedboat engine operating at r revolution per minute (rpm) can be modeled by the function p(r)=-0.0000147r2 + 0.18r - 251. What is the maximum power of this engine to the nearest horsepower? At how many revolutions per minute must be the engine be operating to achieve this power?

300?

which grows faster as x increases x^3 or 3^x

3^x because the bigger the number the more times three is multiplied into it, while with x^3 no matter how large the number is it will still only be multiplied 3 times

find product: (2m-7n)^2

4m^2-28mn+49n^2

evaluate using mental math or changing the base: log*(1/3) 1/243

5

The height of a popular tree in feet, at age t years can be modeled by the function h(t)=6+31n(t+1). Use the model to predict the number of years when the height will be 18ft.

53.5

The pilot of a helicopter plans to release a bucke of water on a forest fire. The height in y in feet of the water t seconds after its release is modeled by y=-16t^2 - 10t + 700. The horizontal distance X in feet between the water and its point of release is modeled by X=92t. At what horizontal distance from the fire should the pilot start releasing water in order to hit the target?

6.31

If log*a b=0, what is the value of a? Explain.

a can be anything because if b is 1 it doesn't matter what a is the equation is zero

A quantity of insulin used to regulate sugar in the blood stream breaks down by about 7.53% each minute. A body weight adjusted dose is usually 16 units. a. How much insulin remains after 17 minutes? b. About how long does it take for half of the dose to remain

a. 4.23 units b. 8.8 minutes

At sea level, the boiling point of water is 212 degrees F. At x thousand feet, the boiling point of water is given by the function f(x)=212-1.85x. Find the inverse, and then find what altitude does the boiling point on water fall to 200 degrees F.

a= 3.19 thousand feet f^-1 (x)= (x-212)/-1.85

find aos, vertex, x-Int, y-Int, then graph y > or equal to x^2 + 2x - 3

aos: -1 vertex: -4 X-Int: 1,-3 y-Int: -3 no graph

find AOS, vertex, y-Int, X-Int, then graph: f(x)=2x^2 - 7x - 4

aos: 7/4 vertex: -81/8 y-Int: -4 X-Int: -1/2, 4 didn't graph

identify base and tells whether the function shows growth or decay: f(x)=(1/4)(8/3)^2

b=8/3 growth

recall that polynomials are classified by degree. Why doesn't an exponential function have a degree?

because the exponential can be infinitely in an exponential function

Why are the absolute value of a complex number and the absolute value of its conjugate equal?

because the formula of absolute value is square root of a^2 + b^2, and even though the conjugate of a complex number is the opposite sign, when you square the numbers they will both be positive. Negative X negative = positive

state shifts and graph: f(X)=-(X + 1)^2 + 2

down, narrow, left 1, up 2, picture in library

state shifts and graph each function: f(X) = -1/2(X - 7/2)^2 + 1

down, wide, right 7/2, up 1, picture in library

Write in vertex form: the parent function f(X) = x^2 is reflected across the X-axis, vertically compressed by a factor of 1/7, translated 7 units right, and 11 units down

f(X)=-1/7(X-7)^2 - 11

What type of graph would a function of the form f(X)=a(X-h)^2 + k have if a=0? What type of function would it be?

f(X)=k only linear function

f(x)= e^x is translated 40 units right, 112 units down, compressed vertically by a factor of 6 and reflected across the x-axis

f(x)= -6(e^[x-40] -112)

Write and equation in standard form for two quadratic functions that have the same vertex but open in different directions

f(x)= 2x^2 g(x)= -2x^2

what is the inverse of f(x)= 3

f^-1 (x)=3

A group of students retake the written portion of a driver's ed test after several months of without reviewing the material. A model used by psychologist describes the retention by the function a(t)=-15log(t+50)+75, where a is the average score at time t (in months). Describe how the model is transformed, then use the model to predict when the average score is 45

t= 50

a veterinarian has instructed Harrison to give his 75lb dog one 325mg aspirin tablet for arthritis. The amount of aspirin A remaining in the dog's body after t minutes can be expressed by A= 325(1/2)^(t/15) Find the time it takes for the amount of aspirin to drop to 30mg.

t=52

What is the complex conjugate of a real number

the complex conjugate of a the real number a is the number a

explain and sketch what would be happening if you knew the discriminant of a quadratic was negative

there would be two complex solution because a negative is less than 0. The quadratic wouldn't cross the X-axis sketch in photo library

state when x-value is undefined: 56x/(2x^2 + 41x - 21)

x=1/2 x=-21

divide using synthetic division: (x^4-10x^3-4x+42)/(x-10)

x^3 - 4 + (2/x-10)