Math midterm

Solve the system 3x+3y+z=10 5x+2y+2z=7 3x-2y+3z=-9

(1,3,-2)

Solve the system of equations 2x-y=6 X+2y=-2

(2,-2)

Factor 6n^2-11n-2

(6n+1)(n-2)

Factor C^2-49

(C-7)(c+7)

Solve each equation, state the number and type of roots X^3+x^2-3x-3=0

-1, - [the square root of] 3, [the square root of] 3 3 real

Solve each equation, state the number and type of roots X^4-5x^2+4=0

-1,1,-2,2 4 real

Simplify (3/2d^-2f^4)^4(-4/3d^5f)^3

-12d^7f^19

Simplify (6w-11w^2) - (4+7w^2)

-18w^2+6w-4

Find the X intercept and the y intercept of the graph of the function. Then graph the equation Y=-2x-4

-2, -4

Solve Y^4-7y^3-18y^2=0

-2,0,9

Find all the zeroes F(X) = x^4-6x^3+6x^2+24x-40

-2,2,3-i, 3+i

Find all the zeroes F(X)=x^4-6x^3+6x^2+24x-40

-2,2,3-i, 3+i

Find the value of the discriminant Describe the number and types or roots Find the exact solutions by the quadratic formula 7x^2+6x+2=0

-20 2 complex -3[plus or minus] i [the square root of] 5 / 7

Simplify (4d^2t^5v^-4)(-5dt^-3v^-1)

-20d^3t^2 / v^5

Simplify -(4w^-3z^-5)(8w)^2

-256/wz^5

Find each product [-15. -9] [ 6. 11 23. -10 ]

-297 -75

Find all of the rational zeroes H(X) = 2x^3-7x^2-21x+54

-3,2,9/2

Find p(-2) and p(3) of each function P(X)=3x^3 -x^2+2x-5

-37; 73

Simplify (10+15i)-(48-30i)

-38+45i

(-6w^3z^4-3w^2z^5+4w+5z) / (2w^2z)

-3wz^3 -3z^4 /2 + 2 / wz + 5 / 2w^2

Preform the indicated operations 2. -1. -6. 9 3. 7. +. 7. -11 14. -9. -8. 17

-4 8 10 -4 6 8

Solve the equation by completing the square X^2 +6x+8=0

-4, -2

Find each value if f(X)=5 / X+2 and g(X) = -2x +3

-5 / 2

Solve each equation by using the square root property, round to the nearest hundredth X^2+8x+16=1

-5,-3

Simplify 6+5i / -2i

-5/2 +3i

Find the slope to the line that passes through each pair of points, express as a fraction in simplest form (3,-8),(-5,2)

-5/4

Solve the system 5x+9y+z=20 2x-y-z=-21 5x+2y+2z=-21

-7 6 1

Solve the equation by using the square root method X^2+10x+25=16

-9,-1

Find the value of the discriminant Describe the number and type of roots Find the exact solutions by using the quadratic formula 9x^2-24x+16=0

0 1 rational 4/3

Solve the equation, state the number and type of roots X^5-81x=0

0, -3, 3, -3i, 3i, (3 real, 2 imaginary)

Find all the rational zeroes F(X)=x^4-49x^2

0, -7, 7

Solve each equation, state the number and types of roots X^5-81x=0

0,-3,3, -3i, 3i, 3 real 2 imaginary

Solve the equation using the quadratic formula 3x^2-13x+4=0

1 / 3, 4

Simplify (X^-4)(x^-4)(x^4)

1 / x^4

Find the zeroes p(x)= x^3+9x-7

1, 1+i[the square root of]6, 1-i[the square root of]6

Solve the system D+3G+h=0 -d+2g+h=-1 4d+g-h=1

1,-1,2

Simplify (28-4i)-(10-30i)

18+26i

If p(X)=3x^2-4 and r(X)=2x^2-5x+1 find each value P(8a)

192a^2 -4

Find each product 2 4 -3 0 7 -1 X 2 5

2 20 -23 -5

Factor 8a^2+2a-6

2(4a-3)(a+1)

Find p(-2) and p(3) for the function P(X)= x^3-x^5

24; -216

Use synthetic substitution to find f(-3) and f(4) function F(X)=2x^4-3x^3+4x^2-2x+1

286, 377

Simplify 2h^4-h^3+h^2+h-3 / h^2-1

2h^2-h+3

Simplify 4p^4-17p^2+14p-3/2p-3

2p^3 +3p^2-4p+1

Simplify 4x^2 -2x+6 / 2x-3

2x + 2 + 12 / 2x-3

2x^2+3x-14 /X-2

2x+7

The area of the base of a rectangular box measures 2x^2+4x-3 square units. The height of the box measures X units. Find a polynomial expression for the volume of the box.

2x^3 + 4x^2 -3x units ^3

Solve the system of equations 5x+9y+z=20 2x-y-z=-21 5x+2y+2z=18

3 1 5

The equation y=2.54x gives the length y in centimeters corresponding to a length X in inches. What is the length in centimeters of a 1 foot ruler

30.48 cm

Solve by using the square root property (round to the nearest hundred) X^2-6x+9=5

3[plus or minus] [the square root of] 5

Solve each system by using the quadratic formula 4x^2-12x+7=0

3[plus or minus] [the square root of]2 / 2

Solve each equation using the quadratic formula 4x^2-12x+7=0

3[plus or minus][the square root of] 2 / 2

Simplify 6k^2m-12k^3m^2+9m^3 / 2km^2

3k/ m - 6k^2 + 9m/ 2k

Simplify 15r^10-5r^8+40r^2 / 5r^4

3r^6-r^4+8 / r^2

Write a quadratic equation in standard form with the given roots 1/3, 2

3x^2-7x+2 =0

Simplify (6y^2-5y-15)(2y+3)^-1

3y-7+6/2y+3

Simplify (2 / 3r^2t^3z^6)^2

4 / 9r^4t^6z^12

Simplify (-3i)(4i)(-5i)

60i

Solve the equation by completing the square X^2-14x+19

7 [plus or minus] [the square root of] 30

Solve each equation by using the quadratic formula X^2-14x+53=0

7 [plus or minus]2i

The length of a rectangle is 2 feet more than its width. Find the dimensions of the rectangle if it's area is 63 squad feet

7 ft by 9 ft

Find the X intercept and the y intercept of the graph of each equation, then graph the equation by using the intercepts 2x+7y=14

7,2

Simplify 3-i/ 2-i

7/5+1/5i

The height of a square pyramid is 3 meters shorter than the sides of ifs base. If the volume of the pyramid is 432 m^3, how tall is it? Use the formula v=1/3Bh

9 m

Simplify (4a^3-8a^2+a^2)(4a)^-1

A^2-2a+a / 4

The formula d=0.05s^2+1.1s estimates the minimum stopping distance d in feet for a car traveling s miles per hours. If a car stops in 200 feet, what is the fastest it could have been traveling when the driver applied the breaks

About 53.2 mi/h

Solve X^2+2x+1[is greater than or equal to]0

All real numbers

solve the inequality x^2+14x+49[is greater than or equal to] 0

All real numbers

Write a polynomial function of least degree with integral coefficients that has the given zeroes -1,4,3i

F(x) = x^4 -3x^3+5x^2-27x-36

Simplify F^2+7f+10 / f+2

F+5

A bicycle maker sold 300 bicycles last year at a profit of $300 each. The maker wants to increase the profit margin this yea, but predicts that each $20 increase in profit will reduce th number of bicycles sold by 10. How many $20 increases in profit can the maker add in and expect to make a total profit of at least $100000

From 5 to 10

Graph Y [is greater than] |x| -1

GRAPH

Graph each function Y=2x^2-2x+1

GRAPH

Solve the system of inequalities X [is greater than] -2 2y[is greater than or equal to] 3x+6

GRAPH

Graph each system of inequalities, name the coordinates of the vertices of the feasible region, find the maximum and the minumum values, x[is greater than or equal to] 0, y[is greater than or equal to] 0, y[is less than or equal to] 6, y [is less than or equal to] -3x + 15 F(X,y) = 3x+y

Maximum 15 Minimum 0

Determine whether each function has a maximum or minimum value, and find that value. Then state the domain and range F(X)=-x^2+4x-1

Maximum 3 Domain all real numbers Range {f(x) | f(x)[ is less than or equal to] 3

Determine whether each function has a maximum of minimum value, find the value, and state the domain and range of the function F(X)=x^2-6x+14

Minimum 5 Domain all real numbers {f(x)|f(x) [is greater than or equal to] 5

Determine whether the function has a maximum or a minimum, state the value, and state the domain and range of the function F(X)= x^2-6x+14

Minimum 5 Domain all real numbers Range {f(x) | f(x) [is greater than or equal to]5

Use the related graph of each equation to determine its solutions 3x^2+X +3=0

No real solutions

Solve each system of equations 2g+3h-8j=10 G-4h=1 -2g-3h+8j=5

No solution

Simplify t^9(t^-8)

T

Describe the translation of the function Y=x^2-3

Translated 3 units down

Given a polynomial and one of its factors, find the remaining factors of the polynomial X^3+5x^2-2x-24; X-2

X+3, X+4

Write a quadratic equation in standard form with the given roots -7,-8

X^2+15x+56=0

Write a quadratic equation in standard form with the given roots -5, 8

X^2-3x-40=0

Simplify (X^4-3x^3-11x^2+3x+10) / (X-5)

X^3 +2x^2-X-2

Write the equation in vertex form, identify the vertex, axis of symmetry, and direction of the opening Y=-4x^2+8x

Y= -4(X-1)^2 +4 (1,4) X=1 Down

Write an equation in slope-intercept form for the line that satisfies each set of conditions Parallel to y=2/3x-10, X intercept at 9

Y= 2/3x-6

Write an equation for a parabola with a vertex at (1,3) that passes through (-2,-15)

Y=-2(X-1)^2+3

Write an equation for a parabola with a vertex at (-3,0) that passes through (3,18)

Y=1/2(X+3)^2

Find the product 1 [4. 0. 2 ]. X 3 -1

[2]

Solve 5n^2+35=0

[plus or minus] i [the square root of] 7

List all possible rational zeroes of each function S(X)=x^4-8x^3+7x-14

[plus or minus]1, [plus or minus]2, [plus or minus]7, [plus or minus]14

Solve the equation using the quadratic formula 3x^2=-54

[plus or minus]3i[the square root of] 2

Solve -x^2+5x-7[is less than of equal to] 0

all real numbers

Solve the equation by factoring 7x^2=4x

{0, 4/7}

Solve each equation by factoring X^2-6x+8=0

{2,4}

9x^2+31x+12[is less than or equal to] 0

{x| -3[less than or equal to] X [less than or equal to] -4/9