Solve the equation.(y - 11) - (y + 10) = 4y
y=-21/4
((7x+7)/5)+((6x-2)/2)=-1
x=-7/22
Find the midpoint of the line segment with the given endpoints.(2, -9) and (-1, 6)
(1/2, -3/2)
Determine the equation of the line described.
Put answer in the slope-intercept form, if possible.Through (5, -3), perpendicular to -7x - 3y = -44
y=(3/7x)-(36/7)
Write the number in scientific notation.0.0000088316
8.
8316 x 10^-6
Write the statement using absolute value notation.The distance between y and -8 is greater than 3.
|y+8|>3
Find the slope of the line through the pair of points.(6, -2) and (4, -2)
Find an equation for the circle.Center (0, -6), radius 11
x^2+(y+6)^2=121
Write the number in decimal form.3.
971 × 10-5
0.00003971
Solve the equation.(x+7)/8 = (x+8)/9
x=1
Write the expression in standard form.i/(2+i)
1/5 +2/5i
Solve the equation graphically by finding x-intercepts.x3 - 6x2 + 12x - 10 = 0
x=3.26
Solve the inequality algebraically.
Write the solution in interval notation.|x+3| <= 6
[-9,3]
Write the product in standard form.(6 + 4i)( 7 - 3i)
54+10i
A rock falls from a tower that is 132.3 m high. As it is falling, its height is given by the formula h = 132.3 - 4.
9t2.How many seconds will it take for the rock to hit the ground (h=0)?
5.2 s
Solve the equation using the quadratic formula.7x2+8x = -2
x=(-4+rad2)/7 or x=(-4-rad2)/7
Write the sum or difference in the standard form a + bi.( 8 + 4i) - ( -9 + i)
17+3i
Solve the equation.x2- 6x + 34 = 0
3+-5i
Solve the equation by factoring.
6x2 - 29x - 5 = 0
x=-1/6 or x=5
Use a method of your choice to solve the equation.|2x-9|=4
x=5/2 or x=13/2
Identify intervals on which the function is increasing, decreasing, or constant.g(x)=0.5(x+6)^2
Increasing: (-6, infinity); Decreasing: (-infinity, -6)
Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. y = 2x - x3
unbounded
Determine algebraically whether the function is even, odd, or neither even nor odd.
f(x) = 8x4 + 5x + 4
neither
Find the domain of the given functionf(x)=x/(x-3)
(-infinity, 3) U (3, infinity)
Find the asymptotes of the given function.h(x)= ((x-1)(x+5))/(x^2-4) vertical asymptotes
x=2, x=-2
Find the range of the function.f(x)=rad(8+x)
[0,infinity)
Use an equation to solve the problem.One positive number is twice another positive number. The sum of the two numbers is 360.
Find the two numbers.
120,240
Find functions f and g so that h(x)=f(g(x))y=|8x+3|
f(x)=|x|, g(x)=8x+3
Find the inverse of the functionf(x)=6/(x+3)
f^-1(x)=6/x -3
Describe how to transform the graph of f into the graph of g.f(x)= radx and g(x)=-rad(x+6)
Shift the graph of f left 6 units and then reflect across the x-axis.
Perform the requested operation or operations.
Find the domain of each.f(x)=6x+8; g(x)=3x^2find (fg)(x)
18x^3+34x^2; domain(-infinity, infinity)
Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression.
exponential regression
Perform the requested operation or operations.f(x)=rad(x+7); g(x)=8x-11
f(g(x))=2rad(2x-1)
Perform the requested operation or operations.f(x) = 7x + 14; g(x) = 4x - 1Find f(g(x)).
f(g(x))=28x+7
Find the inverse of the function.f(x)=x^3+7
f^-1(x)=^3rad(x-7)
Determine whether the power function is even, odd, or neither.f(x)=8x^(8/10)
neither
Find the vertex of the graph of the function.f(x) = 4x2 + 32x + 63
(-4,-1)
Determine if the function is a power function. If it is, then state the power and constant of variation.f(x)=-1/7x^2
Power is 2; constant of variation is -1/7
Write the statement as a power function equation.
Use k as the constant of variation.John kept track of the time it took him to drive to college from his home and the speed at which he drove. He found that the time t varies inversely as the speed r.
t=k/r
Find the axis of the graph of the function.f(x) = (x + 2)2 - 9
x=-2
Choose the one alternative that best completes the statement or answers the question.
Write an equation for the linear function f satisfying the given conditions.f(-1) = -5 and f(5) = 7
f(x)=2x-3
Divide f(x) by d(x), and write a summary statement in the form indicated.f(x) = x2 - 2x + 3d(x) = x - 4Write answers in polynomial form
f(x)=(x-4)(x+2)+11
Find the zeros of the function.f(x) = x3- 49x
0,7,-7
Find all of the real zeros of the function. Give exact values whenever possible.
Identify each zero as rational or irrational.f(x) = x3 + 4x2 - 5x - 20
-4(rational), rad5 (irrational), and -rad5 (irrational)
State how many complex and real zeros the function has.f(x) = x3 - 16x2 + 79x - 120
3 complex zeros; all 3 real
Find all rational zeros.f(x) = x3 - 3x2 - 4x + 12
2,3,-2
Find the remainder when f(x) is divided by (x - k)f(x) = 2x2 + 3x2 + 4x + 18k = - 2
6
Given k = 5 is a zero of f(x) = 5x3 + 6x2 + 2x + 4 , determine if k is an upper-bound.
yes
Find the zeros of the function.f(x) = x3 + 12x2 + 47x + 60
-5,-3,and -4
Solve the problem.In the following formula, y is the minimum number of hours of studying required to attain a test score of x:y=0.52x/(100.5-x)How many hours of study are needed to score 88?
3.66hr
Solve the polynomial inequality.(x + 10)(x + 1)(x - 3) < 0
(-?, -10) ? ( -1, 3)
Solve the inequality.(3x+4)/(7x^2+7)>0
(-4/3,?)
Solve the inequality.9/(x-4) > 7/(x-4)
(4,?)
Solve the polynomial inequality.x4 - 104x2 + 400 < 0
( -10, -2) ? ( 2, 10)
Solve the equation3/(x-4) = 1+5/(x+4)
x=6 or -8
