You can put this solution on YOUR website!
Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the
circle.
x^2+y^2+8x+2y+8=0
**
Standard form of equation for a circle: , (h,k)=(x,y) coordinates of center, r=radius.
x^2+y^2+8x+2y+8=0
complete the square
x^2+8x+y^2+2y+8=0
(x^2+8x+16)+(y^2+2y+1)=-8+16+1
Equation:

..
r^2=9
radius=3
..
center:(-4,-1)
..
x-intercepts:
set y=0
(x+4)^2+1=9
(x+4)^2=8
x+4=±√8
x=-4±√8
x≈-6.83
or
x≈-1.17
..
See graph below:
y=±(9-(x+4)^2)^.5-1

You can put this solution on YOUR website!
For the given equation, list the intercepts and test for symmetry.
y=x^3-512
**
x-intercept
set y=0
x^3-512=0
x^3=512=8^3
x=8
..
y-intercept
set x=0
y=0-512=-512
..
symmetry: none
see graph below:

You can put this solution on YOUR website!
Write the equation of a parabola that as a vertical axis and passes through the origin, (3,-2), and (-2,2).
**
Standard form of parabola with vertical axis of symmetry: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of vertex.
For given parabola:
h=0
equation:
y=Ax^2+k
use given coordinates, (3,-2) and (-2,2), to solve for A and k
..
-2=3^2A+k
2=(-2)^2A+k
..
-2=9A+k
2=4A+k
subtract
5A=-4
A=-4/5
k=2-4A
=2-4*-4/5
=2+16/5
=10/5+16/5
=26/5
equation: y=-4x^2/5+26/5

You can put this solution on YOUR website!
a car covers the first half of the distance between two places at a speed of 40km/hr and second half at 60 km/hr . calculate the average speed of the car
**
let x=total distance between the 2 places
ave speed=distance/travel time
..
travel time=distance/speed
=(x/2)/40+(x/2)/60
=x/80+x/120
=(80x+120x)/(80*120)
=200x/9600
..
ave speed=x/(200x/9600)=9600/200=48
average speed of the car=48 km/hr

You can put this solution on YOUR website!
Write the equation of a circle that has the center on the x-axis, a radius of 1, and passes through the point (((square root of 2)/2),((square root of 2)/2)).
**
Equation of a circle: , (h,k)=(x,y) coordinates of center, r=radius
For given circle:
r^2=1
r=1
k==0
equation:
(x-h)^2+y^2=1
solve for h using coordinates of given point (√2/2, √2/2)
(√2/2-h)^2+(√2/2)^2=1
2/4-√2h+h^2+2/4=1
h^2-√2h+1=1
h^2-√2h=0
h(h-√2)=0
h=0 (reject, does not check)
h=√2
Equation: (x-√2)^2+y^2=1

You can put this solution on YOUR website!
log[2](4)+3x=6
log(4),base 2=2
2+3x=6
3x=4
x=4/3

You can put this solution on YOUR website!
factor 25g^6 -10g^3 +1
set equation=0
25g^6 -10g^3 +1=0
let u=g^3
u^2=g^6
..
25u^2-10u+1=0
(5u-1)(5u-1)=0
u=1/5 (multiplicity 2)
u=1/5=g^3
raise both sides to 1/3 power or take cube root of both sides
g=5^(-1/3)
g≈0.5848...
two factors are: irrational number 0.5848...(multiplicity 2)
The other four factors are 2 pairs of non-real or imaginary numbers)

You can put this solution on YOUR website!
The area (in square inches) of a rectangle is given by the polynomial function A(p)= p^2 +11p+ 18. If the lenght of the rectangle is (p+2) inches. What is the width
**
Area=length*width
Area/length=width
(p^2 +11p+ 18)/(p+2)
=(p+9)(p+2)/(p+2)
width=(p+9)

You can put this solution on YOUR website!
This is a mixture of inequalities and absolute values.
Solve the following absolute value in equalities:
|x+1| is less than or equal to |x-3|
**
|x+1|≤|x-3|
solve for 2 conditions:
x+1≤x-3
1≤-3 (reject, not true)
..
x+1≤-x+3
2x≤2
x≤1
solution: (-∞,1]

You can put this solution on YOUR website!
√(288 x^7 y^3)
=√(144*2*x^6*x*y^2*y)
=12x^3y√2xy

You can put this solution on YOUR website!
60 ml of solution A is mixed with 120 ml of solution B to produce solution C which contains 8% of pure acid. If 80 ml of solution A is mixed with 40 ml of solution B, a solution D containing 10% of pure acid can be produced. Find the percentage of pure acid in solution A.
**
let x=% acid in solution A
let y=% acid in solution B
2 equations:
60x+120y=.08(60+120)=.08(180)=14.4
80x+40y=.10(80+40)=.10(120)=12
..
60x+120y=14.4
80x+40y=12
..
60x+120y=14.4
240x+120y=36
subtract
-180x=-21.6
x=21.6/180=.12
40y=12-80x=12-.12*80=2.4
y=2.4/40=.06
percentage of pure acid in solution A=12%

You can put this solution on YOUR website!
A tennis ball is thrown with an initial upward velocity of 64 feet per second. How long will it take for the ball to hit the ground? Use the formula in which the height above ground after t seconds is given by the quadratic function h = vt – 16t^2, where h represents the height of the object in feet, and v represents the object's initial velocity in feet per second.
The answer is supposed to be in seconds, but I am not at all sure how to get there.
**
When the ball hits the ground,
h=0
vt–16t^2=0
64t-16t^2=0
..
t(64-16t)=0
t=0 (reject, not reasonable)
or
64-16t=0
16t=64
t=64/16=4
How long will it take for the ball to hit the ground? 4 seconds

You can put this solution on YOUR website!
Simplify the following expressions:
log36 - log3 + log2
log[36*2/3]=log[24]
..
6 X log2 - 2 X log4
log2^6-log4^2
=log[2^6/4^2]
=log[64/16]
=log[4]

You can put this solution on YOUR website!
The atmospheric pressure (measured in millibars and given the symbol P) decreases with height (h, in miles) according to:
P = 29.92xe^(-h/5)
..
a) Find the pressure at a height of 4 miles.
P=29.92*e^(-4/5)≈13.44 millibars
..
b) At what height (in miles) is the atmospheric pressure 10 millibars?
10=29.92*e^(-h/5)
10/29.92=e^(-h/5)
take log of both sides
ln(10/29.92)=-h/5 lne
lne=1
-h=ln(10/29.92)*5≈-5.48
h=5.48
Height at which the atmospheric pressure is 10 millibars=5.48 miles

You can put this solution on YOUR website!
I need help on the step by step process on how to analyze the graph of this following function ?



Because the degree of the numerator is one degree higher than that of the denominator,
function has a slant asymptote.
..
To find the equation of the slant asymptote, divide denominator by numerator.
By inspection, you can see you will get x+remainder. You can ignore the remainder.
equation of the slant asymptote: y=x
..
x-intercept:
set R(x)=0
x-5=0
x-intercept=5
..
y-intercept:
set x=0
-125/-49≈2.55
y-intercept≈2.55
..
vertical asymptotes:
set denominator=0
x=7
and
x=-7
..
number line:
<..-...-7...+....5....-....7....+.....>
The graph below shows the basic curve but I don't have the means to draw in the asymptotes.
However, it should be good guide how to graph the entire curve with asymptotes and all.

You can put this solution on YOUR website!
Use interval notation to express the solution set.
Solve
8<2x≤10
divide by 2
4 < x ≤ 5
number line
<......(4<==>5]...........>
solution: (4, 5]

You can put this solution on YOUR website!
Trenton sells electronic supplies.Each week he earns 190 dollars plus commission equal to 4% of his sales. This week his goal is to earn no less than 500 dollars. Write and solve an inequality to find the amount of sales he must have to reach his goal.
**
let x=amount of sales to reach his goal
4%x+190≥500
.04x≥500-190
.04x≥310
x≥310/.04
x≥7750
amount of sales to reach his goal≥7750

You can put this solution on YOUR website!
a bookstore currently sells 15 copies per week of a $20 book. For each $1 discount in price, the store can sell 3 more books.How many discounts will yield sales of $468 per week on this book.
**
let x=no. of $1 discounts
price of each book=20-x
no. of books sold=15+3x
(20-x)(15+3x)=468
300+45x-3x^2=468
3x^2-45x-300+468=0
3x^2-45x-168=0
x^2-15x-56=0
(x-8)(x-7)=0
x=8
or
x=7
No. of $1 discounts that will yield sales of $468 per week: 7 and 8

You can put this solution on YOUR website!
Find the equation of the line containing the point (-3, -12) and having a slope of -4.
**
Standard form of equation for a line: y=mx+b, m=slope, b=y-intercept
y=-4x+b
solve for b using coordinates of given point (-3,-12)
-12=-4*-3+b
b=-24
equation: y=-4x-24

You can put this solution on YOUR website!
5x+17>-2x-4
5x+17≥2x-4
3x≥-21
x≥-7
solution in interval notation:
[-7,∞)

You can put this solution on YOUR website!
Write an equation of an ellipse with center (2, 12), vertical major axis of length 18, and minor axis of length 4
**
Standard form of equation for an ellipse with vertical major axis:
, a>b, (h,k),=(x,y) coordinates of center
center: (2,12)
length of vertical major axis=18=2a
a=9
a^2=81
length of minor axis=4=2b
b=2
b^4
Equation:

You can put this solution on YOUR website!
The questions is to Find the volume. Use 31.4 as the approximate value of pie.
Round answers to the nearest tenth.
Its a cylinder with top 7m and height 11m
Which is the correct answer;
A)423.1m
B)120.9m
C)241.8m
D)1,692.5m
**
volume=area of top*height
=3.14*(7^2/4)*11=423.1
correct ans:
A)423.1m

You can put this solution on YOUR website!
Rationalize the denominator. Assume that all expressions under radicals represent positive numbers.
a√-√b over √a+√b
I assume you meant to write it this way:
√a-√b over √a+√b
=(√a-√b)/(√a+√b)
multiply top and bottom by (√a-√b) (conjugate of (√a+√b))
=(√a-√b)^2/ (√a-√b)*(√a+√b)
=(√a-√b)^2/ (a-b)

You can put this solution on YOUR website!
you have a piece of wood that is 84 inches long. you cut the wood into 3 pieces. the 2nd piece is 8 inches longer than the first piece. the 3rd piece is 16 inches longer than the second piece. write an equation and then solve it to determine the lengths of the 3 pieces.
**
le x=length of 1st piece
x+8=length of 2nd piece
x+8+16=x+24=length of 3rd piece
..
x+(x+8)+(x+24)=84
3x+32=84
3x=84-32=52
x=52/3=17+1/3
x+8=25+1/3
x+24=41+1/3
..
length of 1st piece=17+1/3 in
length of 2nd piece=25+1/3 in
length of 3rd piece=41+1/3 in

You can put this solution on YOUR website!
Write the slope-intercept form of the equation (5,2) and (-5,6)
**
This is an equation of a straight line.
Its standard form: y=mx+b, m=slope, b=y-intercept
slope=∆y/∆x=(6-2)/(-5-5=4/-10=-4/10=-2/5
equation of line: y=-2x/5+b
solve for b using one of given points(5,2)
2=-2*5/5+b
2=-2+b
b=4
Equation:
y=-2x/5+4

You can put this solution on YOUR website!
A ball is tossed from a window that is 10 feet off the ground. The height, h (in feet), of the ball at any time, t (in seconds), is given by the equation h = - 16 t^2 + 12x + 10. What is the maximum height (in feet) that the ball will reach?
**
h = - 16 t^2 + 12x + 10
This is an equation of a parabola that opens downwards (function has a maximum)
Its standard form: y=(x-h)^2+k, (h,k)=(x,y) coordinates of vertex, k=maximum value
complete the square
h=-16(t^2-(12/16)t)+10
=-16(t^2-(3/4)t)+10
=-16(t^2-(3/4)t+9/64)+9/4+10
=-16(t-(3/8)^2+9/4+40/4
h=-16(t-(3/8)^2+49/4
maximum height that the ball will reach=12.25 ft

You can put this solution on YOUR website!
Find the minimum value for the function:
y = x^2 + 9x + 18
This is an equation of a parabola that opens upwards (function has a minimum)
Its standard form: y=(x-h)^2+k, (h,k)=(x,y) coordinates of vertex, k=minimum value
complete the square
y=(x^2+9x+20.25)+18-20.25
y=(x+9/2)^2-2.25
minimum value=-2.25

You can put this solution on YOUR website!
3sqrt(27(x+3))^3
3√[27(x+3)]^3
=3*(27(x+3))^3/2

You can put this solution on YOUR website!
Rationalize the denominator in the following expression
sqrt(75a^3/(2b)
=√(75a^3)/√2b
=√2b/√2b*√(75a^3)/√2b
=√2b*√(75a^3)/2b
=[5a√(5a*2b)]/2b
=[5a√(10ab)]/2b

You can put this solution on YOUR website!
Ten grams of Uranium will decay to 2.5 g in 496,000 years. What is its half-life?
**
Formula for radioactive decay: A/Ao=2^-t/h, A=radioactive material present at time t, Ao=amt present initially, h=material half life.
2.5/10=2^-4.96*10^5/h
.25=2^-4.96*10^5/h
take log of both sides
log.25=-4.96*10^5/h)log2
h(log.25)=-(4.96*10^5)log2
h=-(4.96*10^5)log2/log.25=-2.48*10^5
..
half-life of material=2.48*10^5 yrs

You can put this solution on YOUR website!
A total of 925 tickets were sold for a game for a total of $2,495. if adult tickets sold for $5.00 and childrens sold for $2.00, how many of each kind of ticket were sold?
**
let x=no. of adult tickets sold
925-x=no. of children tickets sold
..
5x+2(925-x)=2495
5x+1850-2x=2495
3x=2495-1850=645
3x=645
x=215
925-x=710
..
no. of adult tickets sold=215
no. of children tickets sold=710
..
you could have continued with your solution by noting that:
a+c=925
c=925-a