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x/12 + 3x/12=4x/12=x/3

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1/m^4/3=16 negative sign in front of exponent means the reciprocal.
We must reverse the process to see what we started with.
1/x =16 substitute x for m^4/3
x=1/16 multiply each side by x/16
1/16^3=1/4096
1/4096^(1/4)=1/8
m=1/8
Check:
(1/8)^-4/3=8^4/3
8^(1/3)=2
2^4=16
Ed

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f(x)=sqrt(1/2x-1)
1/2x-1 can't be less than 0 because square root of a negative number is not a real number.
x must be 2 or greater
x[2,infinity)
Ed

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Ed

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L*w=A
2L+2w=P
.
L*w=926
Our 2nd formula uses the perimeter formula plus the extra fencing to divide the corral in quarters. We have to use 3 instead of 2 for the coeficients of L and w because of the extra fencing to divide the coral into 4ths. we also have to subtract 2 from L and w to account for the 1 m strip of land not used for the corral
3(L-2)+3(w-2)=190
3L-6+3w-6=190
3L+3w-12=190
3L+3w=190+12
3L+3w=202
.
A) L*w=926
B) 3L+3w=202
.
L=926/w
3(926/w)+3w=202 substitute 926/w for L
2778/w+3w=202
2778+3w^2=202w multiply each side by w to eliminate the fraction.
3w^2-202w+2778=0
Quadratic Formula (see below): w=19.26 m, w= 48.06
I made L= 48.06 m and w= 19.26 m
.
Ed

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=7468 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 48.0695984669789, 19.2637348663545. Here's your graph:

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Construc a right triangle with hight 10 and angle opposite the height of 5 deg.
You need to know the length of the line adjacent to the angle (running along the ground).
cot=adj/opp
cot(5)=a/10
a=cot(5)*10
a=114.301 km
Ed

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P(x)=-4x^3+x^2-2x+7, for x=-2.
.
-2 | -4 +1 -2 +7
=======>+8-18 40
--------------------
====>-4 +9-20+47
.
You are correct.
f(-2)=47
.
Ed

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domain: x[-5,5] otherwize the answers would be imaginary numbers.
range: y[0,5]
Ed

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5^(-3x+1)=15625
5^(-3x+1)=5^6 convert to the same base 5
-3x+1=6 use exponents only
-3x=6-1
-3x=5
x=-5/3
Ed

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B.
it is an equation because it has an equal sign with numbers or variables on both sides of it.
It is not linear because the variable is higher than the 1st power.
Ed

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The inequality is false.
No absolute can equal a negative number.
Ed

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x^3-9x=0
x(x^2-9)=0
x(x+3)(x-3)=0
x=0, x=-3, x=3
.
y^2-2y-24=0
(y-6)(y+4)=0
y=6, y=-4
.
Ed

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225000*.06*.6=$8100.

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( 13.0 - 2 3/8 ) + ( 1 1/2 ) / 1.125 x 1.75
Lets change them all to decimals.


I couldn't tell what the denominator was so I did it both ways.
Ed

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a-b/a+b = c-d/c+d
.
ac+ad-bc-bd=ac-ad+bc-bd multiply both sides by (a+b)(c+d) to eliminate fractions.
ad-bc=-ad+bc cancel off ac and bd
2ad=2bc add ad and bc to each side
ad=bc divide each side by 2
a/b=c/d divide each side by bd.
.
Ed

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93/3=31
3,31
Ed

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Let x=number of shares he bought. p=share price he paid
A) xp=1875
B) (p+4)(x-15)=1740
.
A) x=1875/p
B) px+4x-15p-60=1740 Expand
p*1875/p + 4*1875/p - 15p-60=1740 substitute 1875/p for x
1875+7500/p-15p-60=1740 cancel
1875p+7500-15p^2-60p=1740p multiply both sides by p to eliminate fraction.
-15p^2+75p+7500=0
15p^2-75p-7500=0
15(p^2-5p-500)=0
15(p-25)(p+20)=0
p= -20 is extraneous to this problem.
p=$25
x=1875/25= 75 shares Answer
Check:
60*29=$1740.
.
Ed

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All you have to do to answer the above questions is get both equations in the slope-intercept form: y=mx+b
m is the slope if m is different in each equation then the system is consistent and the system has an answer and the lines cross on the graph.
If m is the same number (including sign) in both equations:
I) If b is different in both equations then there is no answer and the graph shows parallel lines and the system is inconsistent.
II) if b is equal in both equations then the equations are equal and consistent and has an infinate number of answers.
.
y=2/3x
2x-y=-4...-y=-2x-4...y=2x+4
m=2/3 in the 1st equ. and 2x in the 2nd so they are consistent and there is a solution.

.
y=-x+2
3x+3y=6...3y=-3x+6...y=-x+2
These are the same equation. infinate number of answers.
.
x+y=4...y=-x+4
2x-y=-7...-y=-2x-7...y=2x+7
Has a solution
.
4x+2y=8...2y=-4x+8...y=-2x+4
2x+y=1...y=-2x+1
slopes are equal; b's are different.
inconsistent, parallel lines

.
Not hard at all, once you know how to do them, huh.
.
Ed

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a=b-1
b=c-1
d=e-1
e=f-1
b=d+e+f
.
d+e+f<10 So must be 1+2+3 or 2+3+4
b= 6 because if it were 9 then c would be 10
So, d+e+f=6
b=6
d=1
e=2
f=3
a=5
c=7
.
The number is: 567123
We didn't need the final clue.
Ed

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1) 5.24 kg
2) 11.017 L
3) 2405 cm
Ed

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I assume that the ladders bases are in the corner of the side opposite which they are leaning.
L=longest ladder, s=shortest
cos(L)=10/30=1/3
cos^-1(1/3)=70.53 deg
.
cos(s)=10/20=1/2
cos^-1(1/2)=60 deg
.
Now we have a triangle with a base of 10 and we know the three angles 70.5,60 and 49.47
a/sin(A)=b/sin(B)
10/sin(49.47)=b/sin(60)
10*sin(60)/sin(49.47)=11.39 ft (one of the sides)
.
Now if you draw a line from the angle of the ladders crossing perpendicular to the base we have the height (h) of the triangle.
It is opposite the 70.53 deg angle and the 60 deg angle. It forms two right triangles. The 11.39 side is the hypotenuse of one of the right triangles.
sin(70.53)=opp/11.39
opp=sin(70.53)*11.39=10.74 ft Answer
.
Ed

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5/2t-t=3+3/2t
5t-2t=6+3t multiply each side by 2 to eliminate fractions.
3t=6+3t
0=6
There is no solution. The equation is false.
Ed

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Since it is an equilateral triangle, all angles are 60 deg.
x+y=60
2x-y=60
--------add
3x=120
x=40 deg
y=20 deg
.
Ed

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m=3s+16 s=number of songs, m=number of megabytes
I assume part of a song can be recorded.
.
A) domain is all real numbers >= 0, range is all real numbers >= 16
.
B) 256=3s+16...3s=240...s=80
domain is all real numbers from: 0=< s <= 80
range is 16 to 256
.
C) 512=3s+16...3s=496...s=165 1/3
domain is all real numbers from: 0=< s <= 165 1/3
Range is 16 to 512
.
Ed

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Vertical assymptote is x when the denominator=0
Vertical assymptote= the line x= -3
Horizontal assymptote: since the degree of the polynomial is the same top and bottom it is the line
y intercept (when x=0) y=1/3
x intercept (when y=0): x=-1/2
Ed

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let g be the cost of the candy he gained on.
let L be the cost of the candy he lost on.
.
g+.2g=1.20
1.2g=1.20
g=1.20/1.2
g=$1.00
.
L-.2L=1.20
.8L=1.20
L=1.20/.8
L=$1.50
.
His cost for the 2 candies was $2.50 and he sold them for $2.40
His loss was 10 cents on the deal.
.
Ed

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I hope this helps.

Ed

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2x/3 were put on sale on tues.
2x/3*2/3=4x/9 were put on sale on wed.
4x/9=8
4x=72
x=72/4
x=18
Check:
1/3 of 18 were sold on mon.
12 were put on sale on tues.
2/3 of 12 were unsold so there was 8 left to be put on sale wed.
Ed

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5m*5m*5m=125m^3

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4 1/5 x 10/21 x 9/20
21/5 * 10/21 *9/20
=1/5 *10 *9/20
=2* 9/20
=9/10
Ed