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Write a linear function that expresses the distance treveled, d, as a function of time, t.
t=d/60
How far have you traveled after 4 hours?
d=60t
d=60(4)
d=240 miles
Write a linear function that expresses the distance to be traveled to reach San Francisco, s as a function of time, t.
t=480-60x where x is the hours you already traveled

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1. 5(x-3)+ 5= 3(x+2)-4 original
5x - 15 + 5 = 3x + 6 - 4 distribute
5x - 10 = 3x + 2
2x = 12
x = 6
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2. 3/4(x-2)+ 3/5= 1/5(x+1) original
(3/4(x-2)+ 3/5= 1/5(x+1))20 multiply the whole equation by 20 to delete fractions
15(x-2) + 12 = 4(x+1)
15x - 30 + 12 = 4x + 4
11x - 18 = 4
11x = 22
x = 2
...........................................
3. one-third of sum of a number and seven
For this equation, what does (1/3)(x+7) equal?

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1. ax + by = c Solve for x.
ax + by = c original
ax = -by + c subtract by from each side
x = (-by + c)/a divide each side by 'a'
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2. Four less nine times a number is one hundred twenty-two. Find the original number
9x-4=122 original equation
9x = 126 add four
x = 14 divide by nine on each side

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7n^5 + 7n^4 - 3n^2 - 6n - 3

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The second is just a lot like the first.
f(x)=(x+3)^2
f(-3)=(-3+3)^2
f(-3)=0
(B) is your second answer.

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(5^-1+x^-1)/(x^2-25^-1)
(5+x)^-1/(x^2-25^-1)
1/((5+x)(x^2-(1/25)))
1/(x^3-(x/25)+5x^2-(1/5))

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f(x) = 2x + 1
g(x) = x^2 - 4
........................................................................
(fg)(x)=(2x+1)(x^2-4)=2x^3+x^2-8x-4
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(g of f)(x) = (2x+1)^2 - 4
= (2x+1)(2x+1) - 4 = 4x^2 + 4x + 1 - 4 = 4x^2 + 4x - 3

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y/x=y/x
(-3)/(5)=y/(-10)
6=y

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(x+7)^(1/2)=(x+1)
(x+7)=(x+1)^2
x+7=x^2+2x+1
x^2+x-6=0
(x+3)(x-2)=0
x=-3 and x=2
If you plug in the -3, you get 2=-2 .... so -3 isn't an answer.
However, 2 is a right answer, so the answer is x=2.

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yx^(2)=yx^(2)
4(5^2)=y(2^2)
4(25)=y(4)
y=25

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g(x) = 3x + 2
f(x) = 2x^2 - 4x + 1
...............................................................
g(f) = 3(2x^2 - 4x + 1) + 2
g(f) = 6x^2 - 12x + 3 + 2
g(f) = 6x^2 - 12x + 5
................................
f[g(0)]=3(0) + 2=2
f(2)=2(4) - 4(2) + 1=1
................................
f[g(1)]=3(1) + 2=5
f(5)=2(25) - 4(5) + 1 = 50 - 20 + 1 = 31

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2e^(2x) = 5^(x+1)
e^(2x) = 5^(x+1)/2
2x = (x+1)ln(5)-ln(2)
2x = 1.6x + 1.6 - 0.69
0.4x = 0.91
x=2.275
The number is about 2.275
.............................................................................
log(x+1)-log(x)=2
log((x+1)/x))=2
(x+1)/(x)=100
x+1=100x
1=99x
x=(1/99)

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y=1/(x-2)
(-2,-.25),(-1,-.333333),(0,-.5),(1,-1),(2,undefined)
Since I do not know how to show this graph, just connect the dots on a cartesian coordinate plane. It should look like an exponential growth.

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a.) Write a linear function that expresses the distance traveled, d, as a function of time, t.
d=60t
b.) How far have you traveled after 4 hours?
d=60t
d=60(4)
d=240
c.) Write a linear function that expresses the distance to be traveled to reach San Francisco as a function of time, t.
t=480/s where s is your speed
d.) How far will I need to travel to reach San Francisco after I have traveled 3 hours?
480 - (3*60) = d
300=d

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distance from vertex to focus (p=1/4a units)
2=1/(4a)
8a=1
a=(1/8)
Directrix: y=-1
Latus Rectum: 1/(A) = (8) units long
use: y=a(x-h)^2+k where the vertex is (h,k)
y=a(x-2)^2-3 also, use the point(-2,-5)
-5=a(-2-2)^2-3
-5=a(-4)^2-3
-2=16a
a=(-1/8)
y=(-1/8)(x-2)^2-3

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4x^2 + y^2 - 8y + 4y + 4 = 0
4x^2 - 8x + y^2 + 4y = -4
4(x^2 - 2x) + (y^2 + 4y) = -4
4(x - 1)^2 + (y + 2)^2 = 4
((x - 1)^2) + ((y + 2)^2)/4 = 1
center (1,-2)
has a vertical major axis
a(length of major axis) = 2
b(length of minor axis) = 1
c^2 = a^2 - b^2
c^2 = 4 - 1
c = 3^(1/2) or -3^(1/2) length cannot be negative so the c is 3^(1/2)
foci: (1+3^(1/2),-2) and (1-3^(1/2),-2)

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a.)A(t)=500e^(-0.05t)
A(0)=500(1)
Initially, the amount was 500 grams.
b.)A(t)=500e^(-0.05t)
A(10)=500e^(-0.5)
Since I do not have a calculator with 'e', I'll let you solve the rest.
c.)250=500e^(-.05t) the end result is half of the initial (500) so (250)
.5 = e^(-.05t)
ln .5 = -.05t take the natural log of each side
(ln .5)/(-.05) = t
The time for half life of the radioactive element is about 13.86 days.

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(x+5)^2 + 4(y-4)^2 = 16 original
((x+5)^2)/16 + ((y-4)^2)/4 = 1 divide by 16 to get the side to equal 1
the major axis is the highest value (16)^(1/2)
the major axis is 4 units long, and the major axis is horizontal
the minor axis, on the other hand, is the lower value (4)^(1/2)
the minor axis is 2 units long
the center is found by: ((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1
where a is the length of the minor axis and b is the length of the minor axis and (h,k) is the center
the center is (-5,4)
...................................................................
To Graph: go to the point (-5,4) and make points 4 units left and right of that point....also, go 2 units up and down from the center....connect the dots (excluding the center) to make an ellipse

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-37-(-18)+5
-37+18+5
-37+23
-14

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N(t)=2000/(1+19e^-0.6t)
N(0)=2000/(1+19(1))
N(0)=2000/(20)
N(0)=100
Initially, 100 people were infected.
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N(t)=2000/(1+19e^-0.6t)
N(2)=2000/(1+19e^(-1.2))
I do not have a calculator on me, so I will let you solve the rest of the equation. Also, all you have to do is plug in the numbers into your calculator, and you will have it all solved. I'll let you finish.

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the equation for a circle is:
(x-h)^2 + (y-k)^2 = r^2 where center is (h,k) and r is the radius
with center (4,-3) and radius 5
(x - 4)^2 + (y + 3)^2 = 25
x^2 - 8x + 16 + y^2 + 6y + 9 - 25 = 0
x^2 + y^2 - 8x + 6y = 0

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3x – 2y = 6 original
3x - 2y + 2y = 6 + 2y add 2y to each side
3x = 6 + 2y combine
(3x)/3 = (6 + 2y)/3 divide each side by 3
x = 2 + (2/3)y

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-3x^4 + 4x^2 - 7x + 10 + 2x^3 - 6x^2 + 5x - 3
-3x^4 + 2x^3 - 2x^2 - 2x + 7

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4/(x+1) - 1/x = 1
multiply by x(x+1)
4x - x - 1 = x^2 + x
x^2 -2x + 1 = 0
(x-1)(x-1) = 0
x=1

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pi: real and irrational
all numbers are real, and pi doesn't repeat nor does it terminate .... so pi is irrational

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put into y=mx+b where m is the slope and b is the y-intercept
4x + y > 4
y > -4x + 4
slope is -4
y-intercept is 4
*The answer is all numbers higher than the line*

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 4/4 = 1. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/1 = 4. Slope is -4/1 = -4. Equation in slope-intercept form: y=-4*x+4.

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the numbers decrease as the x-values go lower....but the y-values never
are equal to or lower than 0 .... so it must be an exponential function!
use y=(a)(b^x)
y=(a)(b^x)
1=a(b^0)
a=1
so: y=b^x
4=b^1
b=4
so your final equation is:
y=4^x
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the domain and range are the same as in the graph as they are in your list
domain: all real number
range: y>0
sorry, I do not know how to plot an exponential growth equation to show you

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a.)the area fora circle is (1/2)(l)(w)
(1/2)(l)(w)=32
(1/2)x^2=32 the sides are equal
x^2=64
x = 8 or -8 a side cannot be negative so the sides are 8 inches while the
hypontenuse is (8192)^(1/2) which is about 90.5 inches
b.)((parallel + parallel)/2)h = area of trapezoid
((parallel + parallel)/2)h = 50
depends on what you want the length of the parallel lines
let us say that the top parallel line is 30 and the bottom parallel line is 20
(((20)+(30))/2)h = 50
(25)h = 50
h = 2

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the area of a parallelogram is the base times height
a=lh
here, we want to find h so:
h=a/l
h=(2x^2 + 9x + 4)/(2x + 1)
h=(x + 4)

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The equation to find the volume for a cone is: V=(1/3)(area of base)(height)
100=2(3.14)(x) where x is the radius for the cirmuference of the base
(100)/((2)(3.14))=x
the radius is about 15.92
V=(1/3)(area of base)(height)
V=(1/3)((15.92)^2(3.14))(14))
V=3,717.38 feet cubed

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Won't a circle fit all the required options.