You can put this solution on YOUR website!
Given:
h = 224t - 16t^2
where
h is height in feet
t is time in seconds
.
To determine when the object hit the ground,
set h to zero (because zero is when the object is on the ground) and solve for t:
h = 224t - 16t^2
0 = 224t - 16t^2
0 = 14t - t^2
factoring the right side:
0 = t(14 - t)
setting each term on the right to zero we get:
t = {0, 14}
.
t=0 is when the object just started its flight
So,
t = 14 seconds (solution)

You can put this solution on YOUR website!
the model M = -0.711+206.6 is used to determine the maximum heart rate of M of and individual who is age A
solve for A
according to this model what is the age of and individual whose maximum heart rate is 155
.
M = -0.711A + 206.6
Where
M is "max heartrate"
A is age
.
M - 206.6 = -0.711A
(M - 206.6)/(-0.711) = A
(206.6-M)/(0.711) = A
.
Plug in 155 for M:
(206.6-155)/(0.711) = A
(51.6)/(0.711) = A
72.6 years old = A

You can put this solution on YOUR website!
Given:
h = -16t^2 + 149t
.
The time (t) when it reaches the "ighest" point would be at the "axis of symmetry":
t = -b/2a = -149/(2*(-16)) = -149/(-32) = 4.66 sec

You can put this solution on YOUR website!
The area of triangle T is 625 square inches. If the length of the base b is half the length of the altitude drawn to that base, then what is the length of the altitude?
.
Let x = altitude
then
x/2 = base
.
(1/2)base*height = area
(1/2)(x/2)x = 625
(x/4)x = 625
x^2/4 = 626
x^2 = 2504
x = 50 inches

You can put this solution on YOUR website!
Find three consecutive integers whose sum is -33.
.
Let x = 1st integer
then
x+1 = 2nd integer
x+2 = 3rd integer
.
x + x+1 + x+2 = -33
3x + 3 = -33
3x = -36
x = -12 (first integer)
x+1 = -11 (2nd integer)
x+2 = -10 (3rd integer)
.
The three integers are: -12, -11 and -10

You can put this solution on YOUR website!
Given:
h=-16t^2+s
Set
s to 300
and
h to 0
.
0=-16t^2+300
16t^2 = 300
t^2 = 18.75
t = 4.33 seconds

You can put this solution on YOUR website!
Express as a product.
log9 y^4
.
It would simply be:
Express as a product.
4log9 y

You can put this solution on YOUR website!
A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 546 pounds after processing, how many pounds did it weigh before processing?
(A) 191
(B) 355
(C) 737
(D) 840
(E) 1560
.
Let x = weight beofre processing
then
x - .35x = 546
x(1-.35) = 546
x(.65) = 546
x = 546/.65
x = 840 pounds

You can put this solution on YOUR website!
A businessman invested $12000 in two ventures. In one he made a profit of 8% and in the other he lost 4%. His net profit for the year was $120. How much did he invest in each venture.
.
Let x = amount invested at 8%
then
12000-x = amount invested at 4%
.
.08x - .04(12000-x) = 120
.08x - 480+.04x = 120
.12x - 480 = 120
.12x = 600
x = $5000 (amount invested at 8%)
.
amount invested at 4%:
12000-x = 12000-5000 = $7000

You can put this solution on YOUR website!





x={4, -4.5}
The negative solution is extraneous, throw it out leaving:
x = 4
.
Details of quadratic to follow:

Solved by pluggable solver: SOLVE quadratic equation with variable

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=289 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, -4.5. Here's your graph:

You can put this solution on YOUR website!
A 26ft. long ladder rest against a wall. The distance from the base of the wall to the bottom of the ladder is x. The height at which the ladder rest against the wall is x + 14. Find the distance, x, from the base of the wall to the bottom of the ladder.
.
Apply the Pythagorean theorem:
.
x^2 + (x+14)^2 = 26^2
x^2 + (x+14)(x+14) = 676
x^2 + (x^2+14x+14x+196) = 676
2x^2 + 28x + 196 = 676
dividing both sides by 2:
x^2 + 14x + 98 = 338
x^2 + 14x - 240 = 0
(x+24)(x-10) = 0
x = {-24, 10}
We can toss out the negative solution leaving:
x = 10 feet

You can put this solution on YOUR website!
x^3+x^2-20x=0
Start by factoring out what is common among all three terms:
x(x^2+x-20) = 0
Factor the expression inside the parenthesis:
x(x+5)(x-4) = 0
.
Set each term to zero, giving you:
x = (-5, 0, 4}

You can put this solution on YOUR website!
Apply the Pythagorean theorem:
.
Let d = length of diagonal
then
d^2 = 15^2 + 10^2
d^2 = 225 + 100
d^2 = 325
d = 18.028 m

You can put this solution on YOUR website!
If 9x^2 - y^2 = 0 then what is the positive value of the x/y ?
.
Notice, I can rewrite:
9x^2 - y^2 = 0
as
(3x)^2 - y^2 = 0
.
This is a "difference of squares", so I can factor as:
(3x-y)(3x+y) = 0
.
The positive value of x/y is then:
3x-y = 0
3x = y
x = y/3
x/y = 1/3 (this is your answer)

You can put this solution on YOUR website!
a glass factory has an order for 1000 glass paper weighs; each is to be form of a cube. if this order requires 8000 cubic inches of glass, what is the surface area of one of the paper weighs?
.
Let x = length of one side of the cube
then
x^3 is the volume of one cube
.
1000x^3 = 8000
x^3 = 8
x = 2 inches
.
Surface of one side of cube:
2^2 = 4 square inches
.
Since there are 6 sides to a cube, the surface area is:
6 * 4 = 24 square inches

You can put this solution on YOUR website!
2x^2+x=42+9x
moving all the terms to the left:
2x^2-8x=42
2x^2-8x-42=0
dividing both sides by 2:
x^2-4x-21=0
factoring:
(x-7)(x+3) = 0
.
x = {-3, 7}

You can put this solution on YOUR website!
if anna can paint a house in 4 hours and joe can paint a house in 6 hours. how long will it take them to do it together?
.
Let x = number of hours working together
then
x(1/4 + 1/6) = 1
multiplying both sides by 24:
x(6 + 4) = 24
10x = 24
x = 2.4 hours
or
x = 2 hours and 24 minutes

You can put this solution on YOUR website!
It takes my brother 15 min to clean one window. It takes me 20 minutes to clean one window. How long will it take us to clean 12 windows.
.
Let x = minutes to clean 12 windows together
the
x(1/15 + 1/20) = 12
multiplying both sides by 300:
x(20 + 15) = 3600
35x = 3600
x = 3600/35
x = 102.86 minutes

You can put this solution on YOUR website!
Lisa can shovel snow from her driveway in 35 minutes. Tom can do the same job in 55 minutes. How long would it take Lisa and Tom to shovel the driveway if they worked together?
.
Let x = minutes if they worked together
then
x(1/35 + 1/55) = 1
Multiplying both sides by 35*55:
x(55 + 35) = 35*55
x(90) = 35*55
x = 1925/90
x = 21.39 minutes

You can put this solution on YOUR website!
I've heard that tossing a coin into a fountain will bring me good luck, so I throw a silver dollar up with a velocity of 5m/sec. and it falls into the fountain 1.3 meters below my hand. How long is the coin in the air?
In this question i just really dont understand how to do quadratic equations when you dont have the acceleration unless its -9.8m/s squared, but really not sure.
.
Yes, gravity is your acceleration.
.
Applying the equation of motion:
h(t) = (1/2)gt + vt + vo
where
h(t) is height
g is gravity
v is initial velocity
t is time
vo is the initial height
.
h(t) = (1/2)(-9.8)t + 5t + 1.3
h(t) = -4.6t + 5t + 1.3
.
set h(t) to zero and solve for t:
0 = -4.6t + 5t + 1.3
applying quadratic formula we get:
t = {-0.217, 1.304}
we can throw out the negative solution leaving:
t = 1.3 seconds
.
Details of quadratic to follow:

Solved by pluggable solver: SOLVE quadratic equation with variable

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=48.92 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.216769932610683, 1.30372645434981. Here's your graph:

You can put this solution on YOUR website!
(6x^2-31x+5)/(x-5)
rewrite numerator as:
(6x^2-30x-x+5)/(x-5)
group terms:
[(6x^2-30x)-(x-5)]/(x-5)
factor:
[6x(x-5)-(x-5)]/(x-5)
factor:
[(x-5)(6x-1)]/(x-5)
canceling like-terms:
6x-11

You can put this solution on YOUR website!
Find the degree measure of an angle of 4.23 radians.
A. 62º B. 242º C. 118º D. 28º
.
since (pi) radians = 180 degrees
.
180/(pi) * 4.23
180/3.14 * 4.23
242.48 degrees
.
Closest answer B

You can put this solution on YOUR website!
what is the area of a triangle if the base is 16 m and the height is 3m?
.
area of any triangle is (1/2)bh
where
b is base
h is height
.
area = (1/2)bh
area = (1/2)(16)(3)
area = (8)(3)
area = 24 square meters

You can put this solution on YOUR website!
An oil tanker can be emptied by the main pump in 5hours. An auxillary pump can empty the tanker in 9 hours. If the main pump is started at 5PM, when should the auxillary pump be started so the tanker is emptied by 9PM?
.
From 5pm to 9pm is 4 hours...
.
Let x = number of hours to run aux pump
then
4(1/5) + x(1/9) = 1
4/5 + x/9 = 1
multiplying both sides by 45:
36 + 5x = 45
5x = 9
x = 9/5 hours
.
9/5 hour is the same as
9/5 * 60 = 108 minutes
1 hour and 48 minutes (time needed to run aux pump)
.
Time to start aux pump:
9 pm minus 1 hour and 48 minutes:
7:12 PM

You can put this solution on YOUR website!
The length of rectangle is 7 m less than twice the width. If the length is decreased by 1m and the width by 4 m, the perimeter will be 66. Find the dimensions of the original rectangle.
.
Let w = width
then
from: "length of rectangle is 7 m less than twice the width"
2w-7 = length
.
Length decreased by 1 m:
2w-7-1 = 2w-8
.
Width decreased by 4 m:
w-4
.
2(width + length) = perimeter
2(w-4 + 2w-8) = 66
dividing both sides by 2:
w-4 + 2w-8 = 33
3w-12 = 33
3w = 45
w = 15 meters (width)
.
length:
2w-7 = 2(15)-7 = 30-7 = 23 meters (length)
.
dimensions:
15 by 23 meters

You can put this solution on YOUR website!
how do you solve for (-2/3) raised to the power of -2
.

You can put this solution on YOUR website!
Two angles are supplementary. One angle has a measure that is five less than four times the other . What is the measure of the larger angle?
.
When two angles are supplementary, the sum of the two angles is 180 degrees.
.
Let x = one angle
then from: "One angle has a measure that is five less than four times the other"
4x-5 = second angle
.
x + 4x-5 = 180
5x-5 = 180
x-1 = 36
x = 37 deg
.
second angle:
4x-5 = 4(37)-5 = 148-5= 143 degrees (larger angle)

You can put this solution on YOUR website!
Starting with:
15-3n=-22
we subtract 15 from both sides:
15-3n-15 = -22-15
-3n = -37
divide both sides by -3:
n = 37/3 (this is your answer)
.
To check, we substitute back in:
15-3n=-22
15-3(37/3)=-22
15-37=-22
-22 = -22

You can put this solution on YOUR website!
Write the equation of the line that passes through (1, 3) and (4, 4) in standard form.
.
Standard form of a line:
Ax + By = C where A is a positive integer, and B, and C are integers
.
First, determine slope between the two points using:
m = (y2-y1)/(x2-x1)
m = (4-3)/(4-1)
m = 1/3 (slope)
.
Next, use one of the two points (1,3) and the slope (1/3) and plug it into the "point-slope" form:
y-y1 = m(x-x1)
y-3 = (1/3)(x-1)
multiplying both sides by 3:
3y-9 = x-1
subtracting x from both sides:
-x + 3y-9 = -1
adding 9 to both sides:
-x + 3y = 8 (this is what they're looking for)

You can put this solution on YOUR website!
an = a1 + (n – 1)d
additional info on arithmetic sequence:
http://www.mathwords.com/a/arithmetic_sequence.htm
.
What is the 30th term in the sequence 14,19,24,29?
arithmetic sequence:
a1 is 14
n is 30
d is 5
.
30th term is:
a1 + (n – 1)d
14 + (30 - 1)(5)
14 + (29)(5)
14 + (145)
159
.
What is the 69th term in the sequence 13,19,25,31?
a1 is 13
n is 69
d is 6
.
69th term is:
a1 + (n – 1)d
13 + (69 – 1)(6)
13 + (68)(6)
13 + 408
421

You can put this solution on YOUR website!
A barrel contains 30 gallons of 40% antifreeze. How many gallons of an 80% antifreeze solution should be added to make the barrel contain 50% antifreeze?
.
Let x = gallons of 80% antifreeze added
then
.40(30) + .80x = .50(30+x)
12 + .80x = 15 + .50x
12 + .30x = 15
.30x = 3
x = 10 gallons