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how long would it take to get 10 miles going 175 miles per hour
applying the "distance formula":
d = rt
10 = 175t
10/175 = t
0.0571 hours = t
or
3.43 minutes = t

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a pipe can fill a pool in 8 hours another pipe fill in 12 hours. if both pipes are applied to fill pool than how many hours it will take???
.
Let x = time (hrs) it takes for both
then
x(1/8 + 1/12)= 1
multiplying both sides by 96:
x(12 + 8)= 96
x(20)= 96
x = 4.8 hours
or
x = 4 hours and 48 minutes

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it takes carolyn 4 hr to type a final exam. it takes Elise 3 hr to do the same job. How long would it take them, working together, to do the typing?
.
Let x = time (hours) it takes for both
then
x(1/4 + 1/3) = 1
multiplying both sides by 12:
x(3 + 4) = 12
x(7) = 12
x = 12/7
x = 1.7 hours
or
x = 1 hour and 43 minutes

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What Is The Slope Of A Line parallel to y = -2/5x + 4/5
.
Two lines are parallel if it has the same slope.
because
y = -2/5x + 4/5
is in "slope-intercept" form:
y = mx + b
we see that the slope is -2/5
.
Answer: -2/5

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2 log 1
Since log(1) = 0
we have
2*0
so, the whole thing is equal to
0

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9x^4-18x^2+5=0
rewrite as:
9x^4-15x^2-3x^2+5=0
group terms:
(9x^4-15x^2)-(3x^2-5)=0
3x^2(3x^2-5)-(3x^2-5)=0
(3x^2-5)(3x^2-1)=0
.
x = {sqrt(5/3), sqrt(1/3)}
rationalize denominators:
x = { , }

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An-Mei owns a business making and selling jackets. She has a fixed cost of $1190. It costs $92 to produce each jacket. The selling price is $109 per jacket. Let x represent the number of jackets produced and sold and write the cost function, C, and revenue function, R.
.
Cost Function:
C(x) = 92x + 1190
.
Revenue function:
R(x) = 109x - (92x + 1190)
R(x) = 17x - 1190

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Use the given conditions to write an equation for the lone in point-slope form slope=6/7, passing through (7,3)
.
"Point-slope" form is:
y - y1 = m(x - x1)
plugging in the given information:
y - 3 = (6/7)(x - 7)

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ln(x) + 8ln(y)
ln(x) + ln(y^8)
ln(xy^8)

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Yes

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3a + 4b=b
subtracting b from both sides:
3a + 3b=0
multiplying both sides by 2:
6a + 6b=0
.
Answer: 'a'

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Write the slope intercept equation for the line that passes through (-9,-5) and has a slope of 2/9.
.
use "point-slope" form:
y - y1 = m(x - x1)
y - (-5) = (2/9)(x - (-9))
y + 5 = (2/9)(x + 9)
y + 5 = (2/9)x + 2
y = (2/9)x + 2 - 5
y = (2/9)x - 3

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ln(2x-3)=4
2x-3=e^4
2x=e^4 + 3
x = (e^4 + 3)/2
x = 28.799

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The domain specifies all values that makes sense for 'x'.
You only have to eliminate numbers that drives the denominator to zero.
x^2+x-6 = 0
(x-3)(x+2) = 0
x = {-2,3} (these are the numbers that must be eliminated)
.
thus the domain (in interval notation) is
(-oo, -2) U (-2,3) U (3, +oo)
where
oo is infinity

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apply Pythagorean theorem
Let d = diagonal
then
d^2 = 16^2 + 30^2
d^2 = 256 + 900
d^2 = 1156
d = 34 feet

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the supplement of an angle is 6 times its complement. Find an angle ?
.
Let x = the angle
then
90-x = the complement
180-x = the supplement
.
180-x = 6(90-x)
180-x = 540-6x
180+5x = 540
5x = 360
x = 72 degrees

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"no slope" describes a horizontal line
whereaas
"undefined slope" describes a vertical line

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I am thinking of two consecutive even integers. The sum of their squares is 340. what are the integers?
.
Let x = first of two consecutive even integers
then
x+2 = second even integer
.
x^2 + (x+2)^2 = 340
x^2 + (x+2)(x+2) = 340
x^2 + x^2+4x+4 = 340
2x^2+4x+4 = 340
x^2+2x+2 = 170
x^2+2x-168 = 0
(x+14)(x-12) = 0
x = {-14, 12}
.
solution:
the two integers are
12 and 14
or
-12 and -14

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Yes.
(y-8)(y+3)

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A 2005 Honda minivan can travel 240 miles in the city on 4 gallons of gas. Find the amount of gas required for 360 miles of city driving. (hint: use a proportion).
.
Let x = amt of gas (gallons) used to drive 360 miles
then
240/4 = 360/x
cross multiplying:
240x = 4(360)
240x = 1440
x = 6 gallons

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An angle is equal to eight times its complement. Determine its measure.
.
Let x = the angle
then
90-x = complement of angle
.
x = 8(90-x)
x = 720-8x
8x = 720
x = 90 degrees

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25 * 8 = 200 square feet

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It means that you leave your answer in the form of a fraction or radicals (square root symbol) -- instead of a decimal answer.

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An Airplane travels in 5hrs. with a speed of 50km/hr. How far does it travel?
.
Distance formula:
d = rt
d = 50*5
d = 250 km

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the diagonal of a square is 24 centimeter.how long is the side of the square
.
apply Pythagorean theorem:
Let x = length of side of square
then
x^2 + x^2 = 24
2x^2 = 24
x^2 = 12
x = sqrt(12)
x = sqrt(2*2*3)
x = 2*sqrt(3) centimeters (exact answer)
.
Or, decimal approx:
x = 3.46 centimeters

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(9-z)/(z-9)
notice if I factor out a -1 from the numerator I get:
-1(-9+z)/(z-9)
then, if I reorder the terms inside the parenthesis:
-1(z-9)/(z-9)
Now, I can cancel like-terms leaving:
-1

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Hello and thank you so much for your help.I got this function 7-6x-x^2=0 it's a parabola that crosses the x-axis on the points -7.0 and 1.0, the vertex it's at the point (-3.0,16). I need to find the equation of the axis of symmetry for this parabola. Thank you again and have a happy 4th of July.
.
You can derive the axis of symmetry from the vertex and "inspecting" the original equation.
First,
Determine whether it is a "vertical" or a "horizontal" parabola. If your equation has a x^2 term -- it is a "vertical" parabola.
Second,
Once you know this, then you can simply use the x-coordinate of the vertex. So, the axis of symmetry is then
x = -3 (vertical line crossing the x-axis at -3)
.
Note:
the axis of symmetry is also derived by:
-b/(2a)
where
'a' and 'b' are the coefficients of the original equation

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ab= 6b + cd (Solve for a)
divide both sides by b:
(ab)/b= (6b + cd)/b
a = (6b + cd)/b
a = 6 + cd/b

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there are 9 books 55% of 9 books are out,how many are left? solve this problem using a proportion show all steps.and explain
.
since 55% are out
100-55 = 45% are left
.
Let x = books left
then
x/9 = 45/100 (this is your proportion)
cross multiplying:
100x = 9*45
100x = 405
x = 4.05
since you can't have fractional book, you have to round down:
there are 4 books left

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How many hours will it take to travel 130 miles at 70 miles per hour?
Apply the "distance formula"
d = rt
where
d is 130
r is 70
.
130 = (70)t
130/70 = t
1.86 hours = t
or
1 hour and 51 minutes