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Linear-equations/339982: find the slope of a line (-9,5)and (9,5)m =
1 solutions

Answer 243657 by nyc_function(2733) on 2010-09-07 16:54:01 (Show Source):

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Let m = slope
m = (5 - 5)/(9 -(-9))
m = 0/(9 + 9)
m = 0/18
m = 0
The slope is zero.

The slope of a horizontal line. A horizontal line has slope 0 because all its points have the same y-coordinate.

Trigonometry-basics/339074: If csc theta = -5/4 and 180degrees < theta < 270degree, find tan theta
a. -4/3
b. 3/4
c. 4/3
d. -4/5
1 solutions

Answer 243655 by nyc_function(2733) on 2010-09-07 16:52:09 (Show Source):

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cosecant = hypotenuse/opposite
180 < theta < 270 tells me that we are in quadrant 3.
We form a right triangle in quadrant 3. The hypotenuse = -5 and the leg opposite the hypotenuse = 4. We are looking for the adjacent side of the right triangle.
Let A = adjacent side
A^2 + 4^2 = (-5)^2
A^2 + 16 = 25
A^2 = 25 - 16
A^2 = 9
sqrt[A^2] = sqrt[9]
A = 3
tangent = opposite side/adjacent
In quadrant 3, tangent is positive.
Answer: tan(theta) = 4/3...CHOICE (C).

Age_Word_Problems/339104:

paul's age is twice the peters age when pauls age as same as the peters age. sum of their ages is 42.find peters age?
1 solutions

Answer 243644 by nyc_function(2733) on 2010-09-07 16:37:50 (Show Source):

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Paul's age = 2x
Peter's age = x

2x + x = 42
3x = 42
x = 42/3
x = 14
Paul is 28 years old and Peter is 14 years old.

Geometry_Word_Problems/339035: If the area of a lawn is 360 square meters, and Dave cuts the lawn at the rate of 12 square meters a minute, what fraction of an hour does it take to cut his lawn?
a 1/6 b 1/4 c 1/3 d 1/2 e 2/3
1 solutions

Answer 243641 by nyc_function(2733) on 2010-09-07 16:34:42 (Show Source):

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(360/12) * (1/60) = 1/2
Choice (D) is the answer.

Unit_Conversion_Word_Problems/339954: If you travel 700ft every ten seconds. How many miles per hour are you traveling?
1 solutions

Answer 243639 by nyc_function(2733) on 2010-09-07 16:29:44 (Show Source):

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There are 3600 in one hour.
So, 10/3600 = (1/360) of an hour.
D = rt
D = distance
r = rate in mph
t = time (in hours)
700 = (1/360)r
700 divided by (1/360) = r
252,000 = r
The miles per hour is 252,000.
We now muct convert 252,000 feet per hour to miles per hour.
252000ft per hour / 5280ft per mile = 47.72727272... miles per hour
Understand?

Numeric_Fractions/339964: What is four ninths of 684?
1 solutions

Answer 243636 by nyc_function(2733) on 2010-09-07 16:23:37 (Show Source):

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4/9 times 684 = 304

Numeric_Fractions/339955: 9/4x=8
1 solutions

Answer 243634 by nyc_function(2733) on 2010-09-07 16:21:46 (Show Source):

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I am thinking that you meant to type (9/4x) = 8. If you meant (9/4)(x) = 8, then the answer is different.
Multiply both sides by 4x.
4x * (9/4x) = 4x * 8
9 = 32x
9/32 = x

logarithm/339800: Rewrite this statement as equivalent exponential equation.
log4 16=x

1 solutions

Answer 243435 by nyc_function(2733) on 2010-09-07 09:08:59 (Show Source):

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Use log_b (y) = x

Let b = 4
Let x = exponent
Let y = 16
4^(x) = 16

Got it?

Polynomials-and-rational-expressions/339810: Provide a radical expression for your classmates to simplify.
1 solutions

Answer 243427 by nyc_function(2733) on 2010-09-07 09:02:11 (Show Source):

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Here is a link with many radical expressions. Copy and paste to see your expressions.
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_radical_simplify.xml

Travel_Word_Problems/339812: A driver who drives at a speed of r mph for t hr will travel a distance d mi given by d = rt mi. How far will a driver travel at a speed of 60 mph for 5 hr?
1 solutions

Answer 243425 by nyc_function(2733) on 2010-09-07 09:00:46 (Show Source):

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Use D = rt.
Let r = 60 and t = 5
D = 60 * 5
D = 300 miles
Get it?

Linear-equations/339760: Find the slope and y-intercept (if possible) of the equation of the line algebraically: 3x+7=0
1 solutions

Answer 243424 by nyc_function(2733) on 2010-09-07 08:59:31 (Show Source):

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Let equation = y.
Then y = 3x + 7.
The slope is the number next to x or 3.
The y-intercept is the number without a letter or 7.
Get it?

Linear-equations/339781: 2x - 7 + 4x = 4x - 10
1 solutions

Answer 243423 by nyc_function(2733) on 2010-09-07 08:57:06 (Show Source):

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2x - 7 + 4x = 4x - 10
6x - 7 = 4x - 10
6x - 4x = -10 + 7
2x = -3
x = -3/2
Did you follow?
By the way, this is a linear equation not linear algebra. Linear algebra is advanced algebra required only for math and engineering majors after completing calculus 1, 2 and 3.

Pythagorean-theorem/339708: A cable 22 feet long runs from the top of a utility pole to a point on the ground 16 feet from the base of the pole. How tall is the utility pole?
1 solutions

Answer 243377 by nyc_function(2733) on 2010-09-06 22:44:39 (Show Source):

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Let h = height of utility pole
h^2 + b^2 = c^2
Let b = 16
Lett c = 22
h^2 + (16)^2 = (22)^2
Can you take it from here?
HINT: Solve for h

Equations/339041: 3+1(x-24)=462
1 solutions

Answer 243376 by nyc_function(2733) on 2010-09-06 22:41:17 (Show Source):

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3+1(x-24)= 462
3 + x -24 = 462
x - 21 = 462
x = 462 + 21
x = 483

Coordinate-system/339066: please help me solve this line c,d is(1,3)and,(4,-2) the slope is what
1 solutions

Answer 243375 by nyc_function(2733) on 2010-09-06 22:19:54 (Show Source):

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Let m = slope
m = difference of y coordinates/difference of x coordinates
m = (-2 - 3)/(4 - 1)
m = -5/3
The slope is -5/3

Divisibility_and_Prime_Numbers/339036: For which of the following values of N is 3N – 1 not a prime number?
(a) 1 (b) 2 (c) 3 (d) 4 (e) 6
1 solutions

Answer 243374 by nyc_function(2733) on 2010-09-06 22:17:34 (Show Source):

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A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1.
The only even prime number is 2. All other even numbers can be divided by 2.
We must replace N by every number on the list to find the one that does not yield a prime number.
Let N = 1, 2, 3, 4 and 6 individually in the given expression and simplify.
3N - 1
3(1) - 1 = 3 - 1 = 2...That's not it.
3N - 1
3(2) - 1 = 6 - 1 = 5...That's not it.
3N - 1
3(3) - 1 = 9 - 1 = 8...This is it! There is no need to go further with the process.
Understood?
The answer is CHOICE (C).

Signed-numbers/339660: Using only the number 5, 5 times in a equation to equal 13?
1 solutions

Answer 243373 by nyc_function(2733) on 2010-09-06 22:16:05 (Show Source):

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Any number raised to the zero power = 1.
Keep in mind that 5^0 = 1.
5 + 5 + 5^0 + 5^0 + 5^0 = 13
10 + 1 + 1 + 1 = 13
10 + 3 = 13
13 = 13
The equation is 5 + 5 + 5^0 + 5^0 + 5^0 = 13

Signed-numbers/339662: How do you use only the number 5, 5 times in a equation to equal 17?
1 solutions

Answer 243371 by nyc_function(2733) on 2010-09-06 22:13:59 (Show Source):

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Any number raised to the zero power = 1.
Keep in mind that 5^0 = 1.
5 + 5 + 5 + 5^0 + 5^0 = 17
15 + 1 + 1 = 17
15 + 2 = 17
17 = 17
The equation is 5 + 5 + 5 + 5^0 + 5^0 = 17

Age_Word_Problems/339652: john is 6 years older than jill 5 years ago john was 3 times as old as jill was then, form equation in x and solve it to find what age jill is now
1 solutions

Answer 243369 by nyc_function(2733) on 2010-09-06 22:10:41 (Show Source):

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John's age now = x + 6

Jill's age now = x

John's age 5 years ago = (x + 6) - 5

Jill's age 5 years ago = x - 5
====================================
(x + 6) - 5 = 3(x - 5)

x - 1 = 3x - 15

x - 3x = -15 + 1

-2x = -14

x = -14/-2

x = 7

Jill is 7 year old.

Did you follow?

Miscellaneous_Word_Problems/339694: Total revenue is the total of money taken in by a business. An appliance firm determines that when it sells washing machines the total revenue R in dollars is given by the polynomial R= 135.52x0.3x to the 2 power. What is the total revenue from the sale of 193 washing machines?

1 solutions

Answer 243367 by nyc_function(2733) on 2010-09-06 22:04:46 (Show Source):

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Just replace every x you see in the function with 193 and solve for R.
R = 135.52(193)-0.3(193)^2
R = 26155.36 - 0.3(37249)

R = 26155.36 - 11174.7

R = 14980.66

The total revenue is $14,980.66 for this question.

Quadratic_Equations/339705: 3x^2-8x=3600
1 solutions

Answer 243366 by nyc_function(2733) on 2010-09-06 22:03:26 (Show Source):

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3x^2-8x = 3600
Subtract 3600 from both sides and then set this quadratic equation
to zero.
3x^2-8x - 3600 = 0
Use the quadratic formula to solve for x.
Can you take it from here?

Miscellaneous_Word_Problems/339701: Total revenue is the total of money taken in by a business. An appliance firm determines that when it sells washing machines the total revenue R, in dollars is given by the polynomial R= 135.52x-0.3x^2. What is the total revenue from the sale of 193 washing machines?

1 solutions

Answer 243363 by nyc_function(2733) on 2010-09-06 22:00:16 (Show Source):

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Just replace every x you see in the function with 193 and solve for R.
R = 135.52(193)-0.3(193)^2
Can you take it from here?

Linear_Equations_And_Systems_Word_Problems/339648: A farmer needs to mix a 20% spray solution with a 50% spray solution to obtain 45 gallons of a recommended 40% spray solution. How many gallons of each solution should he use?
1 solutions

Answer 243307 by nyc_function(2733) on 2010-09-06 19:02:02 (Show Source):

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mixture 1 + mixture 2 = total mixture

0.20x + 0.50x = 0.40(2x + 45)
Can you take it from here?

Angles/339647: An angle measures 5 degrees more than 4 times its compliment. What is the measure of the angle. How is this problem solved?
1 solutions

Answer 243306 by nyc_function(2733) on 2010-09-06 18:59:52 (Show Source):

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Let A = the angle
Let (90 - A) = complement of the angle
A + 5 = 4(90 - A)
A + 5 = 360 - 4A
A + 4A = 360 - 5
5A = 355
A = 355/5
A = 71
The angle is 71 degrees.
Understand?

Divisibility_and_Prime_Numbers/339361: For which of the following values of N is 3N – 1 not a prime number?
(a) 1 (b) 2 (c) 3 (d) 4 (e) 6

1 solutions

Answer 243304 by nyc_function(2733) on 2010-09-06 18:53:52 (Show Source):

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A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1.
The only even prime number is 2. All other even numbers can be divided by 2.

We must replace N by every number on the list to find the one that does not yield a prime number.

Let N = 1, 2, 3, 4 and 6 individually in the given expression and simplify.
3N - 1
3(1) - 1 = 3 - 1 = 2...That's not it.
3N - 1
3(2) - 1 = 6 - 1 = 5...That's not it.
3N - 1
3(3) - 1 = 9 - 1 = 8...This is it! There is no need to go further with the process.
Understood?
The answer is CHOICE (C).

Travel_Word_Problems/339630: The Gibson family drove a total of 540 miles in two days. On Tuesday they drove twice as many miles. How many miles did they drive on Monday?
1 solutions

Answer 243302 by nyc_function(2733) on 2010-09-06 18:46:24 (Show Source):

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Let x = miles on Monday
Let 2x = miles on Tuesday
x + 2x = 540
3x = 540
x = 540/3
x = 180
The Gibson family drove 180 miles on Monday.

Numbers_Word_Problems/339622: find a number such that 24 more than half the number is twice the number
1 solutions

Answer 243301 by nyc_function(2733) on 2010-09-06 18:43:46 (Show Source):

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Let n = the number we are looking for
24 + (1/2)(n) = 2n
24 + (n/2) = 2n
We now multiply every term by 2 to remove the fraction.
48 + n = 4n
48 = 4n - n
48 = 3n
48/3 = n
16 = n
The number we are looking for is 16.
Understand?

Divisibility_and_Prime_Numbers/339532: If k is a positive integer divisible by 3, and if k < 60, what is the greatest possible value of k?
1 solutions

Answer 243278 by nyc_function(2733) on 2010-09-06 15:37:36 (Show Source):

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If k is divisible by 3, we know that k/3.
We also know that there is no remainder.
We also know that k is less than 60.
What is the biggest number less than 60 that is evenly divided by 3?

59/3 = decimal number
58/3 = decimal number
57/3 = 19
The answer is 57.
Let k = 57.
Then k/3 = 57/3 = 19
Did you follow?

Expressions-with-variables/339219: I need your help solving this variable expression. -4(g+8)-(5g+3)
1 solutions

Answer 243277 by nyc_function(2733) on 2010-09-06 15:33:18 (Show Source):

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-4(g+8)-(5g+3) =
-4g - 32 - 5g - 15 =
-9g - 47
Did you follow?
NOTE: There is nothing more that can be done here since both terms are unlike.

Percentage-and-ratio-word-problems/339543: the tuition at a certain college was $25228 last year and increased 5.7% from last year to the current year. How much is this year's tuition?
1 solutions

Answer 243275 by nyc_function(2733) on 2010-09-06 15:31:14 (Show Source):

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Last year's tuition = $25,228
Percent increase = 5.7%
Let T = current year's tuition
NOTE: I selected the letter T but you can use letter of choice.

We write 5.7% in decimal form. It turns out to be 0.057.
Then $25,228 times 0.057 = $1437.996
T = $25,228 + $1437.996
T = $26665.996
T = $26,665

Linear-equations/339541: Write an equation in slope-intercept for: slope -2, passes through (-4,6)
1 solutions

Answer 243274 by nyc_function(2733) on 2010-09-06 15:26:32 (Show Source):

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Use the point-slope formula.
y - y1 = m(x - x1)
Let m = slope
So, m = -2
Let y1 = 6
Let x1 = -4
y - 6 = -2(x -(-4))
y - 6 = -2(x + 4)
y - 6 = -2x - 8
y = -2x - 8 + 6
y = -2x - 2
Did you follow?

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