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Recent problems solved by 'Earlsdon'

Earlsdon answered: 6281 problems
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Circles/271016: In triangle ACD, E is a point on segment AD and B is a point on segment AC , such that segment EB is parallel to segment DC.
If AE = 3, ED = 6, and DC = 15, find the length of segment EB.
1 solutions

Answer 198476 by Earlsdon(6287) on 2010-02-17 21:40:42 (Show Source):

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If my intrepretation is correct, my drawing indicates that you have two similar triangles: ACD and ABE, so...
AE%2FAD+=+EB%2FDC

Substitute AE+=+3

, and

Distributive-associative-commutative-properties/271062: Trying to reverse foil 18x^2-45x Any Thoughts?
1 solutions

Answer 198472 by Earlsdon(6287) on 2010-02-17 21:31:03 (Show Source):

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How about?
18x%5E2-45x+=+9x%282x-5%29

logarithm/271046: Evaluate the logarithm:
log9 1/81
1 solutions

Answer 198471 by Earlsdon(6287) on 2010-02-17 21:28:52 (Show Source):

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Evaluate:
Log%5B9%5D%281%2F81%29+=+x

Rewrite in exponential form:
9%5Ex+=+1%2F81

Substitute 1%2F81+=+1%2F9%5E2

The bases are equal so the exponents are equal.
highlight%28x+=+-2%29

Age_Word_Problems/271049: Trisha is 3 times as old as Lilly, as Lilly is twice as old as Emma. If the sum of the tree girls' ages is 27, how old is Emma?
1 solutions

Answer 198469 by Earlsdon(6287) on 2010-02-17 21:22:13 (Show Source):

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T = 3L "Trisha is 3 times as old as Lilly."
L = 2E "Lilly is twice as old as Emma."
So T = 3(2E) = 6E.
T+L+E = 27 "...the sum of the three girls' ages is 27."
Perform the substitutions:
6E+2E+E = 27 Simplify.
9E = 27 Divide by 9.
E = 3

Rational-functions/270984: This one deals with simplifying a rational function. The problem is written as:
6-x-x^2/3x^2-10x+8
Ive tried every possible combination and can't sem to come into any equations that properly simplify.
1 solutions

Answer 198461 by Earlsdon(6287) on 2010-02-17 21:12:44 (Show Source):

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Simplify:
6-x-x%5E2%29%2F%283x%5E2-10x%2B8%29

Rewrite the numerator by factoring a (-1).
-%28x%5E2%2Bx-6%29%2F%283x%5E2-10x%2B8%29

Now factor the trinomials in the numerator and in the denominator.
-cross%28%28x-2%29%29%28x%2B3%29%2F%283x-4%29cross%28%28x-2%29%29

Cancel the indicated factors.
highlight%28-%28%28x%2B3%29%29%2F%28%283x-4%29%29%29

Age_Word_Problems/271038: Fred is 4 years older than barney, five years ago the sum of their age was 48, how old are they now, please use F for fred and B for barney, thank you
1 solutions

Answer 198451 by Earlsdon(6287) on 2010-02-17 20:57:34 (Show Source):

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F = B+4
(F-5)+(B-5) = 48 Substitute F = B+4
(B+4-5)+(b-5) = 48 Simplify.
2B-6 = 48 Add 6 to both sides.
2B = 54 Divide both sides by 2.
B = 27 and...
F = B+4
F = 27+4
F = 31

Quadratic_Equations/269827: Please help me solve using completing the square: +t%5E2-8t%2B40=0+

1 solutions

Answer 197690 by Earlsdon(6287) on 2010-02-15 14:28:32 (Show Source):

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Solve by completing the square:
t%5E2-8t%2B40+=+0

Subtract 40 from both sides.
t%5E2-8t+=+-40

Now add the square of half the coefficient of the t-term to both sides. This is %28-8%2F2%29%5E2+=+16

Simplify.

Take the square root of both sides.
t-4+=+sqrt%28-24%29

Add 4 to both sides of each solution.
t+=+4%2Bsqrt%28-24%29

This could be further simplified to:
t+=+4%2B2sqrt%28-6%29

Mixture_Word_Problems/269773: JACKIE WANTS TO MAKE A MIXTURE OF NUTS TO SELL IN HER STORE CONSISTING OF HAZELNUTS AND CASHEWS.HAZELNUTS COST $6.50 PER POUND AND CASHEWS COST $4.50 PER POUND. IF JACKIE WANTS 60 POUNDS TOTAL OF MIXTURE AND THE COST TO BE $5.10 PER POUND, HOW MANY POUND OF EACH WILL SHE NEED?
1 solutions

Answer 197661 by Earlsdon(6287) on 2010-02-15 11:28:32 (Show Source):

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Let x = the number of lbs. of hazelnuts at $6.50 per pound and (60-x) = the number of lbs. of cashews at $4.50 per pound.
The mixture (the sum of these two) is to be 60 lbs at $5.10 per pound.
This can be expressed algebraically by:
6.5x+4.5(60-x) = 5.1(60) Simplify.
6.5x+270-4.5x = 306 Combine like-terms.
2x+270 = 306 Subtract 270 from both sides.
2x = 36 Divide both sides by 2.
x = 18
Jackie will need to mix 18 lbs. of hazelnuts @ $6.50 per pound with (60-18 = 42)lbs. of cashews @ $4.50 per pound to obtain 60 pounds of the mixture @ $5.10 per pound.

Miscellaneous_Word_Problems/269618: a rectangular cutting board is 6 inches longer than it is wide. If the area of the cutting board is 216 square inches, find the length and the width.
This is my attempt to the problem but then I am stuck.
A=lw
216=6(L) * w

1 solutions

Answer 197604 by Earlsdon(6287) on 2010-02-14 20:52:20 (Show Source):

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Try this:
A+=+L%2AW

Substitute A = 216, and L = W+6
216+=+%28W%2B6%29%28W%29

Rearrange to:
W%5E2%2B6W-216+=+0

Factor.

so...

Discard the negative solution.
W+=12

and...

so...
The length of the cutting board is 18 inches and the width is 12 inches.

Geometry_Word_Problems/269127: A rectangular box with no top has height 4 feet. The length of the base is three
times the width, and the volume is 300 cubic feet. Find the amount of cardboard
needed to construct the box, and label your answer with appropriate units

1 solutions

Answer 197264 by Earlsdon(6287) on 2010-02-13 10:00:19 (Show Source):

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The volume of the open-top box (V) is given as 300 sq.ft.
For a rectangular prism (a box), the volume is given by:
V+=+L%2AW%2Ah

and, in this problem, V = 300 sq.ft., h = 4 ft., W = W and L = 3W, so...
%283W%29%2A%28W%29%2A4+=+300

Simplify.

Divide by 12.
W%5E2+=+25

and...

ft. (Discard the negative solution from the square root).
L+=+3W

ft.
So, to construct an open-top box with the foregoing dimensions, you would need to start with a rectangular sheet of cardboard with a length (l) of L+2h and a width (w) of W+2h, so...
l+=+15%2B2%284%29

and...

The initial sheet of cardboard has to be 23ft. by 13ft, from which you would cut the four corners measuring 4ft. by 4ft.

Equations/269134: five-sixth of what number is -60
1 solutions

Answer 197259 by Earlsdon(6287) on 2010-02-13 09:41:39 (Show Source):

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Let the number be x, then:
%285%2F6%29%2Ax+=+-60

Multiply both sides by the multiplicative inverse of 5%2F6

which is

%286%2F5%29%285%2F6%29x+=+-60%286%2F5%29

Evaluate.

So, -60 is five-sixths of -72.

Inverses/269035: Please help me solve this problem y/2-6=4
1 solutions

Answer 197173 by Earlsdon(6287) on 2010-02-12 20:49:02 (Show Source):

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Solve:
%28y%2F2%29-6+=+4

Add 6 to both sides.
%28y%2F2%29-6%2B6+=+4%2B6

Multiply both sides by 2.
cross%282%29%28y%2Fcross%282%29%29+=+2%2A10

Equations/269037: x to the third power -x to the second power -20x=
1 solutions

Answer 197169 by Earlsdon(6287) on 2010-02-12 20:45:36 (Show Source):

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x%5E3-x%5E2-2x

= ?
Er...what are w supposed to do with this?
It can't be solved until we know what that the expression is equal to!
Did you want to simplify it???
It would be most helpful if you could articulate your wishes.
Simplify:
x%5E3-x%5E2-2x+=+x%28x%2B1%29%28x-2%29

Complex_Numbers/268901: How can I solve this equation for b?.... i/a+i/b=3/c Please show steps
1 solutions

Answer 197022 by Earlsdon(6287) on 2010-02-12 11:19:35 (Show Source):

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Solve for b:
%28i%2Fa%29%2B%28i%2Fb%29+=+3%2Fc

Add the fractions on the left side.
%28ai%2Bbi%29%2Fab+=+3%2Fc

Cross-multiply.
aci%2Bbci+=+3ab

Subtract bci from both sides.
aci+=+3ab-bci

Factor b on the right side.
aci+=+b%283a-ci%29

Finally, divide both sides by (3a-ci).
highlight%28b+=+aci%2F%283a-ci%29%29

Distributive-associative-commutative-properties/268707: factor the following into the two binomials confirm your answerby multiply the two binomials
x^2-36
1 solutions

Answer 196907 by Earlsdon(6287) on 2010-02-11 20:40:41 (Show Source):

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The difference of two squares is factored thus:
%28A%5E2-B%5E2%29+=+%28A%2BB%29%28A-B%29

so...

You can verify this by multiplying these two factors using the FOIL method.

Polynomials-and-rational-expressions/268711: find the exact area of a triangle with a base of sqrt(30) meters and a height of sqrt(6 meters)
1 solutions

Answer 196903 by Earlsdon(6287) on 2010-02-11 20:33:17 (Show Source):

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Start with:
A+=+%281%2F2%29b%2Ah

for the area of a triangle. Substitute b+=+sqrt%2830%29

and

to get:

A+=+%281%2F2%29%28sqrt%2830%29%29%2A%28sqrt%286%29%29

Substitute sqrt%2830%29+=+sqrt%285%29%2Asqrt%286%29

A+=+%281%2F2%29%28sqrt%285%29%29%2A%28sqrt%286%29%29%2A%28sqrt%286%29%29

Substitute 6+=+sqrt%286%29%2Asqrt%286%29

Simplify.

Sq. meters.

Age_Word_Problems/267552: Mr. Atkins is 33 years old and Mr.s Speyer is 27 years old. How many years ago was Mr. Atkins 1.5 as old as Mr Spyer was then?
1 solutions

Answer 196311 by Earlsdon(6287) on 2010-02-09 11:38:45 (Show Source):

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Let A = Mr. Atkin's present age (33) and S = Mr. Speyer's present age (27).
x years ago, Mr. Atkin's age was 1.5 times Mr. Speyer's age then.
This can be expressed algebraically as:
(A-x) = 1.5(S-x) Substitute A = 33 and S = 27.
(33-x) = 1.5(27-x) Simplify and solve for x.
33-x = 40.5-1.5x Add 1.5x to both sides.
33+0.5x = 40.5 Subtract 33 from both sides.
0.5x = 7.5 Divide both sides by 0.5
x = 15
15 years ago, Mr. Atkin's age was 1.5 times Mr. Speyer's age then.

expressions/267098: whats the answer to -3 to the second power

1 solutions

Answer 196082 by Earlsdon(6287) on 2010-02-08 11:21:27 (Show Source):

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It really depends on whether you are asking %28-3%29%5E2

...

or...

Do you see the distinction?

Money_Word_Problems/267099: If your salary of 33,000 this year was 10% more than last year, what was last years salary?
I tried;
33,000*.1=3,300
33,000-3,300=29,700
so last year salary was $29700
1 solutions

Answer 196079 by Earlsdon(6287) on 2010-02-08 11:15:56 (Show Source):

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Let S be last year's salary, then we have S + 10% of S = $33,000, or...
S+0.1S = $33,000 Simplify.
1.1S = $33,000
S = $33,000/(1.1)
S = $30,000 This was last year's salary.

Mixture_Word_Problems/266027: Bobby and Mike have a summer job mowing the school yard once a week. The school provides them with two riding lawn mowers.One mower requires 7 hours to mow the school yard, while the other could cover the school yard in 6 hours. How long will the job take using both mowers? (Round your answer to the nearest tenth.)
1 solutions

Answer 195504 by Earlsdon(6287) on 2010-02-05 11:43:35 (Show Source):

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The first mower can mow 1%2F7

of the yard in 1 hour.
The second mower can mow 1%2F6

of the yard in 1 hour.
Together, they can mow 1%2F7+%2B+1%2F6+=+13%2F42

of the yard in 1 hour.
So it would take them 42%2F13

hours to mow the entire yard.
42%2F13+=+3.2307

hours.
Rounded to the nearest tenth this would be 3.2 hours.

Inverses/265999: use inverse operations to write the inverse of f(x)=x/5+2

1 solutions

Answer 195501 by Earlsdon(6287) on 2010-02-05 11:29:45 (Show Source):

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Find the inverse of:
f%28x%29+=+%28x%2F5%29%2B2

Substitute y+=+f%28x%29

Now exchange the x and y.
x+=+%28y%2F5%29%2B2

Solve for y.
x-2+=+y%2F5

Substitute f%5E%28-1%29%28x%29+=+y

highlight%28f%5E%28-1%29%28x%29+=+5x-10%29

Check to see if f%28f%5E%28-1%29%28x%29%29+=+x

f%28f%5E%28-1%29%28x%29%29+=+f%285x-10%29

and...

Simplify the right side.
f%285x-10%29+=+%285x-10%2B10%29%2F5

so...

QED

Equations/266000: if
2+3=10
7+2=63
6+5=66
8+4=96
WHAT DOES 9+7=

1 solutions

Answer 195492 by Earlsdon(6287) on 2010-02-05 11:15:09 (Show Source):

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If:
2+3 = 10
7+2 = 63
6+5 = 66
8+4 = 96 Then...
9+7 = 144

Miscellaneous_Word_Problems/265484: A pyramid has a volume of 1875 ft cubed. Its base is a square that is 15 ft on each side. What is the height of the pyramid?
1 solutions

Answer 195201 by Earlsdon(6287) on 2010-02-04 11:08:22 (Show Source):

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Start with the fomula for the volume of a pyramid:
V+=+%281%2F3%29Bh

Where: B = the area (15X15) of the base and h = the height, so...
1875+=+%281%2F3%29225%2Ah

Divide both sides by 75.
highlight%28h+=+25%29

ft.

Surface-area/265045: a machinist drilled a conical hole into a cube of metal. If the cube has sides of length 6 centimeters what is the surface are of the cone shaped hole? 3.14 for pi
please help
have a diagram if you need it
1 solutions

Answer 194969 by Earlsdon(6287) on 2010-02-03 13:51:45 (Show Source):

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I'm assuming that the circular base of the conical hole inscribed in the square side of the cube is an exact fit, that is the circle is tangent to the sides of the square.
And that the depth of the conical hole does not protrude beyond the other side of the cube.
So, given the above, you will have a cone (conical hole) whose circular base has a diameter (D) equal to the length of the side of the cube (D = 6cm.) and the height (h) of the cone (really the depth of the conical hole) is also equal to the length of the side of the cube (h = 6cm.).
The surface area (S) of a right circular cone, such as you have here, is given by:
S+=+%28pi%29R%2Asqrt%28R%5E2%2Bh%5E2%29

Where: R = radius of base of cone = 3cm. and h = height of cone = 6cm. Making the appropriate substitutions...
S+=+%283.14%29%283%29sqrt%289%2B36%29

sq.cm.

Linear-equations/265052: what is the solution of y= -x -3 for the given value of x
you put -1 insted of x
1 solutions

Answer 194966 by Earlsdon(6287) on 2010-02-03 13:20:44 (Show Source):

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Sollve:
y+=+-x-3

Substitute x = -1.
y+=+-%28-1%29-3

Evaluate.

Evaluation_Word_Problems/264504: please help!!! four times a number added to 3 is divided by 8. the result is 7/4 find the number. i set the problem up like this 4x+3/8=7/4 but i cant remember how to work the problem.
1 solutions

Answer 194724 by Earlsdon(6287) on 2010-02-02 13:07:52 (Show Source):

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OK so far:
%284x%2B3%29%2F8+=+7%2F4

Multiply both sides by 8.
4x%2B3+=+8%2A7%2F4

Simplify the right side.
4x%2B3+=+14

Subtract 3 from both sides.
4x=+11

Divide both sides by 4.
highlight%28x+=+11%2F4%29

Miscellaneous_Word_Problems/264497: if a 150 lb person weighs 55 pounds on mars,about how much does a 7000 lb satellite weigh? round your answer to the nearest pound. i have 2566 is this correct?
1 solutions

Answer 194722 by Earlsdon(6287) on 2010-02-02 13:03:20 (Show Source):

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Well, I get...
2566.66... and, when rounded to the nearest pound, as instructed, it comes to...
2567 lbs.

Mixture_Word_Problems/264491: please check my answer. a retirement dinner for two is $65.20 including tax. find the total cost of the dinner if a tip of 15% is added to the cost. i have 74.98
1 solutions

Answer 194720 by Earlsdon(6287) on 2010-02-02 12:58:28 (Show Source):

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Your answer is good!
$65.20+(0.15)($65.20) = $65.20+$9.78 = $74.98

Graphs/264483: How would i graph this 3x-2y+5=0? How Would i Make it able to be put into my calculator to graph?
1 solutions

Answer 194719 by Earlsdon(6287) on 2010-02-02 12:52:46 (Show Source):

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First rearrange the equation by solving for y:
3x-2y%2B5+=+0

Add 2y to both sides.
3x%2B5+=+2y

Now divide through by 2 to get y by itself.
%283%2F2%29x%2B5%2F2+=+y

Now you can graph this by first letting x = 0 and solving for y, then letting y = 0 and solving for x so that you will get two ordered pairs (points) which you can then plot on you coordinate graph paper. Join these two points with a straight line and you will have the graph of the given equation:
y+=+%283%2F2%29x%2B5%2F2

substitute x = 0.
y+=+%283%2F2%29%280%29%2B5%2F2

The first point is (

)

Substitute y = 0.
0+=+%283%2F2x%29%2B5%2F2

Subtract

from both sides.
-5%2F2+=+%283%2F2%29x

Multiply both sides by 2%2F3

The second point is ( -5%2F3

)
The graph looks like this:
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C%283%2F2%29x%2B5%2F2%29

For displaying the graph on your calculator, assuming that you have a graphing calculator such as TI-83, TI-86, etc press the "graph" key then, for y%5B1%5D

enter

followed by the "enter" or "=" key.

Polynomials-and-rational-expressions/264438: find the greatest common factor for the group of terms.
-42a^3,7a^4
I believe -7 is part of the answer, but not sure what to do with the variables.
1 solutions

Answer 194713 by Earlsdon(6287) on 2010-02-02 12:32:34 (Show Source):

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Find the GCF of -42a%5E3

and

.
Write the prime factors of each expression:
-42a%5E3+=+-1%2A2%2A3%2Ahighlight_green%287%2Aa%2Aa%2Aa%29

7a%5E4+=+highlight_green%287%2Aa%2Aa%2Aa%29%2Aa

Now select those factors that are common to both lists and multiply them:
7%2Aa%2Aa%2Aa+=+highlight%287a%5E3%29

= GCF

Polynomials-and-rational-expressions/264460: Factor completely 6y2-2yz. Could you show how you got your awnser cause i would like to know how to complete the rest myself.
1 solutions

Answer 194707 by Earlsdon(6287) on 2010-02-02 12:13:35 (Show Source):

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Factor completely:
6y%5E2-2yz

Rewrite this by factoring each term:
2%2A3%2Ay%2Ay-2%2Ay%2Az

Now take out the common factor in each term.
highlight%282y%283y-z%29%29

...and that's it!

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