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checkley75 answered: 3666 problems
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Quadratic_Equations/199136: : The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what are its dimensions?
1 solutions

Answer 149626 by checkley75(3666) on 2009-06-06 17:48:03 (Show Source):

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L=4W
LW=196
4W*W=196
4W^2=196
W^2=196/4
W=SQRT49
W=7 ANS FOR THE WIDTH.
L=4*7=28 ANS. FOR THE LENGTH.
pROOF:
7*28=196
196=196

Points-lines-and-rays/199139: y=7/5x-3
solve for x
find x and y intercept and slope
1 solutions

Answer 149625 by checkley75(3666) on 2009-06-06 17:44:46 (Show Source):

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Y=mX+b m=slope & b=y intercept.
y=7/5x-3
y=7x/5-3
7x/5=y+3
7x=5(y+3)
7x=5y+15
x=(5y+15)/7
slope=7/5
y intercept=-3
setting y=0 we solve for the x intercept.
0=7x/5-3
7x/5=3
7x=3*5
7x=15
x=15/7 the x intercept.

(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, 7x/5 -3).

Problems-with-consecutive-odd-even-integers/199148: Find three consecutive positive even integers such that the product of the first and second is two less than five times the third.(Only an algebraic solution will be accepted.): Find three consecutive positive even integers such that the product of the first and second is two less than five times the third.(Only an algebraic solution will be accepted.)

1 solutions

Answer 149624 by checkley75(3666) on 2009-06-06 17:37:32 (Show Source):

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Let x, x+2 & x+4 be the 3 even integers.
x(x+2)=5(x+4)-2
x^2+2x=5x+20-2
x^2+2x-5x-18=0
x^2-3x-18=0
(x-6)(x+3)=0
x-6=0
x=6 ans. for the first even integer.
6+2=8 for the second even integer.
6+4=10 for the third even integer.
Proof:
6*8=5*10-2
48=50-2
48=48

Linear_Equations_And_Systems_Word_Problems/199155: 2x < 7 + x
1 solutions

Answer 149622 by checkley75(3666) on 2009-06-06 17:31:40 (Show Source):

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2x < 7 + x
2x-x<7
x<7 ans.
Proof:
Let x=6
2*6<7+6
12<13

Numbers_Word_Problems/199157: Find an equation for which -3 and 4 are solutions
1 solutions

Answer 149621 by checkley75(3666) on 2009-06-06 17:29:41 (Show Source):

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x^2-x-12
(x-4)(x+3)=0
x-4=0
x=4 ans
x+3-0
x=-3 ans.

Linear-equations/199105: Find an equation of a line parallel to 2x-5y=20?

1 solutions

Answer 149583 by checkley75(3666) on 2009-06-05 20:25:43 (Show Source):

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2x-5y=20
5y=-2x+20
y=-2x/5+20/5
y=-2x/5+4 this line has a slope=-2/5.
Thus any line with the same slope is parallel. Two such lines follow.
y=-2x/5-6
y=-2x/5+1

Linear_Equations_And_Systems_Word_Problems/199108: The cost of 12 gallons of regular gasoline and 18 gallons of premium gasoline is $44.46. Premium costs $.22 more per gallon than regular. What is the cost per gallon of each type of gasoline?
1 solutions

Answer 149582 by checkley75(3666) on 2009-06-05 20:21:43 (Show Source):

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12x+18(x+.22)=44.46
12x+18x+3.96=44.46
30x=44.46-3.96
30x=40.50
x=40.50/30
x=1.35 is the price of regular gas per gallon.
1.35+.22=1.57 is the price of premium gas per gallon.
Proof:
12*1.35+18*1.57=44.46
16.20+28.26=44.47
44.46=44.46

Linear-equations/199106: what is the slope for the line: (0,4100),(3,4850)?

1 solutions

Answer 149581 by checkley75(3666) on 2009-06-05 20:14:11 (Show Source):

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(0,4100),(3,4850)?
slope=(y2-y1)/(x2-x1)=(4850-4100)/(3-0)=750/3=250 ans.

Polynomials-and-rational-expressions/198975: In your job as a cashier at the bookstore,a customer gives you a $20 bill to pay for a book that costs $4.27. How much change should you give back?
Please show me the work
Thank you
1 solutions

Answer 149515 by checkley75(3666) on 2009-06-05 07:46:18 (Show Source):

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$20.00-4.27=$15.73 is the change.

Polynomials-and-rational-expressions/198976: Your mother works part-time at the stationery store.Last week, her paycheck was
$97.37 for 13 hours of work. How much does she make per hour?
Please Show work
1 solutions

Answer 149514 by checkley75(3666) on 2009-06-05 07:44:48 (Show Source):

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$97.37/13=$7.49 per hour.

Polynomials-and-rational-expressions/198978: For a garment that you are making, you are
going to need 61/4 yards of fabric at the cost of
$3.32 per yard. How much will the fabric cost?
Show Work Please
Thank you
1 solutions

Answer 149513 by checkley75(3666) on 2009-06-05 07:42:50 (Show Source):

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6.25*3.32=$20.75 IS THE COST FOR THE MATERIAL.

Polynomials-and-rational-expressions/198982: Ten years ago,the Pottery Gallery Museum bought a vase for $18,000. Since then, the value has increased by 6 percent. In Dollars, what is the present value of the vase?
1 solutions

Answer 149512 by checkley75(3666) on 2009-06-05 07:40:08 (Show Source):

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18,000*1.06=$19,080 IS THE PRESENT VALUE.

Travel_Word_Problems/199039: This question is from textbook algebra and trigonometry
Two cyclists, 90 mi apart, start riding toward each other at the same time. One cycles twice as fast as the other. If they meet 2h later, at what average speed is each cyclist traveling?
1 solutions

Answer 149511 by checkley75(3666) on 2009-06-05 07:37:32 (Show Source):

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D=RT
90=(X+2X)2
90=3X*2
90=6X
X=90/6
X=15 MPH FOR THE SLOWER CYCLIST.
2*15=30 MPH FOR THE FASTER CYCLIST.
PROOF;
90=(15+30)2
90=45*2
90=90

Linear-systems/198944: {-3x + y = 4
{-x + y = -2
1 solutions

Answer 149428 by checkley75(3666) on 2009-06-04 10:45:11 (Show Source):

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-3x + y = 4
-x + y = -2 subtract
-------------------------
-2x=6
x=6/-2
x=-3 ans.
-(-3)+y=-2
3+y=-2
y=-2-3
y=-5 ans.

Graphs/198496: Graph the solution: 3x+y=>6 y<= -3x-2
1 solutions

Answer 149426 by checkley75(3666) on 2009-06-04 10:40:05 (Show Source):

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3x+y=>6
y=>-3x+6 (red line)
y<=-3x-2 (green line)

(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions -3x +6 and -3x -2).

Linear_Algebra/198877: what is an equation to a line parallel to, 3x-4y=12 ? possible answers..
y=3x+5
y=-0.75x+8
y=4/3x-3
y=0.75x-6
y=-4/3x+12
1 solutions

Answer 149424 by checkley75(3666) on 2009-06-04 10:28:55 (Show Source):

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3x-4y=12
-4y=-3x+12
y=-3x/-4+12/-4
y=3x/4-3 ans.
Does not match any of your possible answers.

Geometric_formulas/198938: This question is from textbook geometry
can you please help me solve and leave answer in terms of pie ((( Find the area of a circle with radius 4 )))
1 solutions

Answer 149423 by checkley75(3666) on 2009-06-04 10:23:03 (Show Source):

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Area=pi*r^2
Area=pi*4^2
Area=16pi ans.

Quadratic_Equations/198912: A picture frame dimesions are 20cm by 30cm. If a mat was put inside the frame that decreases the picture area by 264cm^2, how wide is the mat?
1 solutions

Answer 149420 by checkley75(3666) on 2009-06-04 10:20:18 (Show Source):

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(20-2X)(30-2X)=264
600-60X-40X+4X^2=264
4X^2-100X+600-264=0
4X^2-100X+336=0
4(X^2-25X+84)=0
4(X-21)(X-4)=0
X-21=0
X=21 ANS.
X-4=0
X=4 ANS.

Graphs/198879: This question is from textbook Algebra Structure and Method Book 1
How do I write an equation in standard form of the line that contains (1,1) and (6,-1)? thanks
1 solutions

Answer 149416 by checkley75(3666) on 2009-06-04 08:27:21 (Show Source):

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(1,1) and (6,-1)
Y=mX+b
m=slope
b=y intercept
slope=(y2-y1)/(x2-x1)
slope=(-1-1)/(6-1)
slope=-2/5
1=-2/5*1+b
1=-2/5+b
b=1+2/5
b=(1*5+2)/5
b=(5+2)/7
b=7/5 y intercept.
y=-2x/5+7/5 is the line equation.

(graph 300x200 pixels, x from -6 to 5, y from -6 to 5, -2x/5 +7/5x).

Equations/198884: what is the value of f(-2) when F(x)=(3x-1)(x^2-10x+6)?
1 solutions

Answer 149415 by checkley75(3666) on 2009-06-04 08:19:48 (Show Source):

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f(-2)
F(x)=(3x-1)(x^2-10x+6)
f(-2)=(3*-2-1)(-2^2-10*-2+6)
f(-2)=(-6-1)(4+20+6)
f(-2)=-7*30
f(-2)=-210

Inequalities/198927: 10x + 2 -5x -6>-2(6 - X)
1 solutions

Answer 149414 by checkley75(3666) on 2009-06-04 08:14:22 (Show Source):

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10x+2-5x-6>-2(6-x)
5x-4>-12+2x
5x-2x>-12+4
3x>-8
x>-8/3

Linear-equations/198929: 5x-5y=3
1 solutions

Answer 149413 by checkley75(3666) on 2009-06-04 08:08:33 (Show Source):

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5x-5y=3
-5y=-5x+3
y=-5x/-5+3/-5
y=x-3/5

(graph 200x200 pixels, x from -6 to 5, y from -6 to 5, x -3/5).

Linear-equations/198932: 5x-y=4
1 solutions

Answer 149412 by checkley75(3666) on 2009-06-04 08:05:21 (Show Source):

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5x-y=4
-y=-5x+4
y=5x-4

(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, 5x -4).

Polynomials-and-rational-expressions/198795: This question is from textbook Intermediate Algebra An Applied Approach
Answer the following question involving fundamental operations on polynomials
Find P(-1/2) if
P(x)=x^4+3x^2+2
1 solutions

Answer 149286 by checkley75(3666) on 2009-06-03 08:59:36 (Show Source):

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Find P(-1/2) if
P(x)=x^4+3x^2+2
p(-1/2)=-1/2^4+3*-1/2^2+2
p(-1/2)=1/16+3/4+2
p(-1/2)=(1+12+32)/16
p(-1/2)=45/16 ans.

Quadratic_Equations/198731: x(8-x)=15
1 solutions

Answer 149255 by checkley75(3666) on 2009-06-02 20:21:28 (Show Source):

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x(8-x)=15
8x-x^2-15=0
x^2-8x+15=0
(x-5)(x-3)=0
x-5=0
x=5 ans.
x-3=0
x=3 ans.

Quadratic_Equations/198732: (3-2y) (5+4y)=0
1 solutions

Answer 149253 by checkley75(3666) on 2009-06-02 20:19:16 (Show Source):

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(3-2y) (5+4y)=0
15+12y-10y-8y^2=0
8y^2-2y-15=0
(4y+5)(2y-3)=0
4y+5=0
4y=-5
y=-5/4 ans.
2y-3=0
2y=3
y=3/2 ans.

Linear-equations/198739: You have 2 solutions of liquid. One contains 10% water and the other contains 30% water. How many quarts of each should you mix in order to obtain 30 quarts of mixture that is 25% water?
1 solutions

Answer 149251 by checkley75(3666) on 2009-06-02 20:14:15 (Show Source):

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.3x+.1(30-x)=.25*30
.3x+3-.1x=7.5
.2x=7.5-3
.2x=4.5
x=4.5/.2
x=22.5 qts. of 30% water.
30-22.5=7.5 qts of 10% water.
Proof:
.3*22.5+.1*7.5=7.5
6.75+.75=7.5
7.5=7.5

Quadratic_Equations/198740: You have a total of $5,000 and decide to invest part in a bank paying 5% simple interest and in a CD that pays 8%. If you receive a total of $300 from your investments, how much was put in each account?
1 solutions

Answer 149249 by checkley75(3666) on 2009-06-02 20:09:38 (Show Source):

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.08x+.05(5,000-x)=300
.08x+250-.05x=300
.03x=300-250
.03x=50
x=50/.03
x=1,666.67 invested @ 8%
5,000-1,666.67=3,333.33 invested @ 5%
Proof:
.08*1,666.67+.05*3,333.33=300
133.33+166.67=300
300=300

Linear-systems/198745: One year ago Walt invested $12000. He invested part of the money at 7% and the rest at 9%. He made a total of $970 in interest. How much was invested at 7%?
I do not know where to place what number in the formula equation
ax2 + bx + c = 0
1 solutions

Answer 149246 by checkley75(3666) on 2009-06-02 20:03:40 (Show Source):

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ax2 + bx + c = 0
This is not the correct formula for this type of problem.
.09x+.07(12,000-x)=970 is the correct formula.
.09x+840-.07x=970
.02x=970-840
.02x=130
x=130/.02
x=6,500 amount invested @ 9%.
12,000-6,500=5,500 amount invested @ 7%.
Proof:
.09*6,500+.07*5,500=970
585+385=970
970=970

Linear_Equations_And_Systems_Word_Problems/198555: Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25% then how much did she invest at each rate?
1 solutions

Answer 149102 by checkley75(3666) on 2009-06-01 16:03:22 (Show Source):

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.04x+.0225(33,000-x)=970
.04x+742.5-.0225x=970
.0175x=970-742.5
.0175x=227.5
x=227.5/.0175
x=13,000 amount invested @ 4%.
33,000-13,000=20,000 amount invested @ 2.25%.
Proof:
.04*13,000+.0225*2450=970
520+450=970
970=970

Radicals/192328: x^3-49x=0
1 solutions

Answer 144362 by checkley75(3666) on 2009-04-21 08:45:40 (Show Source):

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x^3-49x=0
x(x^2-49)=0
x(x+7)(x-7)=0
x+7=0
x=-7 ans.
x-7=0
x=7 ans.
x=0 ans.