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A family made a trip by car.
They traveled 1312 km in 3 days.
On the 2nd day, they traveled 2 times the number of km from the 1st day.
On the 3rd day, they traveled 98 km less than the 2nd day.
Find the distance traveled every day.
===========================================
x= first day travel
2x=2nd day
2x-98=3rd day
==========================
x+2x+2x-98=1312
5x=1312+98
5x=1410
x=282
================
first day = 282
2nd day= 2(282)=564
3rd day = 564-98=466
:)

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a girl has 24 quarters and dimes. togther they had up to 3.60 how many quarters does she have?
q+d=24
.25q+.1d=3.60
=====================
d=24-q
.25q+.1(24-q)=3.60
.25q+2.4-.1q=3.60
.15q=3.6-2.4
.15q=2.4
q=8
================
8+d=24
d=24-8
d=16
:)

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The sum of two numbers is 42. One number plus 2 times the other number is 57. What are the numbers?
x+y=42
x+2y=57
Lets solve by elimination;
so we will multiply the first equation by -1;
(-1)x+y=42
-x-y=-42
==========
Now we will add that equation to the second;


_________
y=15
now plug that into either original equation to find x;
x+15=42
x=27
========================================
The sum of two numbers is 45. Their difference is 9. What are the numbers?
x+y=45
x-y=9
Since one variable will already be eliminated we will not need to multiply anything;


_____________
2x=54
x=27
plug that into either equation for x;
27+y=45
y=45-27
y=18
:)
_________

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(m^2-5mn + 3n^2)(m^2+4mn - 2n^2)
=======================================


Now collect like terms;


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5(x – 5) + 8x = 9x – 25
distribute the 5;
5x-25+8x=9x-25
13x-25=9x-25
13x-9x=-25+25
4x=0
x=0/4
x=0
:)

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5(x – 9) – 4x = x – 7
distribute the 5;
5x-45-4x=x-7
x-45=x-7
x-x=38
The x's cancel out, there is no solution
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4x – 6y = –1
8x + 3y = 3
==============
This is also called elimination, you want to eliminate one of the variables.
So we will try to eliminate the x, so I will multiply the first equation by -2,
(-2)4x-6y=-1
-8x+12y=2----new equation
Now lets take the new equation and add it to the original second;


_________
15y=5


Now we will plug y=1/3 into one of the original equations for y;
4x-6(1/3)=-1
4x-2=-1
4x=1
x=1/4
check:
4(1/4)-6(1/3)=-1
1-2=-1
:)

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carol,ava and cindy swim at a public pool each day . one day carol swam twice as many laps as ava and cindy swam three more laps than ava. if the women swam 27 laps together, how many laps did each swim?
=========================
x=carol
y=ava
z=cindy
==============
x=2y
z=y+3
=============
x+y+z=27
2y+y+y+3=27
4y+3=27
4y=27-3
4y=24
y=6
=============
So Ava swam 6 laps
Carol = 2(6)=12
Cindy=6+3=9
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y<1/2x+2
x-3y<9
=================
first lets put both in slope-intercept form;
the first one already is;
y<1/2x+2
===============
x-3y<9
-3y<-x+9
y>1/3x-3
Now lets graph, the lines are going to be dashed;
The red line is the first equation, you are going to shade the area below the line(don't forget the line is dashed)
The green is the second equation and shade the area above the line(line is dashed)
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The answer is going to be , no solution. When it is worked out, you cancel both variables.
You are close;
4x-12y=5
-x+3y=-1
=================
-x=-1-3y
x=1+3y
================
4(1+3y)-12y=5
4+12y-12y=5

4=5
no solution
:)

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Given f(x) = –x^3 – 3x^2 + 3x + 7, find f(–1), f(0), and f(2)






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Not quite;
5x-2y=-5
y-5x=3
===============
we will go ahead and solve the second equation for y;
y-5x=3
y=3+5x
=============
now put that in for y in the first equation;
5x-2(3+5x)=-5
5x-6-10x=-5
-6-5x=-5
-5x=-5+6
-5x=1
x=-1/5
================
Now plug that in the equation and solve for y;
5(-1/5)-2y=-5
-5/5-2y=-5
-1-2y=-5
-2y=-4
y=2
=============
:)

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The volume of an octagonal prism is 486 cubic millimeters. If the area of the base is 54 square millimeters, what is the height of the prism?
======================
Formula for volume;
V=BH
B= area of base;
486=54H
486/54=h
h=9
:)

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You need to post the problem, we do not all have the same book
:)

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Linear combination would also be elimination method, you add two equations together;
2x+2w=48
x-2w=12
--------
3x=60
x=20
Then you substitute x in either equation for 20 and solve for w;
2(20)+2w=48
40+2w=48
2w=8
w=4
:)

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Linear combination would also be elimination method, you add two equations together;
2x+2w=48
x-2w=12
--------
3x=60
x=20
Then you substitute x in either equation for 20 and solve for w;
2(20)+2w=48
40+2w=48
2w=8
w=4
:)

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write 6.25as a mixed nummer.then subtract 5/8 from the mixed number.what is the difference?





:)

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a train averaged 36 miles per hour and took 8 hours to travel from chicago to st.louis. what is the distance between chicag and st.louis?
let x be amount of miles from Chicago to St.Louis;

x=288
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Find the x-intercept of x - 2y = 9.
To find the x-intercept, just make y=0;
x-2(0)=9
x-0=9
x=9
:)

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400 tickets total sold to game. Student tickets are $2, adults $3. Total $ collected is $1050.
s+a=400
2s+3a=1050
:)

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You need to post the problem, we do not all have that same book
:)

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You need to post the problem, we do not all have that book
:)

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shawn has an annual interest income of $3290 from two investments. he has $7000 more invested at 8% than he has invested at 6%. find the amount invested in each rate ?
=======================================
.08x+.06y=3290
y=x+7000
-------------------
.08x+.06(x+7000)=3290
.08x+.06x+420=3290
.14x=2870
x=20500
.08(20500)+.06y=3290
1640+.06y=3290
.06y=1650
y=27500
===================
At 8% interest = $20500
at 6%interest = $27500
:)

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You are correct, with what you give that's all you can do.
:)

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Great job. you are correct!
:)

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The answer is +5, negative divided by a negative gives you a positive. Your doing everything else correct. Good Job. Just watch your signs.
:)
2x+3y=1
-5x-3y=-16
-3x=-15
x=5

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Solve the following systems by graphing.
2x-y=4
2x-y=6
you need to put them in slope intercept form and graph;
2x-y=4
-y=-2x+4
y=2x-4
--------------
2x-y=6
-y=-2x+6
y=2x-6
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7x-(-3x)=10x
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Which number does not make the number sentence 26 + y> 30 true?
A. 10 B. 4 c. 7 d. 100
===================================
If you plug 4 in for y;
26 +4>30
it is untrue, because it = 30 it is not greater than
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3(x – 4) > 7x – 9
3x-12>7x-9
3x-7x>-9+12
-4x>3
x<-3/4

Since the inequality is less than, you will circle -3/4 and make a line from the circle going left on the number line.
:)

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You should post the problem, we do not all have that book
:)