mymathlab week8 quiz
TRANSCRIPT
To solve this problem, you must plug 109.95 and 151.95 into the equation for C.
109.95 = .25*(t-500)+70.95
109.95-70.95 = .25*t-.25*500
39 = .25*t-125
.25*t = 39+125
t = 164 / .25
t= 656.
Using the same algebraic manipulation, plug 151.95 for C into the equation and solve for t.
151.95 = .25*(t-500)+70.95
t = 824.
Answer is between t = 656 and t = 824.
Personally I think that matrices are the easiest way to solve 2 equations. If you know how to put a matrix into your calculator, it makes the process very simple.
[ .3 −.2.5 .3 ]^(-1) * (
4−717
¿
Answer = (5.8824, -11.1765) when solving the matrix.
To use elimination, you could multiply the top equation by 3 and the bottom by 2.
.9x -.6y = 12
1x+.6y= -14/17
Now if you add these two equations together, you can cancel the y variables.
1.9x+0*y = 190/17
X = ( 19017 )1.9
= 5.8824
Now plug x into either equation and solve for y.
.3*(5.8824)-.2*y = 4
1.7647-.2*y = 4
-.2*y = 2.2353
Y = 2.2353 / -.2 = -11.1765
Consistent because there is at least one solution.
The equations are dependent, both the lines from the two graphs are overlayed upon each other.
Using a matrix, the solution is x = 3 and y = -9. You can obtain the answer by multiplying the top equation by -8 and summing the two equations like this:
-48*x-8*y=-72
7*x+8*y = -51
Sum the two equations: -41*x+0*y = -123, x = -123/-41 = 3.
Now plug x=3 into either the top or bottom equation. You will get y = -9.
Answer as an ordered pair is (3,-9).
Since there is a solution, the system of equations is consistent.
The system represents the graph in C because you can see them intersect at 3,-9.
They want you to plug x = 8 and y = 20 into the equality and see if it’s true.
3*(20)-4*(8) > 7?
60-32> 7?
28 > 7?
Is 28 greater than 7?
Yes the pair is a solution.
The rule of thumb here is this: If you have greater or less than, the data point will be “open” (which means it is represented by a parenthesis in this case).
If you have a “greater than or equal to” or a “less than or equal to” sign, then the data point will be “closed” (which means it is represented by the bracket in this case).
So your answer would be C because it is between 0 and 16, yet it does not include 0 and 16.
Solve this just like any other equation.
a+4 ≤ -17
a≤-21
So your answer would be B because it is less than -21 and it includes -21.
You can solve this any method you like even though they say to solve by substitution.
Multiply the bottom by 3.
-9*x+3*y = 42
9*x + 9*y =54
Add the two equations together and solve for y.
0*x+12*y = 96
Y = 96/12 = 8.
Now plug y = 8 into either equation and solve for x.
-3*x+(8) = 14
-3*x = 6
x= -2
(-2,8) is your final answer.
4 y−3<7 y−4
4 y−3+4<7 y
4 y+1<7 y
1<3 y
13< y
y> 13
Is the final answer.
Plug the numbers they give you in for x and see if they make the equation true.
-6-1 ≥6?
-7 ≥6? No .
3-1≥6? No .
6-1≥6?
5≥6? No .
17-1≥6?Yes .
X+6←4
X←10
For the second equation:
x+6>4
x>-2
Since B is the only one that represents a number less than -10 and greater than -2, that is the answer, B.
*Notice that if the solution was x ≤−10∧x≥−2 ,thenCwould be your answer .
Same as last problem, just solve the two equations separately.
4x+18≥14
4x ≥−4
X≥−1
2x-18≥−14
2x≥4
X≥2
Since X is greater than or equal to -1, you second equation is meaningless.
The answer is B.
If you take the determinant of the system of equations:
5*7- (-7*-5) = 0.
If the determinant of a system of equations is zero, it means there are no solutions.
The equations are inconsistent because there are no solutions.
The graph would be A because the two lines do not intersect.
3*[5m-(m+4)] simplifies to 3*[5m-m-4], which simplifies to 3*[4m-4] = 12m-12
-4(m-6) simplifies to -4m+24.
12m-12¿−4m+24
16m¿36
m¿ 3616
m¿ 94
6y≤−5 x+30
y≤−56x+5
Create a data point at 5.
Go vertical by -5 (down) and go horizontal (right) by 6, that is your slope.
Create another data point by going vertical (up) 5 and going horizontal (left) by 6.
Since y is less than all those values, your y should be shaded on the bottom of the graph but will include the line.
I skipped this one to leave as an exercise for you. Solve all the equations for y and plot them using standard y = mx+b notation. The equation x ≥0 just means that you are only using values from the middle of the graph (x=0) all the way to the far right of the graph (x=∞ ¿
I’ll just put this in a matrix, you can solve this any way you like.
(-5/29, -176/29)
.16*x+.08*y = .1*320.
x+y = 320
Solve the two equations.
80 lbs of soybean and 240 lbs of cornmeal.
Because there is no “greater/less than or equal to”’s, the notation will only be in parenthesis.
The answer is B.
5*x/4 – 1/8 – 5/3 < 1/3
5x/4 – 3/24-40/24 < 8/24
5x/4 -43/24 < 8/24
5x/4 < 51/24
5x < (51/24)*4 = 5x < 204/24.
X < 204 / (120)
X<17/10
2x+2y = 128
X = 7+2*y
Solve the two equations.
Length = 45
Width = 19
9600/.8 = 12000
So the answer is D, greater than or equal to 12,000.
Graph 1 corresponds to y+x≤3
Graph 2 corresponds to 3x≥5 y−15
Graph 3 corresponds to 2x-3y<6
2x+2y = 206
Y = x+33
Solve the two equations.
Width = 35
Length = 68