Answer:
Different ways to solve a system of linear equations:
- isolate one variable in one equation and replace it in the other equation
- multiply/divide one equation by a constant and then add/subtract it to the other one, so that only one variable remains
- graph the equation and look at the intersection point
If you graph the system:
- there is only one solution if the lines intersects at only one point
- there is no solution if the lines don't intersect each other (they are parallel)
- there are infinitely many solutions if the lines overlap each other (they are the same equation multiplied by some constant)
Step-by-step explanation:
1st system
y = -x – 7
y = 4/3 x – 7
solution: x= 0, y = 7
2nd system
y = -3x – 5
y = x + 3
solution: x = -2, y = 1
3rd system
y = -2x + 5
y = 1/3 x – 2
solution: x = 3, y = -1
4th system
3x + 2y = 2
x + 2y = -2
solution: x = 2, y = -2
5th system
x + 3y = -9
2x – y = -4
solution: x = -3, y = -2
6th system
x – 2y = 2
-x + 4y = -8
solution: x = -4, y = -3
7th system
5x + y = -2
x + y = 2
solution: x = -1, y = -3
Answer:
The distribution is skewed, so use the five-number summary. range: 38, median: 16, half of the data are between 9.5 and 25
Step-by-step explanation:
In the picture attached the histogram is shown. We can see that data is skewed to the right, so we have to use the five-number summary. The range of the data is 39 - 1 = 38 (subtraction of the maximum value to the minimum value); the median is (15 + 17)/2 = 16 (if you order the values, 15 and 17 are in the middle); quartile 1 is 9.25 and quartile 3 is 25.5 (see diagram of box and whisker attached), then half of the data are between those values.
Answer:
The length of each smaller piece, l=L/n inches
Step-by-step explanation:
This can be expressed as;
Total length=Length per piece×number of pieces
where;
The total length=L
length per piece=l
number of pieces=n
Substituting in the equation;
L=l×n
To get the length of each smaller piece;
l=L/n inches
solving;
l=30.75/3=10.25 inches
Volume of triangular prism + volume of rectangular prism = total volume
16*4*6+1/2*12*9=V
438=V
The volume of the figure is 438ft²
Answer:
Step-by-step explanation:
159.39(1-25/100)
159.39(100-25)/100
159.39(75)/100
159.39(0.75)
$119.54
