Cheyenne drove 3000miles in 75 hours.at this rate, how long will it take her to drive 4000 miles
1 answer:
You might be interested in
Answer:
252 students at the party like to dance
Step-by-step explanation:
Given:
60% of the students are girls
40% of the students like to dance
20 more boy students
Percentage of the girls in the party = 58%
To Find:
How many students now at the party like to dance=?
Solution:
Let the number of girls be g.
Let the number of total people originally be t.
We know that
----------------------------------(1)
We also know that
-----------------------------(2)
We now have a system of equation from (1) and (2)
3t=5g
------------------------(3)
50g=29t+580------------------------(4)
Substituting 3 in 4, we get
t =589
So originally there was 580 students
In this 580 students 40% liked to dance
Then the number of students liked to dance =
=>
=>
=>
=> 232
We also know that with these people, 20 boys joined, all of whom like to dance.
Now the number of students like to dance = 232+20 = 252 students
Answer:
x = 0; y = -6; z = 1
Step-by-step explanation:
You want to find the solution to the system of equations ...
- 9x+y-3z=-9
- 10x-y+2z=8
- -10x-y+4z=10
This set of equations is conveniently solved using the matrix row-reduction features of a scientific or graphing calculator, spreadsheet, or any of a number of apps or on-line calculators.
The attachment shows the solution to be ...
(x, y, z) = (0, -6, 1)
__
<em>Additional comment</em>
Solving a system of three or more equations "by hand" often can be done by an ad hoc process. It can be done in systematic fashion using Gauss-Jordan reduction techniques, but that often gets messy. Similarly, Cramer's Rule can be used, but that math tends to involve more arithmetic operations than are really necessary.
Adding the first equation to the other two eliminates the y-variable and reduces the system to two equations in two unknowns.
(9x +y -3z) +(10x -y +2z) = (-9) +(8) . . . . adding [1] and [2]
19x -z = -1 . . . . simplified
(9x +y -3z) +(-10x -y +4z) = (-9) +(10) . . . . adding [1] and [3]
-x +z = 1 . . . . simplified
At this point, we could graph the two equations, or we can proceed algebraically.
Adding these two equations gives ...
(19x -z) +(-x +z) = (-1) +(1)
18x = 0 ⇒ x = 0
Using the second of the reduced equations, we find ...
-x +z = 1
0 +z = 1 ⇒ z = 1
And using the second of the original equations, gives us ...
10(0) -y +2(1) = 8
-y = 6 . . . . . subtract 2
y = -6 . . . . multiply by -1
Then the solution is (x, y, z) = (0, -6, 1), as above.
