9514 1404 393
Answer:
(x, y, z) = (-1, 0, -3)
Step-by-step explanation:
We notice that the coefficients of z are such that elimination of the z term from the equations is made easy.
Adding equations 1 and 2:
(2x -3y -2z) +(x +3y +2z) = (4) +(-7)
3x = -3
x = -1
Adding equations 2 and 3:
(x +3y +2z) +(-4x -4y -2z) = (-7) +(10)
-3x -y = 3
Substituting for x, we get ...
(-3)(-1) -y = 3
0 = y . . . . . . . . . . . add y-3 to both sides
Then z can be found from any equation. Substituting for x and y in the second equation gives ...
-1 +2z = -7
2z = -6 . . . . . add 1
z = -3 . . . . . .divide by 2
The solution is (x, y, z) = (-1, 0, -3).
The volume of the original prism is given by:
V1 = (1/2) * (b) * (h) * (H)
Where,
b: base of the triangle
h: height of the triangle
H: prism height
The volume of the prism with new dimensions is:
V2 = (1/2) * (3b) * (3h) * (3H)
Rewriting:
V2 = (3 * 3 * 3) * (1/2) * (b) * (h) * (H)
V2 = (27) * (1/2) * (b) * (h) * (H)
V2 = (27) * V1
Answer:
The relationship between the volumes of the two prisms is:
V2 = (27) * V1
To find the x coordinate of the midpoint, add the x coordinates and divide by 2
(-5+3)/2 = -2/2 = -1
To find the y coordinate of the midpoint, add the y coordinates and divide by 2
(3+-1)/2 = 2/2 = 1
(-1,1)
1. Any number above 13 works. Why? Because 20-7=13, and to be greater than 20, you must add a number larger than 13.
Examples: 14+7 > 20, 30+7 > 20, 100+7 > 20
2. Any number below 25/3 (which is also 8.3 with a repeating 3) works. Why? Because 25/3=8.3 with a repeating 3, and to remain less than 25, you must multiply by a number less than 8.3 with a repeating 3.
Examples: 3(8) < 25, 3(5) < 25, 3(0) < 25
3. 4 buses. 1 bus will hold 60 students, 2 will hold 120, 3 will hold 180, and 4 will hold 240. The question is trying to trick you into putting now 3.3333333333... buses because that's what 200/60 is, but there is no such thing as a third of a bus. So you need at least 4 buses. (There will be an extra 40 spaces for passengers on the 4th bus, but that is okay.)
To find this answer I did 200/60 and got 3.3 with a repeating 3. You must round to the higher whole number. Rounding down to 3 buses leaves you with 20 students without a bus.
4. 19 boxes. 18 boxes will only hold 288 candies. The question is trying to trick you into putting down 18.75 boxes because that's what 300/16 is, but there is no such thing as 75% of a box. So you need at least 19 boxes. (There will be an extra 4 spaces for candies in the 19th box, but that is okay.)
To find this answer I did 300/16 and got 18.75. You must round to the higher whole <span>number. Rounding down to 18 boxes leaves you with 12 candies without a box.</span>
