Find an ordered pair to represent [tex]\vec{t}[/tex] in the equation [tex]\vec{t}=-8 \vec{u}[/tex] if [tex]\vec{u}=\langle-1,4\rangle[/tex] and [tex]\vec{v}=\langle 3,-2\rangle[/tex].
a. [tex] \{8,-32\} [/tex]
c. [tex] \{-32,8\} [/tex]
b. [tex] \langle 16,-4\rangle [/tex]
d. [tex] \langle-4,16\rangle [/tex]

Please select the best answer from the choices provided

The best way to solve a problem like this is to set up two equations. First assign a variable to each thing you are trying to find. In this case, it's two different kinds of cars. Let's call the cars that weigh 3,000 pounds x, and the ones that weigh 5,000 y. The two equations you should write are:
x+y=18 (because the problem tells you there were 18 cars in total) 3000x+5000y=60000 (because that is the total weight in the problem)
Next, you need to solve for one of the variables. I will solve for x first by subtracting y from both sides of the first equation.
x=18-y
Then you have to plug that into the other equation to get:
3000(18-y)+5000y=60000
Simplify and solve for y:
54000-3000y+5000y=60000 54000+2000y=60000 2000y=6000 y=3
Now that you know what y equals, you can put it into the equation we solved for x:
x=18-3 x=15
So there are 15 cars that weigh 3000 pounds and 3 that weigh 5000.

Answered by livingakingsomeday | 2024-06-10

The best way to solve a problem like this is to set up two equations. First assign a variable to each thing you are trying to find. In this case, it's two different kinds of cars. Let's call the cars that weigh 3,000 pounds x, and the ones that weigh 5,000 y. The two equations you should write are:
x+y=18 (because the problem tells you there were 18 cars in total)
3000x+5000y=60000 (because that is the total weight in the problem)
Next, you need to solve for one of the variables. I will solve for x first by subtracting y from both sides of the first equation.
x=18-y
Then you have to plug that into the other equation to get:
3000(18-y)+5000y=60000
Simplify and solve for y:
54000-3000y+5000y=60000
54000+2000y=60000
2000y=6000
y=3
Now that you know what y equals, you can put it into the equation we solved for x:
x=18-3
x=15
So there are 15 cars that weigh 3000 pounds and 3 that weigh 5000. ;

Answered by isistheicecube | 2024-06-12

The solution shows that there are 15 cars weighing 3,000 pounds each and 3 cars weighing 5,000 pounds each in the shipment. We set up a system of equations to find the quantities of each type. After solving, we find the exact numbers of each kind of car in the shipment.
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Answered by livingakingsomeday | 2024-12-23