Answer:
c.
Step-by-step explanation:
From the last row in the matrix z = 1.
From the second row:
y + 5z = -4
y = -4 -5(1) = -9.
From the first row:
x + -1 = -3
x = - 3 + 1
x = -2.
Answer:
The weights of each cylinder and prism are 3 and 4 ounces, respectively.
Step-by-step explanation:
Let be
and
the masses of a cylinder and a prism, measured in ounces, respectively. After a careful reading of the statement we get the following linear equations by interpretation:
i) <em>She found that 4 cylinders and 5 prisms weigh 32 ounces:</em>
(Eq. 1)
ii) <em>And that 1 cylinder and 8 prisms weigh 35 ounces:</em>
(Eq. 2)
Now we solve the system of linear equations algebraically:
From (Eq. 2):

(Eq. 2) is (Eq. 1):





From (Eq. 2):



The weights of each cylinder and prism are 3 and 4 ounces, respectively.
Answer:
The speeds of the cars is: 0.625 miles/minute
Step-by-step explanation:
We use systems of equations in two variables to solve this problem.
Recall that the definition of speed (v) is the quotient of the distance traveled divided the time it took :
. Notice as well that the speed of both cars is the same, but their times are different because they covered different distances. So if we find the distances they covered, we can easily find what their speed was.
Writing the velocity equation for car A (which reached its destination in 24 minutes) is:

Now we write a similar equation for car B which travels 5 miles further than car A and does it in 32 minutes:

Now we solve for
in this last equation and make the substitution in the equation for car A:

So this is the speed of both cars: 0.625 miles/minute