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jarptica [38.1K]
3 years ago
14

What is 1 fourth times 3 sevenths

Mathematics
1 answer:
OlgaM077 [116]3 years ago
4 0

Answer:

3/28

Step-by-step explanation:

1/4*3/7=3/28

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Show work please.<br><br> solve system of equations using matrices.
nadya68 [22]

Answer:

(t, t -1, t)

Step-by-step explanation:

You have three unknowns but only 2 equations, so you can't really SOLVE this...you can get a solution with a variable still in it (I forget what this is called.  I think it refers to infinite many solutions).  Here's how it works:

Set up your matrix:

\left[\begin{array}{ccc}1&-2&1\\2&-1&-1\\\end{array}\right] \left[\begin{array}{ccc}2\\1\\\end{array}\right]

You want to change the number in position 21 (the 2 in the scond row) to a 0 so you have y and z left.  Do this by multiplying the top row by -2 then adding it to the second row to get that 2 to become a 0.  Multiplying in a -2 to the top row gives you:

\left[\begin{array}{ccc}-2&4&-2\\2&-1&-1\\\end{array}\right]\left[\begin{array}{ccc}-4\\1\\\end{array}\right]

Then add, keeping the first row the same and changing the second to reflect the addition:

\left[\begin{array}{ccc}-2&4&-2\\0&3&-3\\\end{array}\right] \left[\begin{array}{ccc}-4\\-3\\\end{array}\right]

The second equation is this now:

3y - 3z = -3.  Solving for y gives you y = z - 1.  Let's let z = t (some random real number that will make the system true.  Any number will work.  I'll show you at the end.  Just bear with me...)

lf z = t, and if y = z - 1, then y = t - 1.  So far we have that y = t - 1 and z = t.  Now we solve for x:

From the first equation in the original system,

x - 2y + z = 2.  Subbing in t - 1 for y and t for z:

x - 2(t - 1) + t = 2.  Simplify to get

x - 2t + 2 + t = 2  and  x - t = 0, and x = t.  So the solution set is (t, t - 1, t).  Picking a random value for t of, let's say 2, sub that in and make sure it works.  If:

x - 2y + z = 2, then t - 2(t - 1) + t = 2 becomes t - 2t + 2 + t = 2, and with t = 2, 2 - 2(2) + 2 + 2 = 2.    Check it:  2 - 4 + 4 = 2 and 2 = 2.  You could pick any value for t and it will work.

6 0
3 years ago
You have purchased 10 large pizzas in order to prepare for a party that will
Anuta_ua [19.1K]

Answer:

s(x) = 10/x

Step-by-step explanation:

There are x number of people. When you divide an amount by x, you get

amount/x

Here, the amount is 10 since you bought 10 pizzas, so each person gets

10 divided by x.

s(x) = 10/x

6 0
2 years ago
Witold says that 50% of a number will always be greater than 20% of any other number. Complete one inequality to support Witold'
Lelu [443]
.50 x 2 < .20 x 100
1 < 20

50% of 2 is not greater than 20% of 100.
4 0
3 years ago
A company produces individually wrapped spherical biscuits. The minimum amount of wrapping material needed to cover a biscuit, a
svetlana [45]
Sphere surface area is A=4pi*r^2. So r is sqrt(A/4pi)
r=4cm. So d=8cm
4 0
3 years ago
Divide 32x4 − 12x2 + 7x by 2x.<br><br> What is the quotient?
miss Akunina [59]
<span> 32x4 - 12x2 + 7x
-------------------
           2x</span>
5 0
3 years ago
Read 2 more answers
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