Answer:
<u>Option b. (x = 3, y = 20, z = -14)</u>
Step-by-step explanation:
Given:
2x + 2y + 3z = 4
5x + 3y + 5z = 5
3x + 4y + 6z = 5
Solve using Cramer’s rule
∴ ![\left[\begin{array}{ccc}2&2&3\\5&3&5\\3&4&6\end{array}\right] =\left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%263%5C%5C5%263%265%5C%5C3%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
∴A = ![\left[\begin{array}{ccc}2&2&3\\5&3&5\\3&4&6\end{array}\right] = -1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%263%5C%5C5%263%265%5C%5C3%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20-1)
Ax = ![\left[\begin{array}{ccc}4&2&3\\5&3&5\\5&4&6\end{array}\right] = -3](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%262%263%5C%5C5%263%265%5C%5C5%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20-3)
Ay = ![\left[\begin{array}{ccc}2&4&3\\5&5&5\\3&5&6\end{array}\right] =-20\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%263%5C%5C5%265%265%5C%5C3%265%266%5Cend%7Barray%7D%5Cright%5D%20%3D-20%5C%5C)
Az = ![\left[\begin{array}{ccc}2&2&4\\5&3&5\\3&4&5\end{array}\right] = 14](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%264%5C%5C5%263%265%5C%5C3%264%265%5Cend%7Barray%7D%5Cright%5D%20%3D%2014)
∴ x = Ax/A = -3/-1 = 3
y = Ay/A = -20/-1 = 20
z = Az/A = 14/-1 = -14
<u>So, the answer is option b. (x = 3, y = 20, z = -14)</u>
Answer:
480 ft³
Step-by-step explanation:
Volume = base area × depth
(32 × 15) × 1
480 ft³
Answer:
First day: $75
Second day: $107
Together: $182
Step-by-step explanation:
First day:
$60 + $15 = $75
Second day:
$95 + $12 = $107
Together: $182
Answer:
Explanation:
The statement is expressed as
y
∝
1
x
inverse means
1
variable
To convert to an equation introduce k, the constant of variation.
y
=
k
×
1
x
⇒
y
=
k
x
To find k use the given condition that y = 8 when x = 4
8
=
k
4
⇒
k
=
4
×
8
=
32
⇒
equation is
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
y
=
32
x
2
2
∣
∣
∣
−−−−−−−−−−−−
x
=
16
→
y
=
32
16
⇒
y
=
2
when
x
=
16