Answer: h = 9
Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.
The matrix given is:
![\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C5%26-7%26-3%5Cend%7Barray%7D%5Cright%5D)
Transform this matrix in a row-echelon form:
![\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C0%260%26-9%2Bh%5Cend%7Barray%7D%5Cright%5D)
For this row-echelon form to have solutions:
-9 + h = 0
h = 9
For this system to be consistent: h = 9.
Answer:
<h3>a)a+c=150,10.25a+7.75c=1470</h3>
Step-by-step explanation:
<h3>to understand this</h3><h3>you need to know about:</h3>
- system of linear equation
<h3>let's solve:</h3>
according to the first condition
according to the second condition
Answer:
f = 2
g = 8
h = -9
k = 40
m = 1
Step-by-step explanation:
Equation 1:
23f - 17 = 29
Add 17 to both sides. This undoes the -17.
23f = 29 + 17
Add 17 to 29 to get 46.
23f = 46
Divide both sides by 23. This undoes the multiplication by 23.
f = 46/23
Divide 46 by 23 to get 2.
f = 2
Equation 2:
2(3g + 4) = 56
Divide both sides by 2. This undoes the multiplication by 2.
3g + 4 = 56/2
Divide 56 by 2 to get 28.
3g + 4 = 28
Subtract 4 from both sides. This undoes the +4.
3g = 28 - 4
Subtract 4 from 28 to get 24.
3g = 24
Divide both sides by 3. This undoes the multiplication by 3.
g = 24/3
Divide 24 by 3 to get 8.
g = 8
Equation 3:
h + 9 = 0
Subtract 9 from both sides. This undoes the +9.
h = 0 - 9
Any number subtracted from 0 gives its negation.
h = -9
Equation 4
3(k - 8) = 96
Divide both sides by 3. This undoes the multiplication by 3.
k - 8 = 96/3
Divide 96 by 3 to get 32.
k - 8 = 32
Add 8 to both sides. This undoes the -8.
k = 32 + 8
Add 8 to 32 to get 40.
k = 40
Equation 5:
5m - 5 = 0
Add 5 to both sides. This undoes the -5
5m = 0 + 5
Anything plus 0 gives itself.
5m = 5
Divide both sides by 5. This undoes the multiplication by 5
m = 5/5
Anything divided by itself gives you 1.
m = 1
700/10 equals 70, so the answer is 70.
Its 23.1 one because in 23 minutes they travel three miles
