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:
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Step-by-step explanation:
The formula for the perimeter of a rectangle is 
.
If the width is 
and the length is 
, then the perimeter becomes:
.
.
.
Therefore the answer is
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Answer:
Caleb arrived first 2 hours before Alyssa
Step-by-step explanation:
To solve the situation, find the speed per hour they were driving by dividing the distance they drove by the time it took.
Alyssa drove 105 miles in 3.5 hours or 105/3.5 = 30 miles per hour.
Caleb drove 168 miles in 4 hours or 168/4 = 42 miles per hour.
Since they both left at the same time and drove the same 210 miles to the beach, Caleb arrived first since he was driving faster.
He arrived in 210/42 = 5 hours.
Alyssa arrived in 210/30 = 7 hours.
He arrived 2 hours before her.
Answer:
240 square feet
Step-by-step explanation:
Hello, I can help you with this
Step one
find the real scale
According to the data
scale is 1 in : 2 ft
also remember 1ft=12 inches
so
scale is 1in: 2(12 inches)
scale is 1 in :24 in
the purpose of use inches a unit in both sides is to eliminate the, the scale must be adimensional
so escales is
1:24 , this means, that a measure on the blueprint must be multiplied by 24 to know its real value
Step 2
with the escale find the real dimensions, you can use a rule of three
Abraham's bedroom is 6 inches wide
blueprint ⇔ bedroom
1 in ⇔ 24 in
6 in ⇔x
x=(6*24)/1
x=144 inches=12 ft
Abraham's bedroom is 10 inches long
1 in ⇔ 24 in
10 in ⇔y
y=(10*24)/1
x=240 inches=20 ft
Step 3
find the area
the area is wide *long
area=x*y
area=12ft*20ft
area=240 square feet.
Have a good day
2/3,2/6,2/8
23 is the greatest because it has larger pieces
2/6 is the second greatest because it is a little smaller than thirds
2/8 is the least because it has the smallest pieces
