Answer:
Step-by-step explanation:
Given the expressions :
The list price of the item is 80 percent of the original price. The price of the item has been reduced by 80 percent.
Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent.
Let the original price = x
Expression 1 : The list price of the item is 80 percent of the original price
List price = 80% of x
List price = 0.8x
Expression 2: The price of the item has been reduced by 80 percent
Price = x - 80% of x
Price = x - 0.8x
Price = 0.2x
Multiply by percentages is different from an Incremental or decrement in percentage. The first expression above signifies a direct multiplication by the stated percentage while the second signifies a decrease in price based on a certain percentage of the original price.
Wording of percentages are so important for clarity in other to understand if the statement signifies a direct application of the percentage prescribed or a change in quantity, amount or size relative to the base unit.
To find the slope of a line that goes through given points with known coordinates, you divide the subtraction of the y of the second point minus the y of the first point, by the subtraction of the x of the second point minus the x of the first point:
m = (yB-yA) / (xB-xA)
Let A(8,5) and B(6,7).
With yB = 7; yA = 5; xB = 6; xA = 8
m = (7-5) / (6-8)
m = 2/-2
m = -1
So the slope of the line that goes through the given points (8,5) and (6,7) is m = -1.
I've added a pic of the line with both points under the answer.
Hope this Helps! :)
Answer:
First Integer = 16
Second Integer = 18
Third integer = 20
Step-by-step explanation:
An even integer is represented by 2n
Where n is any integer
Let :
First Integer = 2n - 2
Second Integer = 2n
Third integer = 2n + 2
The sum of three even consecutive numbers = 2n - 2 + 2n + 2n + 2
= 2n + 2n + 2n - 2 + 2 = 54
= 6n = 54
n = 54/6
n = 9
First Integer = 2n - 2 = 2(9) - 2
= 16
Second Integer = 2n = 2(9)
= 18
Third integer = 2n + 2 = 2(9) + 2
= 20
3 + 5(c + 3) = -17
First, subtract 3 from both sides. / Your problem should look like:
Second, simplify -17 - 3 to get -20. / Your problem should look like:
Third, divide both sides by 5. / Your problem should look like:
Fourth, simplify

to 4. / Your problem should look like:
Fifth, subtract 3 from both sides. / Your problem should look like:
Sixth, simplify -4 - 3 to get -7. / Your problem should look like:

Answer:
c = -7
Answer:
A, B, D, F
Step-by-step explanation:
Matrix operations require that the matrix dimensions make sense for the operation being performed.
Matrix multiplication forms the dot product of a row in the left matrix and a column in the right matrix. That can only happen if those vectors have the same dimension. That is the number of columns in the left matrix must equal the number of rows in the right matrix.
Matrix addition or subtraction operates on corresponding terms, so the matrices must have the same dimension.
The transpose operation interchanges rows and columns, so reverses the dimension numbers. It is a defined operation for any size matrix.
<h3>Defined operations</h3>
A. CA ⇒ (4×7) × (7×2) . . . . defined
B. B -A ⇒ (7×2) -(7×2) . . . . defined
C. B -C ⇒ (7×2) -(4×7) . . . undefined
D. AB' ⇒ (7×2) × (2×7) . . . . defined
E. AC ⇒ (7×2) × (4×7) . . . undefined
F. C' ⇒ (7×4) . . . . defined