3.2.PS-33 Liam has 63 CDs, Alex has 49 CDs, and Michael has 77 CDs. Use the GCF and the Distributive Property to find the tota
1 answer:
Answer:
The total number of CDs Liam, Alex, and Michael have is <u>189</u>.
Step-by-step explanation:
Given:
Liam has 63 CDs, Alex has 49 CDs, and Michael has 77 CDs.
Now, to find the total number of CDs using the GCF and the Distributive Property.
So, the CDs are :
Liam = 63.
Alex = 49.
Michael = 77.
Now, we factorize all the Number of CDs of Liam, Alex and Michael to get the GCF:
The factors of 63 are: 1, 3, 7, 9, 21, 63
The factors of 49 are: 1, 7, 49
The factors of 77 are: 1, 7, 11, 77
Thus, 7 is the GCF.
Now, we use the distributive property to get the total number of CDs Liam, Alex, and Michael have:
Therefore, the total number of CDs Liam, Alex, and Michael have is 189.
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Answer:
See picture and explanation below.
Step-by-step explanation:
With this information, the matrix A that you can find is the transformation matrix of T. The matrix A is useful because T(x)=Av for all v in the domain of T.
A is defined as denotes the vector of coordinates of
respect to the basis
(we can apply this definition because
forms a basis for the domain of T).
The vector of coordinates can be computed in the following way: if then
.
Note that we have all the required information: then
hence
The matrix A is on the picture attached, with the multiplication A(1,1,1).
Finally, to obtain the output required at the end, use the properties of a linear transformation and the outputs given:
In this last case, we can either use the linearity of T or multiply by A.
Answer:
6hours
Step-by-step explanation:
From the given information:
Suppose it took Karl x hours to retile her bathroom,
Then it will take Della 3 hours longer i.e (3+x) hours
If Della and Karl work together or will take them 2 hours
The objective is to determine how long it will take Delia to retile the bathroom alone?
∴
By cross multiplying, we have:
2(2x+3) = 3x+x²
4x + 6 = 3x + x²
3x + x² - 4x - 6
x² - x - 6 = 0
Using quadratic equation
x² -3x +2x - 6 = 0
x(x - 3) + 2(x - 3) = 0
(x +2) (x - 3) = 0
x + 2 = 0 or x - 3 = 0
x = -2 or x = 3
Since we are concerned about the positive integer,
Then, Karl = x = 3 hours while Della which is (3+x) = 3+3 = 6hours