Answer:
![A)\ \ \ \ \left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]](https://tex.z-dn.net/?f=A%29%5C%20%5C%20%5C%20%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Given the matrix: ![\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%265%5C%5C3%268%5C%5C%5Cend%7Barray%7D%5Cright%5D)
, it's inverse is calculated using the formula:
![\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]^{-1}=\frac{1}{det\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] }\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D)
#Therefore, we calculate as;
![\frac{1}{det\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right] }\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right] \\\\\\\\\#det\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right] =1\\\\\\\\=\frac{1}{1}\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right] \\\\\\\\=\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%265%5C%5C3%268%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%5C%5C%5C%23det%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%265%5C%5C3%268%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D1%5C%5C%5C%5C%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B1%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Hence, the inverse of the matrix is ![\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Given A={1,2,3}, B={2,4,6} and C={1,2,3,4,5,6}, then A ∩ (B ∩ C) =
oksian1 [2.3K]
Answer:
Step-by-step explanation:
A={1,2,3}
B={2,4,6}
C={1,2,3,4,5,6}
B∩C={2,4,6}
A∩(B∩C)={1,2,3}∩{2,4,6}={2}
Answer:
x3 – 7x2 + 3------ x3 - 7x2 + 3
3x3 + x2-----------x2 • (3x + 1)
x2 + 4x - 3------------ x2 + 4x - 3
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
((x3) - 7x2) + 3
Step 2 :
Polynomial Roots Calculator :
2.1 Find roots (zeroes) of : F(x) = x3-7x2+3
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 3.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -5.00
-3 1 -3.00 -87.00
1 1 1.00 -3.00
3 1 3.00 -33.00
Hope this helps.
I'm going to use the substitution method.
If y = - 3/2 - 7, then:
1/2x + 5 = - 3/2x - 7
Combine like terms:
4/2x = - 12. Mutiply both sides by 2/4 to get x = -12 (2/4)
Simplify to get:
x = - 6.
Plug - 6 back in for x in either equation.
Y = 1/2( - 6) + 5 which becomes Y = - 3 + 5.
X = - 6, Y = 2
To solve this problem, you will first want to convert 5 pounds into ounces. To do this, first determine how many ounces is in 1 pound.
There are 16 ounces in 1 pound, so to convert 5 pounds into ounces, you simply have to multiply 5 × 16. This will give you 80 ounces total.
Allie give 12 ounces away, so you must first subtract 12 ounces from your total (80 ounces). 80 - 12 gives us 68 ounces.
Allie then divides the trail mix up into 4 ounce portions. To figure out how many small bags she can make, you simply divide your new total (68 ounces) by 4.
68 ÷ 4 = 17
Allie made 17 small bags.
