Answer:
(fog)(x)=f(g(x))=2(3x+2)−1=6x+4−1=6x+3=3(2x+1)
If X is between P and Q, then PQ is the whole line segment and XQ and XP are line segments that add up to PQ. Therefore, you can make an equation where XQ and XP add up to PQ.
XQ + XP = PQ
(3k) + (7k - 2) = 6k + 18
Combine like terms.
10k - 2 = 6k + 18
Add 2 to both sides.
10k = 6k + 20
Subtract 6k from both sides.
4k = 20
Divide both sides by 4.
k = 5
Plug 5 for k into XP.
XP = 7(5) - 2 ⇒ 35 - 2
XP = 33
Answer:
The length of the garden=14 feet
Step-by-step explanation:
<em>Step 1: Determine the dimensions of the garden</em>
length of the garden=x feet
width of the garden=(x-4) feet
<em>Step 2: Determine the area of the garden</em>
Area of the garden=length×width
where;
area=140
length=x
width=x-4
replacing'
x(x-4)=140
x²-4x-140=0, solve the quadratic equation;
x={-b±√(b²-4ac)}/2a
x={4±√4²-4×1×-140}/2×1
x={4±√(16+560)}/2
x={4±√576}/2
x=(4±24)/2
x=(4+24)/2=14, or (4-24)/2=-10, take x=14
The length=14 feet, width=(14-4)=10 feet
The length of the garden=14 feet
Answer:16
Step-by-step explanation: 8(25−3)÷11
8(22)
176 divided by 11= 16
Answer:
![\left[\begin{array}{cc}-\frac{1}{2}&\frac{1}{6}\\-\frac{1}{2}&\frac{1}{3}\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5Cfrac%7B1%7D%7B2%7D%26%5Cfrac%7B1%7D%7B6%7D%5C%5C-%5Cfrac%7B1%7D%7B2%7D%26%5Cfrac%7B1%7D%7B3%7D%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
If a 2x2 matrix is given as:
![\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D)
The inverse is:
![\frac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bad-bc%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Our matrix given is:
![\left[\begin{array}{cc}-4&2\\-6&6\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-4%262%5C%5C-6%266%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<em />
<em>Using the formula, let's find the inverse:</em>
<em>![\frac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]\\=\frac{1}{(-4)(6)-(-6)(2)}\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\frac{1}{-12}\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\left[\begin{array}{cc}-\frac{1}{2}&\frac{1}{6}\\-\frac{1}{2}&\frac{1}{3}\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bad-bc%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%5Cfrac%7B1%7D%7B%28-4%29%286%29-%28-6%29%282%29%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%26-2%5C%5C6%26-4%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%5Cfrac%7B1%7D%7B-12%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%26-2%5C%5C6%26-4%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5Cfrac%7B1%7D%7B2%7D%26%5Cfrac%7B1%7D%7B6%7D%5C%5C-%5Cfrac%7B1%7D%7B2%7D%26%5Cfrac%7B1%7D%7B3%7D%5C%5C%5Cend%7Barray%7D%5Cright%5D)
</em>
