Answer:
The augmented matrix for the system of equations is ![\left[\begin{array}{cccc}0&2&-3&1\\7&0&5&8\\4&1&-3&6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D0%262%26-3%261%5C%5C7%260%265%268%5C%5C4%261%26-3%266%5Cend%7Barray%7D%5Cright%5D)
.
Step-by-step explanation:
This system consists in three equations with three variables (
, 
, 
).The augmented matrix of a system of equations is formed by the coefficients and constants of the system of linear equations. In this case, we conclude that the system of equations has the following matrix:
The augmented matrix for the system of equations is .
<h3>
Answer: 12.5 (choice C)</h3>
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We apply the pythagorean theorem to find this answer.
a = 11 and b = 6 are the given legs
c = unknown hypotenuse
So,
a^2+b^2 = c^2
c = sqrt( a^2+b^2 )
c = sqrt( 11^2 + 6^2 )
c = sqrt( 121 + 36 )
c = sqrt( 157 )
c = 12.52996 approximately
c = 12.5
Side note: once you replace 'a' and b with 11 and 6, you can compute everything with a calculator in one single step more or less. The steps above are shown if you wanted to find the exact value sqrt(157).
Answer:
x=2,x=7
Step-by-step explanation:
-3x^2+27x=42
x^2-9x+14=0
x^2-2x-7x+14=0
x*(xi2)-7(x-2)=0
(x-2)*(x-7)=0
x-2=0
x-7=0
x=2
x=7
1. You have that the circle that defines the part of the planter wall which gets watered by the sprinkler is: (x−10)²+(y+12)²<span>=36.
2. The standard form for the equation of a circle is:
(x-h)</span>²+(y-k)²=r²
(h,k) is the center point.
r is the radius.
3. Keeping this on mind, you can find the value of the radius, as below:
r²=36
r=√36
r=6 m
4. Then, the diameter of the circle is:
D=2r
D=2(6m)
D=12 m
<span>
What is the diameter, in meters, of the circular area that gets watered by the sprinkler?</span>
The answer is: 12 m
