9514 1404 393
Answer:
(x, y, z) = (-3, -1, 3)
Step-by-step explanation:
Many graphing calculators can solve matrix equations handily. Here, we use a combination of methods.
Use the last equation to write an expression for z.
z = 4 -x +4y
Substitute this into the second equation:
y -4(4 -x +4y) = -13
y -16 +4x -16y = -13
4x -15y -3 = 0
In genera form, the first equation can be written as ...
3x +y +10 = 0
Now, the solution to these two equations can be found to be ...
x = (-15(10) -1(-3))/(4(1) -3(-15)) = (-150 +3)/(4+45) = -3 . . . using "Cramer's rule"
y = -(10 +3x) = -(10 -9) = -1 . . . . from the first equation
z = 4 -(-3) +4(-1) = 3 . . . . . . . . from our equation for z
The solution to the system is (x, y, z) = (-3, -1, 3).
_____
<em>Additional comment</em>
Written as an augmented matrix, the system of equations is ...
Answer: She will need 36 yards of material.
Step-by-step explanation:
16 × 2¹/₄ can be done different ways,
First multiply ¹/₄ times 16. that is the same as dividing 16/4 = 4
Then multiply 2 times 16 2×16 = 32
Add 32 + 4 = 36
Another way is to change 2¹/₄ to an improper fraction and multiply
⁹/₄ × 16
16
<u> ×9</u>
54
<u> +9 </u>
144
144/4 = 36
<u />
I’m pretty sure c is supposed to be 37.4 instead of 27.4
Answer:
10
Step-by-step explanation:
In any polygon
exterior angle + interior angle = 180° , thus
exterior angle + 144 = 180 ( subtract 144 from both sides )
exterior angle = 36°
The sum of the exterior angles = 360°
Thus number of sides n is calculated as
n = 360 ÷ 36 = 10