x=31,y=−61
Put the equations in standard form and then use matrices to solve the system of equations.
5x+4y=1,3x−6y=2
Write the equations in matrix form.
(534−6)(xy)=(12)
Left multiply the equation by the inverse matrix of (534−6).
inverse((534−6))(534−6)(xy)=inverse((534−6))(12)
The product of a matrix and its inverse is the identity matrix.
(1001)(xy)=inverse((534−6))(12)
Multiply the matrices on the left hand side of the equal sign.
(xy)=inverse((534−6))(12)
For the 2×2 matrix (acbd), the inverse matrix is (ad−bcdad−bc−cad−bc−bad−bca), so the matrix equation can be rewritten as a matrix multiplication problem.
(xy)=(5(−6)−4×3−6−5(−6)−4×33−5(−6)−4×345(−6)−4×35)(12)
Do the arithmetic.
(xy)=(71141212−425)(12)
Multiply the matrices.
(xy)=(71+212×2141−425×2)
Do the arithmetic.
(xy)=(31−61)
Extract the matrix elements x and y.
x=31,y=−61
Is it a writing assignment?
Answer:
220 m
Step-by-step explanation:
since it takes him 22 min, and each min he travels 100 m, you just have to multiply 22 by 100
22 x 100 = 220
I’m pretty sure that the answer is D
The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.
Depending on the formula you know, you can find the length of a side in 1 of 2 ways.
The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.
c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
c^2 = 400 + 400 - 800(cos 45)
c^2 = 800 - 800(cos 45)
c = sqrt(800 - 800(cos 45)
c = 15.31
The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31
We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using
a = S / (2 tan (180 / n)
a = 15.31 / (2 tan (180 / 8))
a = 18.48
Now solve for the area
Area = ap/2
Area = (18.48)(122.48)/2
Area = 1131.72
perimeter = 122.48
area = 1131.72