Answer:
X=3,y=-2
Step-by-step explanation:
This is a simultaneous equation question and we will have to solve using substitution method
So let's solve
y=-2x+4...(1)
y=-2....(2)
Let's substitute (2) into (1)
-2=-2x+4
Substrate 4 from both sides
-6=-2x
Divide both sides by-2
x=3
Substitute the value of x in (1)
y=-2(3)+4
y=-6+4
y=-2
Therefore x is 3,y is -2
Cos (π/2 - x) = sin x = 3/5
tan x = sin x / cos x = 3/5 / 4/5 = 3/4
csc x = 1/sin x = 1 / 3/5 = 5/3
sec x = 1/cos x = 1 / 4/5 = 5/4
cot x = 1/tan x = 1 / 3/4 = 4/3.
Answer:
Step-by-step explanation:
hello :
x² - 6x = 7
x² - 6x+9-9___= 7
(x - 3 )²= __16_
x - 3= +/-_4__
x-3=4__and x-3 =_-4_
Depth of Hank descends = The point he reached - the point where he worked initially
= 57 - 10
= 47 ft
Hence, Hank descends 47 ft.
Answer:
Step-by-step explanation:
Area = 192 m²
Perimeter= 56 m
Width = x m
Perimeter = 56
2*(length + width) = 56
Divide the equation by 2
l + x = 56/2
l + x = 28
l = 28 - x
Area = 192 m²
l * w = 192
(28 - x)*x = 192
28x - x*x = 192
0 = 192 - 28x + x²
x² - 28x + 192 = 0
2) Equation is a quadratic equation. The roots of this equation will the dimensions of the rectangular plot.
3) The roots represent the width and length of the rectangle.
x² - 28x +192 = 0
Sum = -28
Product =192
Factors = -16 , -12 {-16 +(-12) = -28 & (-12)*(-16) = 192}
x² - 28x + 192 = 0
x² - 12x - 16x + (-16)*(-12) = 0
x(x -12) - 16(x - 12) = 0
(x - 12)(x -16) =0
x -12 = 0 ; x - 16 = 0
x = 12 ; x = 16
x = 12 ,16
4) Sum of the roots = 12 + 16 = 28
Sum of the roots = half of the perimeter
5) Product of the roots = 12*16 = 192 = area of the rectangle.
