Answer:
Step-by-step explanation:
We want to simplify:
Recall the Pythagorean Identity:
So:
Substitute:
Factor. We can use the difference of two squares pattern:
Cancel. Hence:
Answer:
NUMBER 1.)
Step 1
Subtract 3y3y from both sides.
5x=10-3y5x=10−3y
Step 2
Divide both sides by 55.
\frac{5x}{5}=\frac{10-3y}{5}
5
5x
=
5
10−3y
Hint
Undo multiplication by dividing both sides by one factor.
Step 3
Dividing by 55 undoes the multiplication by 55.
x=\frac{10-3y}{5}x=
5
10−3y
Hint
Undo multiplication.
Step 4
Divide 10-3y10−3y by 55.
x=-\frac{3y}{5}+2x=−
5
3y
+2
Hint
Divide.
Solution
x=-\frac{3y}{5}+2x=−5
3y+2
Step-by-step explanation:
NUMBER 2.)
Step 1
Add 4y4y to both sides.
3x=6+4y3x=6+4y
Step 2
The equation is in standard form.
3x=4y+63x=4y+6
Step 3
Divide both sides by 33.
\frac{3x}{3}=\frac{4y+6}{3}
3
3x
=
3
4y+6
Hint
Undo multiplication by dividing both sides by one factor.
Step 4
Dividing by 33 undoes the multiplication by 33.
x=\frac{4y+6}{3}x=
3
4y+6
Hint
Undo multiplication.
Step 5
Divide 6+4y6+4y by 33.
x=\frac{4y}{3}+2x=
3
4y
+2
Hint
Divide.
Solution
x=\frac{4y}{3}+2x= 3
4y+2
Answer: x=-3
Step-by-step explanation:
2x-18=8x
-2x. -2x.
-18=6x
-18/6=6x/6
-3=x
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.
Answer:
340
Step-by-step explanation:
860 ÷ 2 = 430
430 - 90 = 340
