Given:
Length of the rectangle = x + 21
Width of the rectangle = 5
To find:
Perimeter and area of the rectangle
Solution:
Perimeter =
Perimeter units
Area = length × width
Area square units
Substitute perimeter is 100 and find the value of x:
Subtract 52 from both sides.
Divide by 2 on both sides, we get
x = 24
Substitute area is 200 and find the value of x:
Subtract 105 from both sides.
Divide by 5 on both sides, we get
x = 19
If the perimeter is 100, then the value of x is 24.
If the area is 200, then the value of x is 19.
A <em>difference of squares</em> is exactly what it suggests - the difference between two perfect squares. 25 - 9, 4 - 1, x² - 25, and 125 - b² are just a few examples. Differences of squares factor very nicely, too. For any difference of squares x² - y²:
x² - y² = (x + y)(x - y)
We can see that this is true by taking the right side of the equation and distributing:
(x + y)(x - y) = (x + y) · x + (x + y) · (-y) = x² + xy - xy - y² = x² - y²
We notice in our given expression that 36 is a perfect square - namely, 6². We want the expression x² + ?x - 36 to look like x² - 6², which we can accomplish if we replace the question mark with a 0.
Answer:
403.33
Step-by-step explanation:
The price is in square yd not feet so change ft to yds
3 ft = 1 yd
12 ft = 12/3 = 4 yds
10 ft = 10/3 yds
A = l * w = 4 * 10/3 = 40/3 yd^2 = 13 1/3 yd ^2
Now multiply by the price per yd^2
13 1/3 yd^2 * 30.25 = 403.333333
Rounding to the nearest cent
403.33
Answer:
SSS
Step-by-step explanation:
The two triangles both share a side (the middle line), and it is shown that the other lines are congruent to each other. So all 3 sides are congruent, meaning SSS is the postulate that proves this.
Answer:
-4(5x - 9) + 6(2x + 5)
multiplication of:
(-).(-) = +
(-).(+) = -
(+).(-) = -
(+).(+) = +
-4(5x) -4(- 9) + 6(2x + 5)
(-)(+)4(5x) (-)(-)4(9) (+)(+) 6(2x) (+)(+)6( 5)
-20x + 36 + 12x + 30
-20x + 12x + 36 + 30
-8x + 66
Step-by-step explanation: