The shaded region's area is x² + 23x + 49.
Step-by-step explanation:
Step 1; To calculate the area of the shaded region, we subtract the area of the square which has side lengths of (x + 1) from the entire rectangle. So we determine the equations that denote the areas of the two shapes.
Step 2; Area of the square = side length × side length (x + 1)×(x + 1) = x² + x + x + 1 = x² + 2x + 1
Area of the bigger rectangle = length × breadth = (x + 10) × (2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50.
Step 3; The given shaded region's area = Area of the bigger rectangle - Area of the smaller square = 2x² - x² + 25x - 2x + 50 - 1 = x² + 23x + 49.
So the shaded region's area of x² + 23x + 49.
[4^(5/4+1/4)]^1/2
= --------------------------
4^(1/2 * 1/2)
[4^(6/4)]^1/2
= ----------------------
4^(1/4)
4^(3/2 * 1/2)
= ----------------------
4^(1/4)
4^(3/4)
= ---------------
4^(1/4)
= 4^(3/4 - 1/4)
= 4^2/4
= 4^1/2
= √4
= 2
Answer is C. 2
Answer:
slope = -3/14
Step-by-step explanation:
y1 - y2 / x1 - x2
They gave you one value, two total coordinates
5-5 = 1
-3 - 11
-14
1/-14
y=1/-14 + b
11= 1/-14(-3) + b
11 = -3/14 + b
17 + 14
b = 15 3/14
Let's solve for x first.
To find x, use the interior angles on same side of a transversal theorem.
The interior angles on sam side of a transversal are supplemantary angles, and supplementary angles sum up to 180 degrees.
Thus, we have:
(23x - 16) + (8x - 21) = 180
23x - 16 + 8x - 21 = 180
Combine like terms:
23x + 8x - 21 - 16 = 180
31x - 37 = 180
Add 37 to both sides:
31x - 37 + 37 = 180 + 37
31x = 217
Divide both sides by 31:
To find y, use the vertical angles theorem.
Vertical angles are congruent.
Thus we have:
7y - 23 = 23x - 16
Since x = 7, substitute x for 7 in the equation above to find y.
7y - 23 = 23(7) - 16
7y - 23 = 161 - 16
7y - 23 = 145
Add 23 to both sides:
7y - 23 + 23 = 145 + 23
7y = 168
Divide both sides by 7:
x = 7
y = 24
ANSWER:
x = 7
y = 24
I think that would be the answer to your question:
-36-48 +4 =
-80
