Answer:
85 units^2 = Area of Blue Square
and
x = 5 units
Step-by-step explanation:
To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.
Since we know the area of a square is the side length multiplied by itself (or the side length squared),
is the side length of the pink square and
is the side length of the green square.
That means a =
and b =
, so...

35 + 50 = c^2
85 = c^2

Now we need to square the square root of 85 to find the area of the blue square.

85 units^2 = Area of Blue Square
To solve the other question we use the same formula again.

x = 5 units
A) area of square = base*height/////Triangle= 0.5*base*height
=(a^1/3*b^3/4)*(a^2/3*b^1/2)+(1/2*a^1/3*b^3/4*a^2/3*b^1/4)
=(a^1*b^5/4)+(1/2*a^1*b^1)
=(a*b^5/4)+(1/2*a*b)
B) a^2+b^2=c^2 (pythagorean theorem)
((27^2/3)*(16^1/4))^2 + (27^1/3)*(16^3/4)
(9*2=(18^2))=324 + (3*8= 24^2)= 576
324+576= 900
(900)^1/2= 30
hypotenuse= 30
C)( a^2/3*b^1/2)= 36*2(two sides)= 72
(a^1/3b^3/4)=24
(a^2/3*b^1/4)= 18
72+24+18+30(hypotenuse)= 144=perimeter
Answer:
3 inches
Step-by-step explanation:
The green bar reaches all the way to the 3 on the ruler, and each number represents an inch.
Answer:
A
Step-by-step explanation:
Given (x + h) is a factor of f(x) then f(- h) = 0
Given
p(x) = x³ - 4x² + ax + 20 , with (x + 1) as a factor then
p(- 1) = (- 1)³ - 4(- 1)² - a + 20 = 0 , that is
- 1 - 4 - a + 20 = 0
15 - a = 0 ( subtract 15 from both sides )
- a = - 15 ( multiply both sides by - 1 )
a = 15 , thus
p(x) = x³ - 4x² + 15x + 20
If p(x) is divided by (x + h) then p(- h) is the remainder, so
p(- 2) = (- 2)³ - 4(- 2)² + 15(- 2) + 20 , that is
- 8 - 16 - 30 + 20 = - 34 → A