Answer:
b = 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Here m = - 2 , then
y = - 2x + b ← is the partial equation
To find b substitute (5, - 7 ) into the partial equation
- 7 = - 10 + b ⇒ b = - 7 + 10 = 3
9514 1404 393
Answer:
66 cm²
Step-by-step explanation:
The area of the polygon is the sum of the areas of the triangle and the rectangle it sits on. The dimensions of the triangle can be found by examining the top/bottom dimensions shown and the left/right dimensions shown.
The width (base) of the triangle is the difference between the lengths of the bottom and top horizontal lines: (12 -9) cm = 3 cm.
The height of the triangle is the difference between the lengths of the left and right sides of the figure: (9 -5) cm = 4 cm.
The dimensions of the rectangle are shown a the bottom and the left sides of the figure.
triangle area = 1/2bh = 1/2(3 cm)(4 cm) = 6 cm²
rectangle area = LW = (12 cm)(5 cm) = 60 cm²
Total polygon area = 6 cm² + 60 cm² = 66 cm²
1/3 is the correct answer simplified
Answer:
56,275
Step-by-step explanation:
A₅ = 1/16 and r= 1/4
Let see how to build up this formula that is going to give that term of rank n
1st term =a₁ = To be calculated
1st a₁ = a₁ x r°
2nd a₂ = a₁ x r¹
3rd a₃ = a₁ x r²
4th a₄ = a₁ x r³
5th a₅ = a₁ x r⁴
.......................
.......................
nth : a(n) = a₁ x r⁽ⁿ-¹)
Note when that the subscript of a is the same as the exponent mines 1
We know the ratio r =1/4 & the fifth term, a₅ =1/16 (given). Now let's apply the formula to calculate the unknown a₁.
a(n) = a₁ x r⁽ⁿ-¹) ==>a₅ = a₁ x (1/4)⁽⁵⁺¹⁾ ===> 1/16 = a₁ x (1/4)⁴
1/167 = a₁ (1/256) ==> a₁ =16 & the formula becomes
a₅ = 16(1/4)⁴
