Answer:
The area of the sector is 9.43 ft^2
Step-by-step explanation:
Here, we want to find the area of the sector with a central angle of 30 degrees
To do this, we use the formula below;
Area of sector = theta/360 * pi * r^2
theta = central angle = 30 degrees
r = radius = 6 ft
Thus, we have it that;
Area of sector = 30/360 * pi * 6^2
= 30/10 * pi = 3 * 3.142 = 9.43 ft^2
Answer:
The equation of the parallel line is
y = 3x + 9
Step-by-step explanation:
The general equation of a straight line is given as;
y = mx + c
where m is the slope and c is the intercept
If two lines are parallel, their slopes are equal
So the slope of the new line too is 3
Using the point-slope formula
y-y1 = m(x-x1)
y-12 = 3(x-1)
y-12 = 3x-3
y = 3x-3 + 12
y = 3x + 9
Answer:
-10
-5
5
Step-by-step explanation:
From the answers given, you probably mean f(x) = x^3 + 10x2 – 25x – 250
The Remainder Theorem is going to take a bit to solve.
You have to try the factors of 250. One way to make your life a lot easier is to graph the equation. That will give you the roots.
The graph appears below. Since the y intercept is -250 the graph goes down quite a bit and if you show the y intercept then it will not be easy to see the roots.
However just to get the roots, the graph shows that
x = -10
x = - 5
x = 5
The last answer is the right one. To use the remainder theorem, you could show none of the answers will give 0s except the last one. For example, the second one will give
f((10) = 10^3 + 10*10^2 - 25*10 - 250
f(10) = 1000 + 1000 - 250 - 250
f(10) = 2000 - 500
f(10) = 1500 which is not 0.
==================
f(1) = (1)^3 + 10*(1)^2 - 25(1) - 250
f(1) = 1 + 10 - 25 - 250
f(1) = -264 which again is not zero
Answer:
S₁₅ = 645
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
=
[ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Using the nth term formula
= 5n + 3 , then
a₁ = 5(1) + 3 = 5 + 3 = 8
a₂ = 5(2) + 3 = 10 + 3 = 13 , then
d = a₂ - a₁ = 13 - 8 = 5
Thus
S₁₅ =
[ (2 × 8) + (14 × 5) ]
= 7.5( 16 + 70)
= 7.5 × 86
= 645