Answer:
Step-by-step explanation:
Let w represent the width of the rectangle.
The length of a rectangle is 7 inches less than twice the width, w, of the rectangle. It means that the length is (2w - 7) inches
Part A
The function that gives the area as a function of the width is
A(w) = w(2w - 7)
Part B:
If the area of the rectangle is 60 square inches, it means that
w(2w - 7) = 60
2w² - 7w = 60
2w² - 7w - 60 = 0
2w² + 8w - 15w - 60 = 0
2w(w + 4) - 15(w + 4) = 0
2w - 15 = 0 or w + 4 = 0
w = 15/2 or w = - 4
Since w cannot be negative, then
w = 15/2 = 7.5 inches
Answer:
aₙ=(-2)ⁿ*2.
Step-by-step explanation:
1) -4*(-2)=8; 8*(-2)=-16; -16*(-2)=32, ...
2) the required equation is:
aₙ=(-1)ⁿ*2ⁿ*2; ⇒ aₙ=(-2)ⁿ*2 or aₙ=(-1)ⁿ*2ⁿ⁺¹.
The answers are as follows:
1. Triangles are often used to build different types of support structures because of its beneficial properties. Triangles is rigid in shape and it has strength. When force is applied to the side of a triangle, it can not shift into another shape, this is because its sides and angles are fixed.
2. The properties of triangle that make it a desirable geometric shape for building support structures is its fixed sides, fixed angles, rigidity and strength. Triangles are the strongest shapes and they are stable. Thus, triangle can be easily fix together to provide strength and stability over a wide area.
3. There are different types of triangles, these include: equilateral triangle, scalene, isosceles, right triangle, obtuse and acute. Of all these triangles, the best triangle is equilateral triangle.
4. Triangle is preferred over other types of polygon because, it is the strongest. The other polygons can be bent into different other forms that are not regular polygon, but a triangle always retains its shape and can not be deformed.
1. The data is not linear. There's not a constant difference between the f(x) values. (AKA there's not a fixed slope between the data points)
2. The data is exponential, because there's a consistent ratio in the f(x) values:
189/567 = 1/3
63/189 = 1/3
21/63 = 1/3
7/21 = 1/3
Each new y-value (aka f(x)-value) is 1/3 the previous value.
Also, f(0)=567.
If we put that together, we have f(x) = 567 (1/3)^x.
24! If that is not correct please let me know
