Answer:
The slope of the line is -3/1
Step-by-step explanation:
Using the rise over run method I calculated that the slope is -3/1 because every block that the line goes over it goes 3 down.
Answer:
60
Step-by-step explanation:
In the function, the growth factor is "a", the base of the exponent. When the exponent is increased by 1, the value is multiplied by "a".
f(7) = a·f(6) = 4·15
f(7) = 60
_____
As you know, the exponent signifies repeated multiplication. So, an increase of 1 in the exponent means the base is part of the product one more time:
a^6 = a·a·a·a·a·a
a^7 = a·a·a·a·a·a·a = a·(a^6)
You need to do this in several steps.
1) Using the given length and width of the rectangle, find its area.
2) Then using the base and height of the triangle, find its area.
3) Since the areas are equal, set the expressions equal to each other, and solve for x.
4) Using the value of x you found, find the length and width of the rectangle and find its perimeter.
1) The area of the rectangle is A = LW
Area of Rectangle = (x + 2)x = x^2 + 2x
2) The area of the triangle is A = (1/2)bh
Area of Triangle = (1/2)(24)x = 12x
3) Set the areas equal and solve for x
x^2 + 2x = 12x
x^2 - 10x = 0
x(x - 10) = 0
x = 0 or x = 10
Since a width cannot be 0, we discard x = 0, and keep x = 10.
4) The length is x + 2 = 10 + 2 = 12
The width is x = 10
The perimeter is 2(L + W) = 2(10 + 2) = 2(22) = 44
The perimeter is 44 cm.
Answer:
D. 2019
Step-by-step explanation:
So I started by rewriting the function f(x)
1000 = 10^3 so
f(x)=10^3 times 1.03^x
1.03 = 103/100 so
f(x)= 10^3 times (103/100)^x
to raise a fraction to a power you just raise the numerator and denominator to that power so
f(x)= 10^3 times 103^x/100^x
change it to exponential form with a base of 10
f(x)=10^3 times 103^x/10^2x
then you can reduce it with the 10^3
f(x)=103^x/10^2x-3
so now that thats in more of a standard form you can find the intersection of the two functions
which is at (9.012,1305.244)
x is the number of years after 2010, so they will be equal ~9 years after 2010, which is 2019.