Answer:
Length: 5 ft; width: 4 ft.
Step-by-step explanation:
A = LW formula for area of rectangle
(2x + 1)(2x) = 20 substitute length, width, and area into formula
4x² + 2x - 20 = 0 use the distributive property to multiply out left side
2x² + x - 10 = 0 divide both sides of equation by 2
(2x + 5)(x - 2) = 0 factor out trinomial
2x + 5 = 0 or x - 2 = 0 use zero product rule to solve for x
2x = -5 or x = 2 subtract 5 from both sides; add 2 to both sides
x = -5/2 or x = 2
We discard x = -5/2 since it would give negative length and width, and the length and width cannot be negative.
Length: 2x + 1 = 2(2) + 1 = 5
Width: 2x = 2(2) = 4
Length: 5 ft; width: 4 ft.
Alright, so you have the basic formula- good.
You have the A value (400), the interest rate r (7.5% -> .075 in decimal), and the final P value (8500). So, we only need to solve for t.
8500 = (400)(1+.075)^t
/400 /400
21.25 = 1.075^t
logarithms are the inverse of exponents, basically, if you have an example like
y = b^x, then a logarithm inverts it, logy(baseb)=x
Makes sense if you consider a power of ten.
1000 = 10^3
if you put logbase10(1000), you'll get 3.
Anyways, though, to solve the problem make a log with a base of 1.075 in your calculator
log21.25(base 1.075) = t
also, because of rules of change of base (might want to look this up to clarify), you can write this as log(21.25)/log(1.075) = t
Thus, t is 42.26118551.
Rounded to hundredths, t=42.26
Substitute 3x+1 for x. Then solve from there
First let's reduce the feet to miles
there are 5280 feet in a mile therefore
26400 feet=5 miles
31680 feet=6 miles
Jet A(the first jet) descends 5 miles in 96 miles
Jet B(the second jet) descends 6 miles in 120 miles
We can compare these as fractions to see which is steeper. This can be viewed as slope and the origin (0,0) is the airport.
slope: 6/120=?=5/96
1/20=?=5/96
Now we know that 5/100 =1/20 so 5/96 must be bigger than 5/100 because you are dividing by a smaller number.
so 1/20<5/96
So Jet B is descending steeper than Jet A.
As for linear model, I don't exactly know what your teacher means but I think I actually used the linear model when I'm thinking of steepness as slope in the coordinate plane, I will include a picture.
In this extremely zoomed out graph, you can see the blue line is just slighly higher than the red line(slope as in explanation is way easier to tell) this could be seen as the linear model) :) Hope it helped!
Answer:
x
Step-by-step explanation:
;\
