Hannah's monthly housing budget is $1,750. her monthly costs are $230 for insurance, $98 for utilties, and $250 for
taxes. which of these houses can she afford?
ob
house a; monthly payment of $1,300
house b; monthly payment of $1,200
house c; monthly payment of $1,100
с

The house which Hannah's can afford is whose monthly payment is below $ 1,172  , I.e House C of $ 1,100

Step-by-step explanation:

Given as :

The monthly housing budget of Hannah's = $ 1750

The insurance monthly cost = $ 230

The cost for utilties = $ 98

The taxes she pay = $ 250

So, The amount of Hannah's expenses = The insurance monthly cost + The cost for utilties + The taxes she pay

Or, The amount of Hannah's expenses = $230 + $98 + $250 = $578

Now, The remaining amount for housing budget = $ 1750 - $ 578

∴ The remaining amount for housing budget = $ 1,172  .  

Hence The house which Hannah's can afford is whose monthly payment is below $ 1,172  , I.e House C of $ 1,100    Answer

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.