Quadratic equation: ax² + bx + c =0
x' = [-b+√(b²-4ac)]/2a and x" = [-b-√(b²-4ac)]/2a
6 = x² – 10x ; x² - 10x -6 =0
(a=1, b= - 10 and c = - 6
x' = [10+√(10²+4(1)(-6)]/2(1) and x" = [10-√(10²+4(1)(-6)]/2(1)
x' =5+√31 and x' = 5-√31
Answer:
<h2>14mph</h2>
Step-by-step explanation:
Given the gas mileage for a certain vehicle modeled by the equation m=−0.05x²+3.5x−49 where x is the speed of the vehicle in mph. In order to determine the speed(s) at which the car gets 9 mpg, we will substitute the value of m = 9 into the modeled equation and calculate x as shown;
m = −0.05x²+3.5x−49
when m= 9
9 = −0.05x²+3.5x−49
−0.05x²+3.5x−49 = 9
0.05x²-3.5x+49 = -9
Multiplying through by 100
5x²+350x−4900 = 900
Dividing through by 5;
x²+70x−980 = 180
x²+70x−980 - 180 = 0
x²+70x−1160 = 0
Using the general formula to get x;
a = 1, b = 70, c = -1160
x = -70±√70²-4(1)(-1160)/2
x = -70±√4900+4640)/2
x = -70±(√4900+4640)/2
x = -70±√9540/2
x = -70±97.7/2
x = -70+97.7/2
x = 27.7/2
x = 13.85mph
x ≈ 14 mph
Hence, the speed(s) at which the car gets 9 mpg to the nearest mph is 14mph
<span>For the question "Mike's closing costs will add up to 4 percent and he'll make a down payment of 20 percent on a house that costs $210,000. Over the life of his loan, he will pay $197,040.76 in monthly payments. What is the total cost of his house?"
To obtain the total cost of the house, we first obtain the amount he paid as the closing costs and the down payment he paid which we will add to the total amount paid in monthly payments.
Closing cost = 4% of $210,000 = 0.04 x 210,000 = $8,400
Down payment = 20% of $210,000 = 0.2 x 210,000 = $42,000
Total monthly payments = $197,040.76
Total cost of the house = $8,400 + $42,000 + $197,040.76 = $247,440.76</span>
Answer:
THIS IS A RIDDLE
Step-by-step explanation:
GO TO THE RIDDLE SECTION
