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

4 0

3 years ago

4. Lee wanted to buy his mother flowers for Mother's Day. He bought 8

enot [183]

Answer:

Each tulip costs $1.50

Step-by-step explanation:

First, write an equation using the numbers given. It should look like this:

2.25(8) + 5x = 25.50

Next, multiply 2.25 by 8 to get: 18 + 5x = 25.50. Then, subtract 18 from both sides:

18 + 5x = 25.50

-18 -18

5x = 7.50

Finally, divide both sides of the equation by 5 to get $1.50

So, each tulip costs $1.50. Hope this helped!

3 0

2 years ago

Please help me solve thisss

Lorico [155]

The Vertical angle for <HKJ is <OKL or #12

6 0

3 years ago