Answer:
2
Step-by-step explanation:
Replace the number with x, then the equation would be:
7x-4=x+8
7x-x=8+4
6x=12
6x/6=12/6
x=2
Answer:
cant see the picture
Step-by-step explanation:
Answer: its C
Step-by-step explanation: cause i did that already
We are going to solve this problem two ways:
Solution 1. Graphical
If you plot the equation of temperature
![y(x) = -0.005x^2 + 0.45x + 125](https://tex.z-dn.net/?f=y%28x%29%20%3D%20-0.005x%5E2%20%2B%200.45x%20%2B%20125)
for x between 0 and 160 minutes you'll get the plot in the attachement.
The blue curve represents the variation of the temperature in time. Notice that it crosses the red line (132 degrees <span>Fahrenheit</span>) twice, at around 20 F and 70 F.
So the answer is yes, if will reach 132 F.
Solution 2. Analytical
In order to see if the variation of temperature y(x) intersects 132 F line means to solve the equation:
![-0.005x^2 + 0.45x + 125 = 132](https://tex.z-dn.net/?f=-0.005x%5E2%20%2B%200.45x%20%2B%20125%20%3D%20132)
Step 1. Write the equation in the quadratic form:
![-0.005x^2 + 0.45x - 7 = 0](https://tex.z-dn.net/?f=-0.005x%5E2%20%2B%200.45x%20-%207%20%3D%200)
Step 2. Calculate the discriminant:
![\Delta = b^2 - 4ac = 0.45^2-4 \cdot (-0.005) \cdot (-7) = 0.06](https://tex.z-dn.net/?f=%5CDelta%20%3D%20b%5E2%20-%204ac%20%3D%200.45%5E2-4%20%5Ccdot%20%28-0.005%29%20%5Ccdot%20%28-7%29%20%3D%200.06)
Only by looking at the discriminant we can see that it is positive, which means that it crosses the 132 F line in two points, which also means that there are two roots of the equation, both real numbers.
Step 3 (optional). Calculate the roots of the equation.
![x_1 = \frac{-b+ \sqrt{\Delta}}{2a} = \frac{-0.45+ \sqrt{0.06}}{2 \cdot (-0.005)}=20.5](https://tex.z-dn.net/?f=x_1%20%3D%20%5Cfrac%7B-b%2B%20%5Csqrt%7B%5CDelta%7D%7D%7B2a%7D%20%3D%20%5Cfrac%7B-0.45%2B%20%5Csqrt%7B0.06%7D%7D%7B2%20%5Ccdot%20%28-0.005%29%7D%3D20.5)
![x_2 = \frac{-b- \sqrt{\Delta}}{2a} = \frac{-0.45- \sqrt{0.06}}{2 \cdot (-0.005)}=69.5](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cfrac%7B-b-%20%5Csqrt%7B%5CDelta%7D%7D%7B2a%7D%20%3D%20%5Cfrac%7B-0.45-%20%5Csqrt%7B0.06%7D%7D%7B2%20%5Ccdot%20%28-0.005%29%7D%3D69.5)
As you can see, tha analytic solution matches the graphic solution. At time x=20.5 minutes the temperatures reaches 132 F and is still rising. At time x=69.5 minutes the temperature is again 132 F but this time is decreasing.