<span>Because the four numbers are consecutive, we can call the first one x, and the other three are x+1, x+2, and x+3, respectively.
x * (x+1) = (x+2) * (x+3) - 38
x^2 + x = x^2 + 5x +6-38
x^2 + x = x^2 + 5x - 32
-4x = -32
x=8
The four numbers are 8, 9, 10, and 11
check solution: 8*9=10*11-38
72=110-38
72=72</span>
Answer:
![\huge\boxed{x=8;\ y=1\to(8;\ 1)}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bx%3D8%3B%5C%20y%3D1%5Cto%288%3B%5C%201%29%7D)
Step-by-step explanation:
![\left\{\begin{array}{ccc}y=x-7&(1)\\5+2y=7&(2)\end{array}\right\\\\\text{Substitute (1) to (2) and solve for x:}\\\\5+2(x-7)=7\qquad\text{use the distributive property}\\\\5+(2)(x)+(2)(-7)=7\\\\5+2x-14=7\\\\2x+(5-14)=7\\\\2x-9=7\qquad\text{add 9 to both sides}\\\\2x-9+9=7+9\\\\2x=16\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{16}{2}\\\\\boxed{x=8}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dy%3Dx-7%26%281%29%5C%5C5%2B2y%3D7%26%282%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7BSubstitute%20%281%29%20to%20%282%29%20and%20solve%20for%20x%3A%7D%5C%5C%5C%5C5%2B2%28x-7%29%3D7%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%7D%5C%5C%5C%5C5%2B%282%29%28x%29%2B%282%29%28-7%29%3D7%5C%5C%5C%5C5%2B2x-14%3D7%5C%5C%5C%5C2x%2B%285-14%29%3D7%5C%5C%5C%5C2x-9%3D7%5Cqquad%5Ctext%7Badd%209%20to%20both%20sides%7D%5C%5C%5C%5C2x-9%2B9%3D7%2B9%5C%5C%5C%5C2x%3D16%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5C%5C%5C%5Cdfrac%7B2x%7D%7B2%7D%3D%5Cdfrac%7B16%7D%7B2%7D%5C%5C%5C%5C%5Cboxed%7Bx%3D8%7D)
![\text{Substitute it to (1):}\\\\y=8-7\\\\\boxed{y=1}](https://tex.z-dn.net/?f=%5Ctext%7BSubstitute%20it%20to%20%281%29%3A%7D%5C%5C%5C%5Cy%3D8-7%5C%5C%5C%5C%5Cboxed%7By%3D1%7D)
If he runs 6 mph for 1.5 hours, he will run a total of 9 miles
Answer:
The function has 2 zeros:
![x = -1 - \frac{1}{\sqrt{3}}\\x = -1 + \frac{1}{\sqrt{3}}](https://tex.z-dn.net/?f=x%20%3D%20-1%20-%20%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%5C%5Cx%20%3D%20-1%20%2B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D)
Step-by-step explanation:
When you have a polynomial function, you can identify the grade of the function (the grade is the maximum potency) and this is the number of zeros that the function will have. In this case, you have a second-grade polynomial function that has 2 zeros.
It has 0 solution there are no meeting points of the two given lines.