They are equal so...
15x+2 = 9x+20
15x-9x = 20-2
6x =18
x = 18/6 = 3
x = 3
Answer:
x = -4, x = 1
Step-by-step explanation:
Now I do not know why you said done, but just saying, if you are done with a question, you should delete it. Now I am just going to assume you knew this and move on with the solution of the problem.
When you factor this equation, you will get (x+4)(x-1).
You can then solve for x using zero product property. The first root is -4 and the second root is 1.
Answer:
q=26.92 p=31.13
Step-by-step explanation:
![p^{2} +16q=1400\\\\q=\frac{1400-p^{2} }{16} ;\\\\700-p^{2} +10q=0\\\\q=\frac{p^{2}-700 }{10} ;\\\\](https://tex.z-dn.net/?f=p%5E%7B2%7D%20%2B16q%3D1400%5C%5C%5C%5Cq%3D%5Cfrac%7B1400-p%5E%7B2%7D%20%7D%7B16%7D%20%3B%5C%5C%5C%5C700-p%5E%7B2%7D%20%2B10q%3D0%5C%5C%5C%5Cq%3D%5Cfrac%7Bp%5E%7B2%7D-700%20%7D%7B10%7D%20%3B%5C%5C%5C%5C)
![q=q\\\\\frac{1400-p^{2} }{16} =\frac{p^{2}-700 }{10} \\\\10(1400-p^{2})=16(p^{2}-700)\\\\14000-10p^{2}=16p^{2}-11200\\\\14000+11200=16p^{2}+10p^{2}\\\\25200=26p^{2}\\\\p^{2}=\frac{25200}{26} \\\\p=+\sqrt{\frac{25200}{26}} \\\\p=31.13](https://tex.z-dn.net/?f=q%3Dq%5C%5C%5C%5C%5Cfrac%7B1400-p%5E%7B2%7D%20%7D%7B16%7D%20%3D%5Cfrac%7Bp%5E%7B2%7D-700%20%7D%7B10%7D%20%5C%5C%5C%5C10%281400-p%5E%7B2%7D%29%3D16%28p%5E%7B2%7D-700%29%5C%5C%5C%5C14000-10p%5E%7B2%7D%3D16p%5E%7B2%7D-11200%5C%5C%5C%5C14000%2B11200%3D16p%5E%7B2%7D%2B10p%5E%7B2%7D%5C%5C%5C%5C25200%3D26p%5E%7B2%7D%5C%5C%5C%5Cp%5E%7B2%7D%3D%5Cfrac%7B25200%7D%7B26%7D%20%5C%5C%5C%5Cp%3D%2B%5Csqrt%7B%5Cfrac%7B25200%7D%7B26%7D%7D%20%5C%5C%5C%5Cp%3D31.13)
replace p in any equation and
![q=\frac{1400-p^{2} }{16} \\\\q=\frac{1400-(31.13)^{2} }{16}\\\\q=26.92](https://tex.z-dn.net/?f=q%3D%5Cfrac%7B1400-p%5E%7B2%7D%20%7D%7B16%7D%20%5C%5C%5C%5Cq%3D%5Cfrac%7B1400-%2831.13%29%5E%7B2%7D%20%7D%7B16%7D%5C%5C%5C%5Cq%3D26.92)
Answer:
Cost of a coffee is <u>$2.5</u> and cost of a latte is <u>$4.25.</u>
Step-by-step explanation:
Let cost of 1 coffee be 'c' and cost of 1 latte be 'l' dollars.
Given:
4 coffees and 12 lattes cost $61.
12 coffees and 7 lattes cost $59.75.
∵ 1 coffee cost = ![c](https://tex.z-dn.net/?f=c)
∴ 4 coffees cost =
and 12 coffee cost = ![12c](https://tex.z-dn.net/?f=12c)
∵ 1 latte cost = ![l](https://tex.z-dn.net/?f=l)
∴ 12 lattes cost =
and 7 lattes cost = ![7l](https://tex.z-dn.net/?f=7l)
Now, as per question:
![4c+12l=61-----1\\12c+7l=59.75----2](https://tex.z-dn.net/?f=4c%2B12l%3D61-----1%5C%5C12c%2B7l%3D59.75----2)
Now, multiplying equation (1) by -3 and adding the result to equation (2). This gives,
![-3(4c+12l)=-3(61)\\\\-12c-36l=-183\\12c+7l=59.75\\+\\----------\\0-29l=-123.25\\\\l=\frac{-123.25}{-29}=\$4.25](https://tex.z-dn.net/?f=-3%284c%2B12l%29%3D-3%2861%29%5C%5C%5C%5C-12c-36l%3D-183%5C%5C12c%2B7l%3D59.75%5C%5C%2B%5C%5C----------%5C%5C0-29l%3D-123.25%5C%5C%5C%5Cl%3D%5Cfrac%7B-123.25%7D%7B-29%7D%3D%5C%244.25)
Now, plug in the value of 'l' in equation 1 to solve for 'c'. This gives,
![4c+12(4.25)=61\\\\4c+51=61\\\\4c=61-51\\\\4c=10\\\\c=\frac{10}{4}=\$2.5](https://tex.z-dn.net/?f=4c%2B12%284.25%29%3D61%5C%5C%5C%5C4c%2B51%3D61%5C%5C%5C%5C4c%3D61-51%5C%5C%5C%5C4c%3D10%5C%5C%5C%5Cc%3D%5Cfrac%7B10%7D%7B4%7D%3D%5C%242.5)
Therefore, cost of a coffee is $2.5 and cost of a latte is $4.25.