so we have the points of (0,-7),(7,-14),(-3,-19), let's plug those in the y = ax² + bx + c form, since we have three points, we'll plug each one once, thus a system of three variables, and then we'll solve it by substitution.
well, from the 1st equation, we know what "c" is already, so let's just plug that in the 2nd equation and solve for "b".
well, now let's plug that "b" into our 3rd equation and solve for "a".
![\bf -19=9a-3b-7\implies -12=9a-3b\implies -12=9a-3(-1-7a) \\\\\\ -12=9a+3+21a\implies -15=9a+21a\implies -15=30a \\\\\\ -\cfrac{15}{30}=a\implies \blacktriangleright -\cfrac{1}{2}=a \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{and since we know that}}{-1-7a=b}\implies -1-7\left( -\cfrac{1}{2} \right)=b\implies -1+\cfrac{7}{2}=b\implies \blacktriangleright \cfrac{5}{2}=b \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{2}x^2+\cfrac{5}{2}x-7~\hfill](https://tex.z-dn.net/?f=%5Cbf%20-19%3D9a-3b-7%5Cimplies%20-12%3D9a-3b%5Cimplies%20-12%3D9a-3%28-1-7a%29%20%5C%5C%5C%5C%5C%5C%20-12%3D9a%2B3%2B21a%5Cimplies%20-15%3D9a%2B21a%5Cimplies%20-15%3D30a%20%5C%5C%5C%5C%5C%5C%20-%5Ccfrac%7B15%7D%7B30%7D%3Da%5Cimplies%20%5Cblacktriangleright%20-%5Ccfrac%7B1%7D%7B2%7D%3Da%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Band%20since%20we%20know%20that%7D%7D%7B-1-7a%3Db%7D%5Cimplies%20-1-7%5Cleft%28%20-%5Ccfrac%7B1%7D%7B2%7D%20%5Cright%29%3Db%5Cimplies%20-1%2B%5Ccfrac%7B7%7D%7B2%7D%3Db%5Cimplies%20%5Cblacktriangleright%20%5Ccfrac%7B5%7D%7B2%7D%3Db%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20y%3D-%5Ccfrac%7B1%7D%7B2%7Dx%5E2%2B%5Ccfrac%7B5%7D%7B2%7Dx-7~%5Chfill)
4 and 3
The LCM of these two numbers is 12.
Added together, their sum is 7.
Each girl started with 15 dollars.
4$ is the ending amount
x= the amount of money each girl received
4= 2x - 2(13)
Since there were two girls who both received x amount of money, x is multiplied by two. Since both the girls spent 13 dolars on lunch, their original amount is subtracted by 13 times two, since there are two lunches being bought. The end amount of money is four.
to solve:
4= 2x - 2(13)
4= 2x - 26 Simplify by combining like terms
30= 2x Isolate the variable by adding 26 to both sides
15=x Continue to isolate the variable by dividing both sides by two
Each girl started with 15 dolars. Each girl spent thirteen dolars on lunch and had two dolars left over. Each girls' two dolars left over adds up to four dollars.
It was the temperature peak 89.4 without this there would be no difference.
To use an equation to predict a pattern, we substitute the value of the input variable in the equation.
<h3>What are equations?</h3>
- Equations are used to represent expressions of equal values
- Equations are represented by the "=" sign
<h3>Using equation to predict a pattern</h3>
To use an equation to predict a pattern, we simply substitute the value of the independent variable in the equation.
Take for instance, we have the following equation that represents a pattern
In the above equation, we have:
- x represents the independent variable i.e. the input
- y represents the dependent variable i.e. the output
When x = 1, y = 3
When x = 2, y = 5
When x = 3, y = 7
So, a pattern from the equation could be 3, 5, 7....
Read more about equation and patterns at:
brainly.com/question/15590116
