9514 1404 393
Answer:
C. define all variables
Step-by-step explanation:
Equations for word problems will depend on the problem. Not all of the equations will be linear equations. Even if they are, they are not necessarily easily written in any particular form, or easily solved when they are written in that form. The nature of the equations will depend on the problem.
One thing that must be done in any case is <em>define all variables</em>. It is usually a good idea to define the units of the variable(s) as well. Sometimes problems are posed with numbers in incompatible dimensions, or they may ask for an answer in dimensions different from those used in the given information. In order to avoid confusion and to be sure you have the desired answer, you need to make sure the variables and their dimensions are compatible with the solution process.
Step-by-step explanation:
Hey there!
The points of line AB are; (-1,-4) and (2,11).
Note:
- Use double point formula and simplify it to get two eqaution.
- Use condition of parallel lines, perpendicular lines to know whether the lines are parallel or perpendicular or nothing.
~ Use double point formula.
![(y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)](https://tex.z-dn.net/?f=%28y%20-%20y1%29%20%3D%20%20%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D%20%28x%20-%20x1%29)
~ Keep all values.
![(y + 4) = \frac{11 + 4}{2 + 1} (x + 1)](https://tex.z-dn.net/?f=%28y%20%20%2B%204%29%20%3D%20%20%5Cfrac%7B11%20%2B%204%7D%7B2%20%2B%201%7D%20%28x%20%2B%201%29)
~ Simplify it.
![y + 4 = \frac{15}{3} (x + 1)](https://tex.z-dn.net/?f=y%20%2B%204%20%3D%20%20%5Cfrac%7B15%7D%7B3%7D%20%28x%20%2B%201%29)
![y + 4 = 5x + 5](https://tex.z-dn.net/?f=y%20%2B%204%20%3D%205x%20%2B%205)
![5x - y + 1 = 0](https://tex.z-dn.net/?f=5x%20-%20y%20%2B%201%20%3D%200)
Therefore this is the equation of line AB.
Now, Finding the equation of line CD.
Given;
The points of line CD are; (1,1) and (4,10).
~ Using formula.
![(y - y1) = \frac{y2 - y1}{x2 - x1}(x - x1)](https://tex.z-dn.net/?f=%28y%20-%20y1%29%20%3D%20%20%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D%28x%20-%20x1%29%20)
~ Keep all values.
![(y - 1) = \frac{10 - 1}{4 - 1} (x - 1)](https://tex.z-dn.net/?f=%28y%20-%201%29%20%3D%20%20%5Cfrac%7B10%20-%201%7D%7B4%20-%201%7D%20%28x%20-%201%29)
~ Simplify it.
![y - 1 = 3 x - 3](https://tex.z-dn.net/?f=y%20-%201%20%3D%203%20x%20-%203)
![3x - y - 2 = 0](https://tex.z-dn.net/?f=3x%20-%20y%20-%202%20%3D%200)
Therefore, 3x - y- 2 = 0 is the eqaution of line CD.
Use condition of parallel lines.
m1= m2
Slope of equation (i)
![m1 = \frac{ - coeff. \: of \: x}{coeff \: of \: y}](https://tex.z-dn.net/?f=m1%20%3D%20%20%5Cfrac%7B%20-%20coeff.%20%5C%3A%20of%20%5C%3A%20x%7D%7Bcoeff%20%5C%3A%20of%20%5C%3A%20y%7D%20)
![m1 = \frac{ - 5}{ - 1}](https://tex.z-dn.net/?f=m1%20%3D%20%20%5Cfrac%7B%20-%205%7D%7B%20-%201%7D%20)
Therefore, m1 = 5
Slope of second equation.
![m2 = \frac{ - coeff \: .of \: x}{coeff \: .of \: y}](https://tex.z-dn.net/?f=m2%20%3D%20%20%5Cfrac%7B%20-%20coeff%20%5C%3A%20.of%20%5C%3A%20x%7D%7Bcoeff%20%5C%3A%20.of%20%5C%3A%20y%7D%20)
![m2 = \frac{ - 3}{ - 1}](https://tex.z-dn.net/?f=m2%20%3D%20%20%20%5Cfrac%7B%20-%203%7D%7B%20-%201%7D%20)
Therefore, m2 = 3.
Now, m1≠m2.
So, the lies are not parallel.
Check for perpendicular.
m1*m2= -1
3*5≠-1.
Therefore, they aren't perpendicular too.
So, they are neither.
<em><u>Hope </u></em><em><u>it</u></em><em><u> helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>
Answer:
x = 9
Step-by-step explanation:
2x - 1 + 1 = 17 + 1
2x = 18
(2x=18)/2
x = 9
The ladder leaning against the wall forms a right angled triangle with the gound and the wall. So we can use the formula:a² + b² = c²The ladder is the hypotenuse c²The vertical leg is b²The base or horizontal leg is a²We need to find the length of the base a², so:a² = c² - b²a² = 5² - 4²a² = 25 - 16a² = 9a = √9a = 3<span>Therefore the bottom of the ladder must be 3 feet from the wall.
Example:
</span>If the 24 foot ladder is leaned on the house with the bottom 8 feet from the base the wall of the house, then it will form a right angled triangle.The base of the triangle will be 8 feet while the 24 foot ladder forms the hypotenuse. We need to find out the height from the base of that wall to the point the ladder touches the wall.Let the hypotenuse be CLet the base be BLet the height be AWe use this formula: A squared + B squared = C squaredA sq + 8 sq = 24 sqA sq + 64 = 576A sq = 576 - 64A sq = 512A = Square root 512A = 22.6To the nearest 10th this will be 23<span>So the answer is 23 feet.</span>