To get the solution of a set of equations means to get a point that satisfies both equations.
Part (1):The first line has a rate of change of 7, this means that slope of first line is 7
The second line has a rate of change of -7, this means that slope of second line is -7
Since the slope of the first line = - slope of the second line, then these two lines are definitely perpendicular to each other.
Two perpendicular lines will meet only in one point. This means that one point only will satisfy both equations (check the image showing perpendicular lines attached below)
Therefore, only one solution exists in this casePart (2): The first given equation is:
2x + 3y = 5.5
The second given equation is:
4x + 6y = 11
If we simplified the second equation we will get: 2x + 3y = 5.5 which is exactly similar to the first equation.
This means that the two given equations represent the same line.
Therefore, we have infinite number of solutionsPart (3):We are given that the two lines are parallel. This means that the two lines are moving the same path side by side. Two parallel lines can never intersect. This means that no point can satisfy both equations (check the image showing parallel lines attached below).
Therefore, we have no solutions for this case.
Step-by-step explanation:
Total cost
= Cost of tools + Cost of materials
= $130 + 100 * $10
= $1,130.
This is an incomplete problem. The missing information is
Each bulleted statement describes how the amount of income tax is determined for
yearly income in different ranges.
1) Yearly incomes of $8,925 or less are taxed at a flat rate of 10%.
2) For yearly incomes from $8,926 to $36,250, the first $8,925 is taxed at 10%
and any income beyond $8,925 is taxed at 15%.
3) For yearly income greater than $36,250, the first $8,925 is taxed at 10%, the
next $27,325 is taxed at 15%, and any income beyond $36,250 is taxed at
25%
The taxable income of Mr. Vance corresponds to number 2.
⇒ 8,925 * 10% = 892.50
⇒ 35,675 - 8,925 = 26,750 * 15% = 4,012.50
Total tax = 892.50 + 4,012.50 = 4,905
Option I: 10 candy bars for $6.75
<span>6.75/10 = 0.68 </span>
<span>Option II: 12 candy bars for $7.25 </span>
<span>7.25 / 12 = 0.60 </span>