For which values of x and w is line a parallel to line d? Image shows that line a and line d are parallel. There is an intersecting line that creates these angles: (45x-5)°;(16x+2)°;(26^w)°. Choose one answer choice.
1. x=3, w=5
2. x=3, w=6
3. x=1, w=5
4. x=5, w=3
To determine when line a is parallel to line d, we need to compare the corresponding angles between the two lines: (45x-5)° and (26^w)°.
Since both angles are equal, we can set up an equation:
45x - 5 = 26^w
Now let's examine the answer choices:
1. x = 3, w = 5
Plug in the values: 45(3) - 5 = 26^5
This equation is not true, so this option is not correct.
2. x = 3, w = 6
Plug in the values: 45(3) - 5 = 26^6
This equation is not true, so this option is not correct.
3. x = 1, w = 5
Plug in the values: 45(1) - 5 = 26^5
This equation is true, so this option could be correct.
4. x = 5, w = 3
Plug in the values: 45(5) - 5 = 26^3
This equation is not true, so this option is not correct.
Therefore, the answer is option 3, x = 1 and w = 5.
To determine when line a is parallel to line d, we need to compare the slopes of the two lines.
The slopes of the lines can be determined by the coefficients of x in their respective equations.
For line a, the slope is 45.
For line d, the slope is 16.
Since the slopes are different, line a and line d are not parallel.
Therefore, none of the answer choices are correct.
Please let me know if there is anything else I can help you with.
To determine which values of x and w make line a parallel to line d, we need to compare the corresponding angles formed by these lines.
In the given information, the angles formed by line a are (45x-5)° and (16x+2)°.
The angle formed by line d is (26^w)°.
For two lines to be parallel, the corresponding angles formed by the lines must be equal.
Therefore, we can set up the following equation to find the values of x and w:
(45x-5)° = (16x+2)° = (26^w)°
Since all three angles must be equal, we can equate any two pairs of them to each other.
Let's equate the first two angles:
(45x-5)° = (16x+2)°
To solve this equation, we can simplify and solve for x:
45x - 5 = 16x + 2
45x - 16x = 2 + 5
29x = 7
x = 7/29
Now that we have the value of x, we can substitute it into the third angle equation to find the value of w:
(26^w)° = (45x-5)°
(26^w)° = (45 * (7/29) - 5)°
To solve this equation, we need to know more about the exponentiation term (26^w). Does it mean that 26 is raised to the power of w? Or is it 26 multiplied by w, and the exponent of the resulting product is w? Please clarify the exact meaning of (26^w).
Once we have the clarification, we can proceed to solve for w and determine the correct values of x and w that make line a parallel to line d.