The equation to solve this problem is 114 + 2.75x = 320.25. Solving this equation, we find that the cost of labor per hour, represented by x, is $75.
The problem you're trying to solve involves the labor cost per hour of the technician who worked on Caroline's computer. From the problem, we know that the total cost of the repair was $320.25. This includes the cost of parts, which was $114, and the labor the technician invested, which we know took 2.75 hours but we aren't sure of the per hour cost. Let's denote this unknown cost as x. Therefore, our equation would be 114 + 2.75x = 320.25.
We can solve for x, the cost of labor per hour, by isolating this variable on one side of the equation. Firstly, subtract 114 from both sides: 2.75x = 320.25 - 114 which results in 2.75x = 206.25. Then, divide both sides by 2.75 to find x: x = 206.25/2.75 which equals $75. Therefore, the cost of labor per hour is $75.
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Answer:
1/16
Step-by-step explanation:
To have one real solution, the discriminant must be 0.
b² − 4ac = 0
1² − 4a(4) = 0
1 − 16a = 0
a = 1/16
image attached
Step-by-step explanation:
this is only asking about the functional values.
in what intervals are the functional values going up (when increasing x from left to right), and in what intervals is the functional value going down (again, when increasing x from left to right) ?
and so we see in the graph,
it is increasing (y-values are going up) in
(-infinity, -1], (2, +infinity)
it is decreasing (y- values are going down) in
(-1, 2]
please consider the used types of brackets.
"(", ")" means the corresponding interval end is NOT included.
"[", "]" mags the corresponding interval end is included.
"infinity" is only a concept and not a value, so it can never be included.
and I wanted the intervals to have no overlap. so, I included "-1" in one and excluded it in the connecting interval. the same for "2".
but if your teacher prefers to have the interval ends overlapping, then please change these brackets to "["as needed. it all depends on what your teacher defined for you.
Answer:
42.4 miles per day
Step-by-step explanation:
212 miles ÷ 5 (days) = 42.4 miles
which means Lena can go at the rate of
42.4 miles per day
Reflection: in the line y=−1
The image of triangle △RST after the glide reflection, which involves a translation of (x, y) → (x - 3, y) followed by a reflection in the line y = -1, is △R'S'T' with vertices R'(1, -2), S'(4, -5), and T'(3, -6).
To graph triangle △RST with vertices R(4, 1), S(7, 3), and T(6, 4), and its image after the glide reflection, we'll follow these steps:
Start by plotting the original triangle △RST using the given vertices:
R(4, 1)
S(7, 3)
T(6, 4)
Now, let's apply the translation to every vertex of the triangle.
The translation (x, y) → (x - 3, y) shifts each point 3 units to the left (in the negative x-direction).
Apply this translation to each vertex:
R' = (4 - 3, 1) = (1, 1)
S' = (7 - 3, 3) = (4, 3)
T' = (6 - 3, 4) = (3, 4)
Next, we'll apply the reflection in the line y = -1 to the translated vertices. The reflection in this line flips each point across the line.
To do this, we'll calculate the distance between each point and the line y = -1 and then move the same distance in the opposite direction.
R'' is reflected across the line y = -1 to (1, -2).
S'' is reflected across the line y = -1 to (4, -5).
T'' is reflected across the line y = -1 to (3, -6).
Now, we have the vertices of the image triangle △R'S'T'.
You can plot these points on the same graph as the original triangle to visualize the glide reflection transformation.
For similar question on image of triangle.
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Answer:
Step-by-step explanation:
Points R(4,1) S(7,3) T(6,4) after translation
R(4-3, 1) S(7-3, 3) T(6-3, 4)
R'(1, 1) S'(4, 3) T'(3, 4)
Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection
R''(1, -3) S''(4, -5) T''(3, -6)
B. 1 hr. 40 min.
C. 10 hr. 20 min.
D. 11 hr.