HURRYYY HELP! Triangle ABC is congruent to triangle FDE, and both triangles have the same orientation, as shown. What is the slo
pe of DF, which also the slope of AC?
1 answer:
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Answer:
The interval of the decreasing function is (-∞ , -1) ⇒ g(x)
The interval of the decreasing function is (-∞ , 0) ⇒ f(x)
Step-by-step explanation:
* Lets explain how to solve it
- Decreasing function means a function with a graph that moves
downward as it is followed from left to right.
- For example, any line with a negative slope is decreasing function
- Lets look to the attached graph to understand the meaning of the
decreasing function
∵ f(x) = IxI ⇒ green graph
∵ g(x) = Ix + 1I - 7 ⇒ purple graph
- From the graph f(x) translated 1 unit to the left and 7 units down to
form g(x)
- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}
- The range of f(x) is {y : y ≥ 0}
- The range of g(x) is {y : y ≥ -7}
# For f(x)
- The slope of the green line from (-∞ , 0) is negative
- The slope of the green line from (0 , ∞) is positive
# For g(x)
- The slope of the purple line from (-∞ , -1) is negative
- The slope of the purple line from (-1 , ∞) is positive
∵ The line with negative slope represent decreasing function
∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)
∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)
Answer:
There is enough evidence to support the claim that the true proportion of monitors with dead pixels is greater than 5%.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 300
p = 5% = 0.05
Alpha, α = 0.05
Number of dead pixels , x = 24
First, we design the null and the alternate hypothesis
This is a one-tailed(right) test.
Formula:
Putting the values, we get,
Now, we calculate the p-value from excel.
P-value = 0.00856
Since the p-value is smaller than the significance level, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.
Conclusion:
Thus, there is enough evidence to support the claim that the true proportion of monitors with dead pixels is greater than 5%.
Answer:
The triangular prism shown has 2 triangular face(s) and 3 lateral face(s).
The area of one triangular face is 7.5 mm²
The surface area of the triangular prism is 135 mm²
Step-by-step explanation:
A triangular face of the prism is the face that has a three sided figure while the lateral faces are faces with four-sided figure. As seen from the triangular prism, it has 2 triangular faces since it is made up of 2 right angled triangles and has 3 lateral faces since it is made up of 3 rectangles which are 4 sided each.
Area of one triangular face =
Given base = 2.5 mm and height = 6 mm
Area of one triangular face =
Surface area of triangular prism = bh + pH
b= base of the triangle = 2.5 mm
h- height of the triangle = 6 mm
p= perimeter of the triangle = base + height + slant height = 2.5+6+6.5
p = 15 mm
H= height of the prism = 8mm
Surface area of triangular prism = 2.5(6)+15(8)
Surface area of triangular prism = 15 + 120
Surface area of triangular prism = 135mm²
