To solve an absolute inequality first step is to isolate absolute value expression.
Hence remove -4 from the left side. So, add 4 to each sides of the inequality.
2|x + 7|−4 ≥ 0
2|x + 7|−4 +4≥ 0 +4
2|x + 7| ≥ 4 Combine the like terms.
Divide each sides by 2.
|x + 7| ≥2
Next step is to remove the absolute value sign. So,
x + 7≥2 and x+7≤-2.
x≥2-7 and x≤-2-7
x≥-5 and x≤-9
So, the correct choice is C. {x | x ≤ -9 or x ≥ -5}.
A random variable is used like this:
You close your eyes and point anywhere on the table to choose a number. Since the given random number table is made up of 3 digits, you only get the first two digits. We are also given a 70% of catching a fish, that means that the number you choose should not have a first two digit number greater than 70. If that happens, you go down to the next value. If you reach the bottom, you go up to the next column. This is done 3 times and multiplying the three numbers to get the chance for 1 trials. This is repeated 20 times and the average is obtained.
Answer: No, the page content of the atlas cannot be replicated on the eReader.
Please check explanations below for solution to question (b)
Step-by-step explanation: The dimensions of the eReader screen is given as 8 inches by 6 inches. In order to move a rectangular shape such as the atlas onto it would require the same measurements or, a measurement that has the same ratio as both the length and width of the screen, but a reduced size.
This brings us to similar shapes. When two shapes (rectangles in this case) are similar, it simply means there is a common ratio between the corresponding sides, that is the length and the width. If rectangle 1 has its side measuring 8 inches, then rectangle 2 would have the corresponding side having a common ratio with that of rectangle 1. This means the corresponding side in rectangle 2 can either be an enlargement (which would mean 8 times a scale of enlargement) or a reduction (which means 8 divided by a scale of reduction).
In the question given, the eReader screen has dimensions of 8 inches by 6 inches. The atlas has dimensions given as 19 inches by 12 inches. By observation we can see that the width of the atlas is times 2 of the screen. The length of the atlas however is not times 2 of the screen. That is;
Ratio = Rectangle 1 : Rectangle 2
Ratio of Width = 6 : 12
Ratio of Width = 1 : 2
Likewise
Ratio of Length = 8 : 19
Ratio of Length ≠ 1: 2
This proves that the atlas cannot be scaled down to fit properly into the screen. A solution to make this possible would be to resize the length of the atlas to become times 2 of the eReader screen. This would result in the atlas having new dimensions given as
Length = 16 inches
Width = 12 inches
This would ensure that both rectangular shapes are similar and the atlas can now be scaled down by a factor of 2 to fit in properly into the eReader screen.
Answer:
No
Step-by-step explanation:
Given:
Volume of cone = 144 in³
Diameter of 12 inch
Find:
Volume of cylinder[Same height and radius] is 144 in³ or not
Computation:
Volume of cone = [1/3][π][r²][h]
144 = [1/3][3.14][(12/2)²][h]
144 = 37.68 h
Height of cone = 3.82
Volume of cylinder[Same height and radius] = [π][r²][h]
Volume of cylinder[Same height and radius] = [3.14][6²][3.82]
Volume of cylinder[Same height and radius] = 431.81
Volume of cylinder[Same height and radius] = 432 in³
So,
Volume of cylinder[Same height and radius] is not 144 in³
Answer:
Awnser is C
Vertex (1, -2), Axis of symmetry is x = 1