QUESTION 33
The length of the legs of the right triangle are given as,
6 centimeters and 8 centimeters.
The length of the hypotenuse can be found using the Pythagoras Theorem.
![{h}^{2} = {6}^{2} + {8}^{2}](https://tex.z-dn.net/?f=%20%7Bh%7D%5E%7B2%7D%20%20%3D%20%20%7B6%7D%5E%7B2%7D%20%20%2B%20%20%7B8%7D%5E%7B2%7D%20)
![{h}^{2} = 36+ 64](https://tex.z-dn.net/?f=%20%7Bh%7D%5E%7B2%7D%20%20%3D%2036%2B%2064)
![{h}^{2} = 100](https://tex.z-dn.net/?f=%20%7Bh%7D%5E%7B2%7D%20%20%3D%20100)
![h = \sqrt{100}](https://tex.z-dn.net/?f=h%20%3D%20%20%5Csqrt%7B100%7D%20)
![h = 10cm](https://tex.z-dn.net/?f=h%20%3D%2010cm)
Answer: C
QUESTION 34
The triangle has a hypotenuse of length, 55 inches and a leg of 33 inches.
The length of the other leg can be found using the Pythagoras Theorem,
![{l}^{2} + {33}^{2} = {55}^{2}](https://tex.z-dn.net/?f=%20%7Bl%7D%5E%7B2%7D%20%20%2B%20%20%7B33%7D%5E%7B2%7D%20%20%3D%20%20%7B55%7D%5E%7B2%7D%20)
![{l}^{2} = {55}^{2} - {33}^{2}](https://tex.z-dn.net/?f=%20%7Bl%7D%5E%7B2%7D%20%20%3D%20%20%7B55%7D%5E%7B2%7D%20%20-%20%20%7B33%7D%5E%7B2%7D%20)
![{l}^{2} = 1936](https://tex.z-dn.net/?f=%20%7Bl%7D%5E%7B2%7D%20%20%3D%201936)
![l = \sqrt{1936}](https://tex.z-dn.net/?f=l%20%3D%20%20%5Csqrt%7B1936%7D%20)
![l = 44cm](https://tex.z-dn.net/?f=l%20%3D%2044cm)
Answer:B
QUESTION 35.
We want to find the distance between,
(2,-1) and (-1,3).
Recall the distance formula,
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Substitute the values to get,
![d=\sqrt{( - 1-2)^2+(3- - 1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28%20-%201-2%29%5E2%2B%283-%20-%201%29%5E2%7D)
![d=\sqrt{( - 3)^2+(4)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28%20-%203%29%5E2%2B%284%29%5E2%7D)
![d=\sqrt{9+16}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B9%2B16%7D)
![d=\sqrt{25}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B25%7D)
![d = 5](https://tex.z-dn.net/?f=d%20%3D%205)
Answer: 5 units.
QUESTION 36
We want to find the distance between,
(2,2) and (-3,-3).
We use the distance formula again,
![d=\sqrt{( - 3-2)^2+( - 3- 2)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28%20-%203-2%29%5E2%2B%28%20-%203-%202%29%5E2%7D)
![d=\sqrt{( - 5)^2+( - 5)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28%20-%205%29%5E2%2B%28%20-%205%29%5E2%7D)
![d=\sqrt{25+25}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B25%2B25%7D)
![d=\sqrt{50}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B50%7D)
![d=5\sqrt{2}](https://tex.z-dn.net/?f=d%3D5%5Csqrt%7B2%7D)
Answer: D
Answer:
The conclusion is Mr. Keene has sufficient vitamin K.
Step-by-step explanation:
Consider the provided statement.
The law of detachment involves two quantities, one is hypothesis and another is conclusion.
In the provided statement hypotheses and conclusion is:
Hypotheses (P): Person has insufficient vitamin K
Conclusion (Q): There will be a prothrombin deficiency.
Here if a person has insufficient vitamin K that means there must be prothrombin deficiency, but if a person has prothrombin deficiency we can't say anything.
Now it is given that Mr. Keene does not have a prothrombin deficiency.
That means he has sufficient vitamin K
Hence, the conclusion is Mr. Keene has sufficient vitamin K.
The required diagram is shown in figure.
Answer: 5.4
Step-by-step explanation:
Answer:
B) (2x + 3)(2x - 3)
Step-by-step explanation:
Use the FOIL method for each answer choice.
FOIL = First, Outside, Inside, Last
(2x)(2x) = 4x²
(2x)(-3) = -6x
(3)(2x) = 6x
(3)(-3) = -9
4x² -6x +6x -9
Simplify. Combine like terms:
4x² (-6x + 6x) - 9
4x² - 9
4x² - 9 = 4x² - 9 ∴ B) (2x + 3)(2x - 3) is your answer
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