Please find the attachment for a better understanding of the explanation to this question.
As we can see from the diagram attached, the X axis represented by XX' and the Y axis represented by YY' intersect each other at the origin represented by O. Further, we notice that this intersection is at the angle 90 degrees or in other words the intersection is perpendicular. Thus, we have seen that the the x and y axes in the xy plane intersect perpendicularly. And hence, the answer is TRUE.
Please note that this is always the case and this is also known as orthogonality.
Answer:
C.6
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
Square roots have a neat property: 
provided <em>a</em> and <em>b</em> are positive real numbers.
This property is what's behind simplifying square roots. You look for perfect square factors (4, 9, 16, 25, 36, ...) inside the square root sign.
Example: 
.
In this problem, both factors are perfect squares.
Answer:
Yes
Step-by-step explanation:
The correct answer is: [B]: "4 " .
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Explanation:
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Refer to the table (provided within the actual question).
Note that the "inputs" ; or "x-values" ; are all listed in "chronological order" ; and are all "one (1) unit apart. and range from: "x = -3" to "x = 3" .
When "x = 0" ; the "output" ; or "f(x)" is "1/4" .
When "x = 1" ; the "output" ; or "f(x)" is: "1" .
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So; the ratio of these two "outputs" is: "¼ : 1" ; or, write as:
" (¼) / 1 " ; and note that: " (¼) / 1 = (¼) ÷ 1 = ¼.
However; note that: "1/4" ; or "1:4" is NOT among the [answer choices given].
However, the ratio of the 2 (two) corresponding "outputs"; chronologically,
going from when "x = 1" ; to "x = 0" ; is: "1 : ¼" ; or; write as: "1 / (¼)" ;
And note that: "1 / (¼)" = " 1 ÷ (¼) " = 1 * (4/1) = 1 * 4 = "4" .
This corresponds to: Answer choice: [B]: "4<span>" .
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Let us further confirm that this answer is correct:
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When x = 3; the "output" is: "16" .
When x = 2; the "output" is: "4" .
The ratio: "16/4 = ? 4 ? " ; → Yes!
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When x = 2; the "output" is: "4" .
When x = 1; the "output" is: "1" .
The ratio: "4/1 = ? 4 ? " ; → Yes!
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When x = 1; the "output" is: "1" .
When x = 0; the "output" is: "(¼)" .
The ratio: "1 / (¼) = ? 4 ? " ;
→ "1 / (¼)" = " 1 ÷ (¼) " = 1 * (4/1) = 1 * 4 = "4" . YES!
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When x = 0; the "output" is: "(¼)" .
When x = -1; the "output" is: "(¹/₁₆)" .
The ratio: "(¼) / (¹/₁₆) = ? 4 " ? ;
→ "(¼) / (¹/₁₆) = "(¼) ÷ (¹/₁₆) " = "(¼) * (¹⁶/₁) = (1*16) / (4*1) = 16/4 = "4" . Yes!
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When x = -1; the "output" is: "(¹/₁₆)" .
When x = -2; the "output" is: "(¹/₆₄)" .
The ratio: "(¹/₁₆) / (¹/₆₄) = ? 4 " ? ;
→ "(¹/₁₆) / (¹/₆₄) = "(¹/₁₆) ÷ (¹/₆₄)" = "(¹/₁₆) * (⁶⁴/₁)" = (1*64) / (16*1) = 64/16 = "4" . Yes!
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When x = -2; the "output" is: "(¹/₆₄)" .
When x = -3; the "output" is: "(¹/₂₅₆)" ,
The ratio: "(¹/₆₄)/(¹/₂₅₆) = ? 4 " ? ;
→ "(¹/₆₄) / (¹/₂₅₆)" ;
= " (¹/₆₄) ÷ (¹/₂₅₆)" = " (¹/₆₄) * (²⁵⁶/₁) " = (1*256) / (64*1) = 256/164 = "4 " . Yes!
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→ So; as calculated; the ratio is: "4" ; which is:
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→ Answer choice: [B]: "4" .
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