Answer:
9.5 = 8 + AB (M1)
Note: Award (M1) for correct substitution into Pythagoras’ theorem.
AB = 5.12 (cm) (5.12347…)
Step-by-step explanation:
<h3>Answer:</h3>
Yes, ΔPʹQʹRʹ is a reflection of ΔPQR over the x-axis
<h3>Explanation:</h3>
The problem statement tells you the transformation is ...
... (x, y) → (x, -y)
Consider the two points (0, 1) and (0, -1). These points are chosen for your consideration because their y-coordinates have opposite signs—just like the points of the transformation above. They are equidistant from the x-axis, one above, and one below. Each is a <em>reflection</em> of the other across the x-axis.
Along with translation and rotation, <em>reflection</em> is a transformation that <em>does not change any distance or angle measures</em>. (That is why these transformations are all called "rigid" transformations: the size and shape of the transformed object do not change.)
An object that has the same length and angle measures before and after transformation <em>is congruent</em> to its transformed self.
So, ... ∆P'Q'R' is a reflection of ∆PQR over the x-axis, and is congruent to ∆PQR.
Answer:
(x-9)²+(y-5)²=64
Step-by-step explanation:
Centre is (9,5) and radius is 16*pi/2*pi=8. Plug it in the equation of circles
The answer: " x = ⅓ " .
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Given: " 3x − 2 (x + 3) = 4x −<span> 7 " ; Solve for "x" ;
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Start with the following term on the "left-hand side" of the equation:
" - 2 (x + 3) " ;
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Note the "distributive property of multiplication" :
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a(b + c) = ab + ac ;
a(b </span>− c) = ab <span>− ac ;
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As such,
" -2 (x + 3) = -2(x) + -2(3) = -2x + (-6) = -2x </span>− 6 ;
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So, we can rewrite our equation:
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" 3x − 2 (x + 3) = 4x − 7 " ; substituting: " -2x − 6" (for " −2 (x + 3)" ; as follows:
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3x − 2x − 6 = 4x − 7 ;
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On the left-hand side off the equation;
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We can combine the "like terms" ; as follows:
3x − 2x = 1x = x ; and rewrite the equation:
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x − 6 = 4x − 7 ;
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We can subtract "4x" from each side of the equation; and add "6" to each side of the equation:
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x − 6 − 4x + 6 = 4x − 7 − 4x + 6 ;
to get: -3x = -1 ;
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Now, we divide EACH SIDE of the equation by "-3" ; to isolate "x" on ONE SIDE OF THE EQUATION; and to solve for "x" ;
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-3x / 3 = -1/-3 ;
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to get: x = <span>⅓ .
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</span> → Now, let us check our answer by plugging in "<span>⅓" for all values of "x" in the ORIGINAL GIVEN EQUATION; to see if the equation holds true:
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</span> → 3x − 2 (x + 3) = 4x −<span> 7 ;
</span>→ [3 * (⅓) ] − 2 [ (⅓) + 3) = ? 4(⅓) − 7 ?? ;
<span>
</span>→ (1) − 2(3 ⅓) =? (⁴/₃) − 7 ?? ;
<span>
</span>→ (1) − 2(3 ⅓) =? (⁴/₃) − 7 ?? ;<span>
</span>→ (³/₃) − 2(¹⁰/₃) =? (⁴/₃) − (²¹/₃) ?? ;
→ (³/₃) − (²⁰/₃) =? (⁴/₃) − (²¹/₃) ?? ;
→ ⁽³ ⁻²⁰⁾/₃) =? ⁽⁴⁻²¹⁾/₃) ??
→ ⁻¹⁷/₃ = ? ⁻¹⁷/₃ ?? Yes! Our answer "makes sense"!
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90 can go into 3 only 1/30 of one time.
