Answer:
yes, it is a right triangle and ∡Q is the right angle
Step-by-step explanation:
if the slope of QR is the opposite reciprocal of QS then the two segments are perpendicular and form a 90° angle
slope of QR: -3 - (-1) ÷ 2 - 0 = -2 ÷ 2 = -1
slope of QS: -3 - (-1) ÷ 2 - 4 = -2 ÷ -2 = 1
-1 and 1 are opposite and reciprocal so m∡Q = 90°
16, 16.02, 16.15, 16.819, 16.85
Assuming you are referring to the area of a "trapezoid"; in which one calculates the Area, "A", as follows:
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<span> A = 1/2* h(b1+b2) ;
in which: A = Area = 16 (given);
h = height = 4 (given);
b1 = length of one of the two bases = 3 (given);
b2 = length of the other of the two bases = ? (what we want to solve for) ;
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Using the formula: </span>A = 1/2 h(b1+b2) ;
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Let us plug in our known values:
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→ 16 = (1/2) * 4*(3 + b2) ; → Solve for "b2".
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→Note: On the "right-hand side" on this equation: "(1/2)*(4) = 2 ."
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So, we can rewrite the equation as:
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→ 16 = 2*(3 + b2) ; → Solve for "b2".
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We can divide EACH side of the equation by "2"; to cancel the "2" on the "right-hand side" of the equation:
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→ 16 / 2 = [2*(3 + b2)] / 2 ; → to get:
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8 = (3 + b2) ;
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→ Rewrite as: 8 = 3 + b2;
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Subtract "3" from EACH side of the equation; to isolate "b2" on one side of the equation; and to solve for "b2" :
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→ 8 - 3 = 3 + b2 - 3 ; → to get:
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b2 = 5; From the 2 (TWO) answer choices given, this value,
"b2 = 5", corresponds with the following answer choice:
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b2= [16-6]/2= 5 ; as this is the only answer choice that has: "b2 = 5".
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As far getting "</span>b2 = 5" from: "b2= [16-6]/2= 5"; (as mentioned in the answer choice), we need simply to approach the problem in a slightly different manner. Let us do so, as follows:
<span>_____________________________________
Start from: </span>A = 1/2 h(b1+b2); and substitute our known (given) values):<span>
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</span>→ 16 = (1/2) *4 (3 + b2) ; → Solve for "b2".
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Note that: (½)*4 = 2; so we can substitute "2" for: "(1/2) *4" ;
and rewrite the equation as follows:
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→ 16 = 2 (3 + b2) ;
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Note: The distributive property of multiplication:
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a*(b+c) = ab + ac ;
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As such: 2*(3 + b2) = (2*3 + 2*b2) = (6 + 2b2).
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So we can substitute: "(6 + 2b2)" in lieu of "[2*(3 + b2)]"; and can rewrite the equation:
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→ <span>16 = 6 + 2(b2) ; Now, we can subtract "6" from EACH side of the equation; to attempt to isolate "b2" on one side of the equation:</span>
<span>________________________________________________
</span>→ 16 - 6 = 6 + 2(b2) - 6 ;
→ Since "6-6 = 0"; the "6 - 6" on the "right-hand side" of the equation cancel.
→ We now have: 16 - 6 = 2*b2 ;
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Now divide EACH SIDE of the equation by "2"; to isolate "b2" on one side of the equation; and to solve for "b2":
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→ (16 - 6) / 2 = (2*b2) / 2 ;
→ (16 - 6) / 2 = b2 ;
→ (10) / 2 = b2 = 5.
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NOTE: The other answer choice given:
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"<span>16= 1/2* 4(3+b2)= 6+2b2" is incorrect; since it does not solve for "b2".</span>
Answer:
93.1%
Step-by-step explanation:
