G ( x ) = - 2 x² + 9
If this function is translated vertically downward by 8 units it becomes:
f ( x ) = g ( x ) - 8
f ( x ) = - 2 x² + 9 - 8
Answer:
f ( x ) = - 2 x² + 1
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>
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</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>
It could be 6,459 or another thousand number with the digit 6
Answer:
Throw this sample out and start over again with a better sampling method
Step-by-step explanation:
Biased sampling leads wrong results, since the sample doesn't represent the population which is aimed to be surveyed. Higher/lower confidence level or t distribution cannot correct it.
Confidence level gives the probability of rejecting null hypothesis while it is true. And t-interval is used when the sample size is small or population standard deviation is unknown.
Before choosing confidence level or type of the statistic to infer results, one must follow random sampling not biased.
