Answer:
x = -0.17 and x = -5.83
Step-by-step explanation:
We are asked to solve the quadratic equation
We use the quadratic formula using a = 1, b = 6 and c = 1
for a general quadratic equation of the form: 
Then, the solutions are given by;
which produces the two following answers (rounded to two decimals):
x = -0.17 and x = -5.83
Answer: The height of the triangle is: " 3.5 cm " .
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<u>
Note</u>: The formula/equation for the area, "A" , of a triangle is:
A = (1/2) * b * h ; or write as: A = (b * h) / 2 ;
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in which: "A = area of the triangle" ;
"b = base length" ;
"h = "[perpendicular] height" ;
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Given: h = (b/2) ;
A = 12.25 cm²
{Note: Let us assume that the given area was "12.25 cm² " .}.
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We are to find the height, "h" ;
The formula for the Area, "A", is: A = (b * h) / 2 ;
Let us rearrange the formula ;
to isolate the "h" (height) on one side of the equation;
→ Multiply EACH side of the equation by "2" ; to eliminate the "fraction" ;
2*A = [ (b * h) / 2 ] * 2 ;
to get: " 2A = b * h " ;
↔ " b * h = 2A " ;
Divide EACH SIDE of the equation by "b" ; to isolate "h" on one side of the equation:
→ (b * h) / b = (2A) / b ;
to get:
→ h = 2A / b ;
Since "h = b/2" ; subtitute "b/2" for "h" ;
Plug in: "12.25 cm² " for "A" ;
→ b/2 = 2A/b ; → Note: " 2A/b = [2* (12.25 cm²) ] / b " ;
Note: " 2* (12.25 cm²) = 24.5 cm² ;
Rewrite as:
→ b/2 = (24.5 cm²) / b ;
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Cross-multiply: b*b = (24.5 cm²) *2 ;
to get: b² = 49 cm² ;
Take the "positive square root" of each side of the equation" ;
to isolate "b" on one side of the equation ; & to solve for "b" ;
→ +√(b²) = +√(49 cm²) ;
→ b = 7 cm ;
Now, we want to solve for "h" (the height) :
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→ h = b / 2 = 7 cm / 2 = 3.5 cm ;
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Answer: The height of the triangle is: " 3.5 cm <span>" .
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X=1.464102
Simplifies to: (1/2x)+1=1.732051
Step 1: Subtract 1 from both sides.
1/2x + 1 -1=1.732051-1
(1/2x)=0.732051
Step 2: Multiply both sides by 2
2*(1/2x) = (2) * (0.732051)
X=1.464102
Answer:
Median and Mode.
Step-by-step explanation:
The data could be represented in table form in ascending order as:
<u>Number of meals</u> <u> Frequency</u>
2 2
3 3
4 2
19 1`
On the basis of the data now we find the mean, median and mode:
Mean= average of the data
Mean=\dfrac{2\times 2+3\times 3+4\times 2+19\times 1}{2+3+2+1}=\dfrac{40}{8}=5
Hence mean is 5.
Median is the central tendency of the data
on looking at our data we see that the Median=3.
also the mode of the data is the entry corresponding to the highest entry.
Hence the highest frequency is 3 and the corresponding value is 3.
Hence, Mode=3
Hence, the most appropriate measure of center for this situation is :
Median and Mode.
