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2 years ago

Write the quadratic equation in general form. (x - 3)^ 2 = 0

2 answers:

5 0

The answer is: x² – 6x + 9 = 0 .
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Explanation:
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Given: (x – 3)² = 0 ; write as: general form: "ax² + bx + c = 0"; a ≠ 0 .
<span>
Note: </span>(x – 3)² = (x – 3)(x – 3) = x² – 3x – 3x + 9 = x² – 6x + 9 ;
___________________________________________________
Rewrite: (x – 3)² = 0 ; →
as: x² – 6x + 9 = 0 ; which is our answer.
____________________________________________
→ x² – 6x + 9 = 0 ; is in "general form", or "standard equation format"; that is: " ax² + bx + c = 0 "; (a ≠ 0) ;
→ in which:
a = 1 (implied coefficient, since anything multiplied by "1" is that same value);
b = -6;
c = 9
_______________________________________________________

Kisachek [45]2 years ago

5 0

Easy
expand
(x-3)^2=0
(x-3)(x-3)
foil
first: x time x=x²
outter: -3 times x=-3x
inner:x times -3=-3x
last: -3 times -3=9
add them
x²-3x-3x+9=0
x²-6x+9=0

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The vertex of this parabola is at (-3, -2). which of the following could be its equation?

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Answer:

Since the vertex is (-3,-2) The x value should be +3

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2 years ago

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Are the marks one receives in a course related to the amount of time spent studying the subject? To analyze this mysterious poss

sertanlavr [38]

Answer:

a) 98.522

b) 0.881

c) The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time.

Step-by-step explanation:

As the mentioned in the given instruction the co-variance is first computed in excel by using only add/Sum, subtract, multiply, divide functions.

Marks y Time spent x y-ybar x-xbar (y-ybar)(x-xbar)

77 40 5.1 1.3 6.63

63 42 -8.9 3.3 -29.37

79 37 7.1 -1.7 -12.07

86 47 14.1 8.3 117.03

51 25 -20.9 -13.7 286.33

78 44 6.1 5.3 32.33

83 41 11.1 2.3 25.53

90 48 18.1 9.3 168.33

65 35 -6.9 -3.7 25.53

47 28 -24.9 -10.7 266.43

$Covariance=\frac{sum[(y-ybar)(x-xbar)]}{n-1}$

Co-variance=886.7/(10-1)

Co-variance=886.7/9

Co-variance=98.5222

The co-variance computed using excel function COVARIANCE.S(B1:B11,A1:A11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted co-variance is 98.52222.

The correlation coefficient is computed as

$Correlation coefficient=r=\frac{sum[(y-ybar)(x-xbar)]}{\sqrt{sum[(x-xbar)]^2sum[(y-ybar)]^2} }$

(y-ybar)^2 (x-xbar)^2

26.01 1.69

79.21 10.89

50.41 2.89

198.81 68.89

436.81 187.69

37.21 28.09

123.21 5.29

327.61 86.49

47.61 13.69

620.01 114.49

sum(y-ybar)^2=1946.9

sum(x-xbar)^2=520.1

$Correlation coefficient=r=\frac{886.7}{\sqrt{520.1(1946.9)} }$

$Correlation coefficient=r=\frac{886.7}{\sqrt{1012582.69} }$

$Correlation coefficient=r=\frac{886.7}{1006.2717 }$

$Correlation coefficient=r=0.881$

The correlation coefficient computed using excel function CORREL(A1:A11,B1:B11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted correlation coefficient is 0.881.

The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time. It means that as the study time increases the marks of student also increases and if the study time decreases the marks of student also decreases.

The excel file is attached on which all the related work is done.

Download xlsx

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2 years ago

Quadrilateral LMNO is similar to quadrilateral PQRS. Find the measure of side QR.

dalvyx [7]

Answer:

The measure of the side $QR$ is 8.8.

Step-by-step explanation:

Since $LMNO \sim PQRS$ , then $SP \propto OL$ , $RS \propto ON$ , $RQ \propto MN$ and $QP \propto LM$ . From figure we have the following relationship: