Maths Equations ||Part 1|| Shashaank Blogspot

MATH

EQUATIONS

1. If (3x+4)2 +(3x-2)2=(6x+5)(3x-2)+12 then find the value of x

1. 2

2. 1

3. -3

4.-2

Solution:-

(D)

(3x+4)2 +(3x-2)2=(6x+5)(3x-2) + 12

→ 9x2 + 24x+16 + 9x2 + 12x + 4 = 18x2 + 3x - 10 + 12

→ 18x2 + 12x +20 = 18x2 +3x + 2

→ 9x + 18

→ x = -2

NOTE :-

→ You guys can see 9x2,18x2

→ It Means 9 to the power of 2

2. The sum of numerator and denominator of a fraction is 11. If 1 is added to the numerator and 2 is subtracted from the denominator it becomes 2 by 3. Find the fraction.

Solutions :-

→ Let the numerator = x

→ denominator = y

According to question,

→ x + 1 / y + 1 = 2 / 3

→ 3x + 3 = 2y + 2

→ 3x - 2y = -1 ----------------1

→ x - 1 / y - 1 = 3 / 5

→ 5x - 5 = 3y - 3

→ 5x - 3y =2 ------------------2

We get 2 question , Now by Elimination Method ,

→ 3x - 2y = -1 × 5

→ 5x - 3y = 2 × 3

→ 15x - 10y = -5

→ 15x - 9y = 6

→ -y = -11

→ y = 11

Now put the value of in equation 1

→ 3x - 2(11) = - 1

→ 3x - 22 = -1

→ 3x = 21

→ x = 7

→ So that the value of x is and y is 11.

→ We know numerator = x and denominator = y

→ Numerator / Denominator = 7 / 11

→ So that the fraction is 7 / 1

3. If (x+1/x+2 )2 = x+2/x+4 then x = ?

Solutions : -

4.The length of a rectangle is $3$ times its breadth, if the length is decreased by $3$ cm and the breadth increased by $5$ cm the area of the rectangle is increased by $5 7cm2. Find the perimeter of rectangle.$ $Solution:-$

Correct option is

$48$ cm

Let the breadth of the rectangle be $x$ cm.
Then, length = $3$ $x$ cm

New breadth = $(x + 5)$ cm
New length = $(3 x - 3)$ cm

Then, $(x + 5) (3 x - 3) - 3 x \times x = 57$
$\Rightarrow 3 x^{2} + 12 x - 15 - 3 x^{2} = 57$
$\Rightarrow 12 x = 57 + 15 = 72 \Rightarrow x = 6$
$∴$ Breadth = $6$ cm, Length = $18$ cm
Perimeter = $2 (6 c m + 18 c m) = 2 \times 24 c m = 48$ cm

5. Two irrational numbers between 2 and 3

Solution:-

Answer:

→

is the irrational no between 2 and 3

Correct option is C

2.2

The given equation is

$\frac{x ^{2} - 5 x + 6}{x ^{2} - 7 x + 1 2}$ =x2+7x+10x2−x−6
$⟹ \frac{( x - 3 ) ( x - 2 )}{( x - 3 ) ( x - 4 )} = \frac{( x - 3 ) ( x + 2 )}{( x + 5 ) ( x + 2 )}$
$⟹ \frac{x - 2}{x - 4} = \frac{x - 3}{x + 5}$
$⟹ x^{2} + 3 x + 10 = x^{2} - 7 x + 12$
$⟹ 10 x = 22$
$⟹ x = 2.2 .$

HOPE IT HEPLS

👍👍👍👍

$^{2 The perimeter of the rectangle is}$

Histogram || Shashaank Blogspot

Histogram A histogram is what we call an area diagram. It indicates the frequency of a class interval. The class interval or the range of values is known as bins or classes with reference to histograms. A bar indicates the number of data points within a specific class. That means the higher the frequency of a particular class, higher the bar. Let us see an example of a Histogram. From the below-given table of the various heights of trees in a region, we will draw a histogram to illustrate how it is done. Let us look at the frequency table now. Height of Trees (ft) No. of trees 60-65 3 65-70 3 70-75 8 75-80 10 80-85 5 85-90 2 Now here the heights of the tree are continuous data. These class intervals are the bins. And the number of trees are obviously the frequency. And now let us draw a histogram (given below) that represents the above data. Histograms vs Bar Charts In bar graphs, each bar represents one value or category. On the other hand in a histogram...

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Maths Equations ||Part 1|| Shashaank Blogspot

$48$ cm

5. Two irrational numbers between 2 and 3

2.2

$^{2 The perimeter of the rectangle is}$

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48 cm

Let the breadth of the rectangle be x cm.Then, length = 3x cmNew breadth =(x+5) cmNew length =(3x−3)cmThen, (x+5)(3x−3)−3x×x=57⇒3x2+12x−15−3x2=57⇒12x=57+15=72⇒x=6∴ Breadth = 6 cm, Length = 18 cmPerimeter =2(6cm+18cm)=2×24cm=48 cm

5. Two irrational numbers between 2 and 3

2.2

The given equation isx2−7x+12x2−5x+6​=x2+7x+10x2−x−6​⟹(x−3)(x−4)(x−3)(x−2)​=(x+5)(x+2)(x−3)(x+2)​⟹x−4x−2​=x+5x−3​⟹x2+3x+10=x2−7x+12⟹10x=22⟹x=2.2.

2The perimeter of the rectangle is

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$48$ cm

$^{2 The perimeter of the rectangle is}$