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3 years ago

63x−8≤23 OR −4x+26≥6

Mathematics

1 answer:

Misha Larkins [42]3 years ago

7 0

Answer:

63x-8<23

63x<23+8

63x < 31

63. 63

x < 0.492

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Sofian's current age is (2x + 3) times Mastura's age. Given that Mastura's current age is (x + 5) years and 6 years ago, the sum

Sliva [168]

${\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}$

★ Sofian's current age is (2x + 3) times Mastura's age.

★ Mastura's current age is (x + 5) years

★ 6 years ago, the sum of their ages is 44 years.

${\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}$

★ The value of x.

${\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}$

According to the question,

Present age of Mastura = (x + 5) years

Present age of Sofian = (2x + 3) (x + 5) years, i.e :

$\longrightarrow \tt (2x + 3) (x + 5)$

$\longrightarrow \tt 2 {x}^{2} + 10x + 3x + 15$

$\longrightarrow \tt 2 {x}^{2} + 13x + 15 \: years$

Now,

Mastura's age 6 years ago = (x + 5) - 6

=> x + 5 - 6

=> x - 1

Sofian's age 6 years ago = 2x² + 13x + 15 - 6

= 2x² + 13x + 9

Using the condition provided by the question, 

Mastura's age 6 years ago + Sofian's age 6 years ago = 44

$\longrightarrow \tt (x - 1) + (2 {x}^{2} + 13x + 9) = 44$

$\longrightarrow \tt x - 1 + 2 {x}^{2} + 13x + 9 = 44$

$\longrightarrow \tt 2 {x}^{2} + 14x + 8 = 44$

$\longrightarrow \tt 2 {x}^{2} + 14x + 8 - 44 = 0$

$\longrightarrow \tt 2 {x}^{2} + 14x - 36= 0$

• Taking "2" common.

$\longrightarrow \tt 2 ({x}^{2} + 7x - 18) = 0$

$\longrightarrow \tt {x}^{2} + 7x - 18 = \dfrac{0}{2}$

$\longrightarrow \tt {x}^{2} + 7x - 18= 0$

• Using splitting the middle term

$\longrightarrow \tt {x}^{2} + 9x - 2x - 18 = 0$

$\longrightarrow \tt x(x + 9) - 2(x + 9) = 0$

$\longrightarrow \tt (x + 9) (x - 2) = 0$

either $\tt (x + 9) = 0 \: \: or \: \: (x - 2) = 0$

$\longrightarrow \tt x = - 9 \: \: or \: \: x = 2$

[As the age cannot be negative. So x = - 9 is rejected]

$\therefore \tt \: x = \red{ 2}$

${\large{\textsf{\textbf{\underline{\underline{Verification :}}}}}}$

According to the condition provided by the question, 

• Mastura's age 6 years ago + Sofian's age 6 years ago = 44

$\longrightarrow \tt x - 1 + 2 {x}^{2} + 13x + 9 = 44$

Putting x = 2 we get,

$\longrightarrow \tt 2 - 1 + 2( {2})^{2} + 13(2) + 9 = 44$

$\longrightarrow \tt 1 + 2 \times 4 + 26+ 9 = 44$

$\longrightarrow \tt 1 + 8 + 26+ 9 = 44$

$\longrightarrow \tt 9 + 26+ 9 = 44$

$\longrightarrow \tt 18 + 26 = 44$

$\longrightarrow \tt 44 = 44$

Hence verified.

$\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}$

Hope it helps you! :))

6 0

3 years ago

Find the measure of b.

Alika [10]

Answer:

b = 55°

Step-by-step explanation:

The angle at the centre is twice the angle on the circle subtended by the same arc, then

a = 0.5 × 110° = 55°

Angles on the circumference subtended by the same arc are congruent, so

b = a = 55°

5 0

3 years ago

Write an equation of the line parallel to given that contains C(6,-2);=-3/2x+6

Nataly_w [17]

Answer:

3/-2-2

Step-by-step explanation:

this should be parrallel

8 0

3 years ago

PLEASE HELP GIVING BRAINLIEST! :)

QveST [7]

Answer:

Step-by-step explanation:

3a+b - 4

Let a =3 and b = 5

3(3) +5 -4

Multiply

9+5-4

Add and subtract

14-4

6 0

3 years ago

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What is the lcd of 3/10an -4/15?

aniked [119]

30 is the lcd, with each number then being 9/30 and -8/30.

3 0

3 years ago