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leonid [27]
2 years ago
8

1. Solve the given linear equations for 'x':

Mathematics
1 answer:
postnew [5]2 years ago
4 0

i ) 3(2x - 3) = 4(2x + 4)

6x - 9 = 8x +1 6 \\  \\ 6x - 8x = 16 + 9 \\  \\  - 2x = 25 \\  \\ x =   - \frac{25}{2} .

ii )2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)

2x + 4 + 5x + 25 = 4x - 32 + 2x - 4 \\  \\ 7x + 29 = 6x - 36 \\  \\ 7x - 6x =  - 36 - 29 \\  \\ x =  - 65.

<h2>----------------------</h2>

2. 3x /4 - 7 /4 = 5x + 12

\frac{3x}{4}  -  \frac{7}{4}  = 5x + 12 \\  \\  \frac{3x}{4}  - 5x = 12 +  \frac{7}{4}  \\  \\  \frac{3x - 20x}{4}  =  \frac{48 + 7}{4}  \\  \\  \frac{ - 17x}{4}  =  \frac{55}{4}

cancel 4 from both sides

- 17x = 55 \\  \\ x =  \frac{ - 17}{55} .

<h2>-------------------</h2>

3. x +7 - 8x/3 = 17/6 - 5x/8

x + 7 -  \frac{8x}{3}  =  \frac{17}{6}  -  \frac{5x}{8}

put x = 4

4 + 7 -  \frac{ 8\times 4}{3}  =  \frac{17}{6}  -  \frac{5 \times 4}{8}  \\  \\ 11 -  \frac{32}{3}  =  \frac{17}{6}  -  \frac{20}{8}  \\  \\  \frac{33 - 32}{3}  =  \frac{68 - 60}{24}  \\  \\  \frac{1}{3}  =  \frac{8}{24}  \\  \\  \frac{1}{3}  =  \frac{1}{3} .

L.H.S. = R.H.S.

<h2>--------------------</h2>

4. Let 3 consecutive integers : x , x+1 , x+2

As per the question : 2x + 3(x+1) + 4(x+2) = 56

9x + 11 = 56

Transpose 11 to RHS

9x = 45

Divide both sides by 9

x = 5 ,

x + 1 = 5 + 1 = 6

x + 2 = 5 + 2 = 7

Numbers are 5 , 6 and 7 .

<h2>-----------------------</h2>

5. Let the age of Jane’s younger sister is x.

Age of Jane will be x + 6

As per the question, after 10 years the sum of their ages will be 50.

After 10 years,

age of Jane = x + 16

age of her younger sister = x + 10

Therefore,

x + 16 + x +10 = 50

2x + 26 = 50

2x = 24

x = 12

Thus, the present age of Jane’s younger sister is 12 years.

And of Jane’s is 12 + 6 = 18 years.

<h2>---------------------</h2>

6. Let the breadth of rectangular swimming pool be x metres.

Then, its length = (2x + 2) metres.

We know that the Perimeter of a rectangle

= 2(Length + Breadth)

= 2(2x + 2 + x) = 6x + 4

According to the given condition, we have

6x + 4 = 154

6x = 154 − 4

6x = 150

[Dividing both sides by 6]

x = 25

Thus, breadth = 25 m and

length = 25 × 2 + 2 = 52 m .

<h2>---------------------</h2>

7. Let the digit in ten's .

Place be x and the digit in the one's place be y.

x − y = 5 ⟶ (i)

Two digit number = 10x + y

Two digit after reversing the digits = 10y + x

According to question ,

10x + y + 10y + x = 99

11x + 11y = 99

x + y = 9 ⟶ (ii)

On adding (i) and (ii),

2x = 14

x = 7

Putting the value of x in equation (i)

x − y = 5

y = 2

Number = 10x + y

=72 .

<h2>-----------------------</h2>

8. Let the speed of the steamer in still water be x km/h.

Then , the speed downstream = (x+2) km/h

and the speed upstream = (x−2) km/h

Given , distance covered in 4 hours downstream = distance covered in 5 hours upstream

4(x + 2) = 5(x − 2)

4x + 8 = 5x − 10

4x − 5x = − 10 − 8

[Transposing 5x to LHS and 8 to RHS]

−x = −18 or x = 18 km/h .

<h2>-----------------------</h2>

9. Let the number of notes of different denomination be x.

∴ Numbers of Rs 100 notes , 50 notes and Rs 10 notes will be 2x , 3x and 5x respectively.

Amount of 100 Rs notes ⇒Rs 100 × 2x = 200x

Amount of 50 Rs notes ⇒Rs 50 × 3x = 150x

Amount of 10 Rs notes ⇒Rs 10 × 5x = 50x

As per the question

Total amount = 400000

200x + 150x + 50x = 400000

400x = 400000 , x = 1000

No of Rs 100 notes = 2x = 2 × 1000 = 2000

No of Rs 50 notes = 3x = 3 × 1000 = 3000

No of Rs 10 notes = 5x = 5 × 1000 = 5000 .

<h2>------------------------</h2>

10. Let the age of the man be x

Then age of his son becomes (x − 24)

2 years later from now,

Age of man will be = x + 2

and age of his son will be = (x − 24 + 2) = x − 22

According to question,

2(x − 22) = x + 2

i.e., 2x − 44 = x + 2

i.e., x = 46

Therefore ,

Present age of man = 46 years

And present age of his son = 46 − 24 = 22 years .

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4 questions 20 points
Dvinal [7]
1. Cross multiply
35x = 5(11)
35x = 55
Divide both sides by 35
x = 55/35
x = 11/7

2.  (x - 2)/x = 3/8
Cross multiply
3x = 8(x - 2)
3x = 8x - 16
Subtract 8x from both sides
-5x = -16
divide both sides by -5
x = -16/-5
x = 16/5 OR  3 1/5

3.  (a + 1)/(a - 1) = 5/6
cross multiply
6(a + 1) = 5(a - 1)
distribute
6a + 6 = 5a - 5
subtract 5a from both sides
a + 6 = -5
subtract 6 from both sides
a = -11

4.  (1/3)x - 4 = (2/3)x + 6
multiply each term by 3 to clear the fractions
x - 12 = 2x + 18
subtract x from both sides
-12 = x + 18
subtract 18 from both sides
-30 = x


3 0
3 years ago
The point g (2,2) is translated 3units to the right and 4units up what are the coordinates of this resulting point, g?
Svetlanka [38]

Answer:

(5,6)

Step-by-step explanation:

<em>Generally, is the coordinate (x,y) is translated right by a units and up by b units, the resulting coordinate wil be;</em>

g(X, Y)  = (x+a, y+b)

To the right is along the positive x axis while up is along the positive y axis

Given a = 3 and b = 4

g(X,Y) = (2 + 3, 2 + 4)

g(X, Y) = (5, 6)

Hence the resulting coordinate of g is (5,6)

7 0
3 years ago
It’s my birthday little cuties (:
Dmitrij [34]

Answer:

HAPPY BURFDAY

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A lighthouse keeper has a 10 degrees angle of depression between the horizontal light beam and the line of sight from the ship.
Andrei [34K]
107.75m
This is a trigonometric ratio problem. the angle of depression (10) is opposite the height (19m) and the distance is adjacent to the distance (x). opposite ad adjacent sides to the angle is a tangent problem.
tan \theta = \frac{opp}{adj}
plus in values, we know.
tan (10) = \frac{19}{x}
switch tan(10) and x using the products property.
x = \frac{19}{tan (10)}
plug in to calulator to get answer
x=107.75

4 0
3 years ago
A machine can pack 80 cans in 5 minutes. Choose all of the values that show the ratio of cans to minutes.​
Drupady [299]

Answer:

16 cans per minute

Step-by-step explanation:

Its simple 80 divided by 5 is 16 so ever minute 16 cans are packed.

4 0
2 years ago
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