1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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 .

You might be interested in
If w is a string of english letters a–z (all uppercase for the purposes of this problem), let wr denote the reverse of w; (train
Dennis_Churaev [7]

Answer:

f(x)=\left \{\begin{array}{rl}26^{\frac{k}{2}}&\text{for k even}\\26^{\frac{k+1}{2}}&\text{for k odd}\end{array}\right.

Step-by-step explanation:

Half the length of the palindrome can be any possible sequence of the 26 available letters. The other half is constrained to be the reverse of the same sequence. For odd length sequences, the middle letter can be any of the 26.

So, for k even, the number of palindromes is 26^(k/2). For k odd, the number is 26·26^((k-1)/2) = 26^)((k+1)/2).

5 0
3 years ago
PLEASE HELP!!-What two rotations would provide the following images.
GREYUIT [131]
Reflection and rotation
3 0
3 years ago
True or False: A bisector of an angle divides the angle into right angles.
kenny6666 [7]
False. A bisector divides the angle evenly, not into right angles.
5 0
3 years ago
Need help with this data table need it to end up to 1024 thanks
Iteru [2.4K]
1 2 4 8 16 32 64 128 256 512 1024. each one is 2 times the previous

3 0
3 years ago
The following frequency table shows the number of fish caught by each of Igor's family members.
Maslowich

Step-by-step explanation:

The values on the left of the table represent the number of fish caught, and the number of the right of the table represents how many family members caught that amount of fish.

Therefore, the first row means that 0 family members caught 0 fish.

The second row means that 3 family members caught 1 fish.

The third row would mean 1 family member caught 2 fish.

The next row would mean 0 family members caught 3 fish.

And the final row would mean 4 family members caught 4 fish.

The question does not ask for the total amount of fish caught; rather is ask for the maximum number of fish that a single family member caught.

Therefore, the maximum amount of fish that a single family member catches is 4. (And 4 family members did so. But individually, the maximum amount of fish one person caught is 4).

6 0
3 years ago
Other questions:
  • This is the question is Estimate. 9.8 * 5.2 Choose 1 answer: a 5 b 50 c 500 d 5000
    5·2 answers
  • Use the zero product property to find the solutions to the equation x2 – 13x + 30 = 0.
    8·1 answer
  • 1) PLS HELP ASAP!!!!<br><br> BRAINLIEST AND 10 POINTS :)
    10·1 answer
  • The result of subtracting 2 from its opposite is?<br> 0<br> 1<br> 4<br> -4
    7·2 answers
  • Notebooks cost $ 1.20 each. This weekend they will be on sale for $ 0.80. What percentage is the sale
    14·2 answers
  • Given that the series kcoskt kº +2 k=1 converges, suppose that the 3rd partial sum of the series is used to estimate the sum of
    6·1 answer
  • If 1/3 gallon of paint will cover 1/9 of a wall, how much paint will be needed for the entire wall?
    12·2 answers
  • Help me with this please
    6·2 answers
  • 2. Find the surface area of the regular pyramid shown to the nearest whole<br> number.
    10·1 answer
  • Huang bought 12 boxes of floor tiles that weight 288 pounds each. how much is this in kilograms
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!