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### Math Questions Solutions | Solved Math Questions and Solutions

In math questions solutions every questions are solved with rationalization.
The questions are based mostly from completely different subjects. Care has been taken to
clear up the questions in such a method that college students can perceive every and
each step.

1. Which is bigger than 4?

(a) 5,

(b) -5,

(c) -1/2,

(d) -25.

Resolution:

5 larger than 4.

2. Which is the smallest?

(a) -1,

(b) -1/2,

(c) 0,

(d) 3.

Resolution:

The smallest quantity is -1.

3. Mix phrases: 12a + 26b -4b – 16a.

(a) 4a + 22b,

(b) -28a + 30b,

(c) -4a + 22b,

(d) 28a + 30b.

Resolution:

12a + 26b -4b – 16a.

= 12a – 16a + 26b – 4b.

= -4a + 22b.

4. Simplify: (4 – 5) – (13 – 18 + 2).

(a) -1,

(b) –2,

(c) 1,

(d) 2.

Resolution:

(4 – 5) – (13 – 18 + 2).

= -1-(13+2-18).

= -1-(15-18).

= -1-(-3).

= -1+3.

= 2.

5. What’s |-26|?

(a) -26,

(b) 26,

(c) 0,

(d) 1

Resolution:

|-26|

= 26.

6. Multiply: (x – 4)(x + 5)

(a) x2 + 5x – 20,

(b) x2 – 4x – 20,

(c) x2 – x – 20,

(d) x2 + x – 20.

Resolution:

(x – 4)(x + 5).

= x(x + 5) -4(x + 5).

= x2 + 5x – 4x – 20.

= x2 + x – 20.

7. Issue: 5x2 – 15x – 20.

(a) 5(x-4)(x+1),

(b) -2(x-4)(x+5),

(c) -5(x+4)(x-1),

(d) 5(x+4)(x+1).

Resolution:

5x2 – 15x – 20.

= 5(x2 – 3x – 4).

= 5(x2 – 4x + x – 4).

= 5{x(x – 4) +1(x – 4)}.

= 5(x-4)(x+1).

8. Issue: 3y(x – 3) -2(x – 3).

(a) (x – 3)(x – 3),

(b) (x – 3)2,

(c) (x – 3)(3y – 2),

(d) 3y(x – 3).

Resolution:

3y(x – 3) -2(x – 3).

= (x – 3)(3y – 2).

9. Remedy for x: 2x – y = (3/4)x + 6.

(a) (y + 6)/5,

(b) 4(y + 6)/5,

(c) (y + 6),

(d) 4(y – 6)/5.

Resolution:

2x – y = (3/4)x + 6.

or, 2x – (3/4)x = y + 6.

or, (8x -3x)/4 = y + 6.

or, 5x/4 = y + 6.

or, 5x = 4(y + 6).

or, 5x = 4y + 24.

or, x = (4y + 24)/5.

Due to this fact, x = 4(y + 6)/5.

10. Simplify:(4x2 – 2x) – (-5x2 – 8x).

Resolution:

(4x2 – 2x) – (-5x2 – 8x)

= 4x2 – 2x + 5x2 + 8x.

= 4x2 + 5x2 – 2x + 8x.

= 9x2 + 6x.

= 3x(3x + 2).

11. Discover the worth of three + 2 • (8 – 3)

(a) 25,

(b) 13,

(c) 17,

(d) 24,

(e) 15.

Resolution:

3 + 2 • (8 – 3)

= 3 + 2 (5)

= 3 + 2 × 5

= 3 + 10

= 13

12. Rice weighing 33/4 kilos was divided equally and positioned in 4 containers. What number of ounces of rice have been in every?

Resolution:

33/4 ÷ 4 kilos.

= (4 × 3 + 3)/4 ÷ 4 kilos.

= 15/4 ÷ 4 kilos.

= 15/4 × 1/4 kilos.

= 15/16 kilos.

Now we all know that, 1 pound = 16 ounces.

Due to this fact, 15/16 kilos = 15/16 × 16 ounces.

= 15 ounces.

13. Issue: 16w3 – u4w3

Resolution:

16w3 – u4w3.

= w3(16 – u4).

= w3(42 – ((u2)2).

= w3(4 + u2)(4 – u2).

= w3(4 + u2)(22 – u2).

= w3(4 + u2)(2 + u)(2 – u).

Reply: w3(4 + u2)(2 + u)(2 – u).

14. Issue: 3x4y3 – 48y3.

Resolution:

3x4y3– 48y3.

= 3y3(x4 – 16).

= 3y3[(x2)2 – 42].

= 3y3(x2 + 4)(x2 – 4).

= 3y3(x2 + 4)(x2 – 22).

= 3y3(x2 + 4)(x + 2)(x -2).

Reply: 3y3(x2 + 4)(x + 2)(x -2)

15. What’s the radius of a circle that has a circumference of three.14 meters?

Resolution:

Circumference of a circle = 2πr.

Given, circumference = 3.14 meters.

Due to this fact,

2πr = Circumference of a circle

or, 2πr = 3.14.

or, 2 × 3.14r = 3.14,[Putting the value of pi (π) = 3.14].

or, 6.28r = 3.14.

or, r = 3.14/6.28.

or, r = 0.5.

16. The journey from Carville to Planesborough takes 4(frac{1}{2}) hours when travelling at a relentless velocity of 70 miles per hour. How lengthy, in hours, does the journey take when travelling at a relentless velocity of 60 miles per hour.

Resolution:

Distance = Pace × Time

Distance kind Carville to Planesborough = 70 × 4(frac{1}{2}) miles

= 70 × (frac{9}{2}) miles

= 315 miles

Now travelling the identical distance (315 miles) at a relentless velocity of 60 miles per hour.

Time = (frac{Distance}{Pace})

= (frac{315}{60}) hours

= 5.25 hours

Time taken to journey Carville to Planesborough a relentless velocity of 60 miles per hour = 5.25 hours.

17. The desk beneath exhibits the variety of hours Simon labored this week at his job. Days: Hours: Monday 6 2/3. Tuesday 4 1/2. Thursday 7 1/4. He earns \$12 an hour at his job. How a lot will Simon receives a commission for the hours he labored this week?

Resolution:

Whole hours Simon labored this week = 6 2/3 + 4 1/2 + 7 1/4

= (frac{20}{3}) + (frac{9}{2}) + (frac{29}{4}) hours

= (frac{80}{12}) + (frac{54}{12}) + (frac{87}{12}) hours

= (frac{80 + 54 + 87}{12}) hours

= (frac{221}{12}) hours
He earns \$12 an hour at his job.

Simon receives a commission for the hours he labored this week = \$ (frac{221}{12}) × 12 = \$ 221

18. Carlos is seeking to purchase a home the place the ground plan exhibits the ratio of the realm of the lounge to the kitchen to the bed room is 5 : 3 : 4. If the mixed space of these three rooms is 360 sq. toes, how a lot bigger, in sq. toes, is the lounge than the bed room?

The world of the lounge = (frac{5}{5 + 3 + 4}) × 360 sq. toes

= (frac{5}{12}) × 360 sq. toes

= 5 × 30 sq. toes

= 150 sq. toes

The world of the mattress room = (frac{4}{5 + 3 + 4}) × 360 sq. toes

= (frac{4}{12}) × 360 sq. toes

= 4 × 30 sq. toes

= 120 sq. toes

Due to this fact, front room is (150 – 120) sq. toes = 30 sq. toes bigger than the mattress room.

19. Frank runs a enterprise referred to as Frank’s Contemporary Farm Produce. As soon as every week he drives to farms the place he buys the absolute best contemporary produce for his prospects. Frank can journey 600 miles on a full tank of gasoline. Often Frank has time to go to just one farm on every journey, however one week he decides to go to each Stan’s and Louisa’s farms.

● When Frank drives from his retailer to Stan’s farm and again, he is aware of he makes use of 5/12 of a tank

● When Frank drives to Louisa’s farm and again, he makes use of 1/3 of a tank.

From a map of the realm, he learns that there’s a street from Stan’s farm to Louisa’s farm that’s 120 miles lengthy. He realizes that he can drive from his retailer to Stan’s farm, then to Louisa’s farm, after which again to his retailer on a loop. Frank can inform by taking a look at his gas gauge that he has 5/8 of a tank of gasoline. Can he drive this loop with out having to cease for gas? Or ought to he purchase gasoline earlier than he begins his journey?

Resolution:

Frank drives from his retailer to Stan’s farm and again, he is aware of he makes use of 5/12 of a tank

Frank can journey 600 miles on a full tank of gasoline.

So, for five/12 tank of gasoline he can journey = 600 × 5/12 = 50 × 5 = 250 mi

Due to this fact, the gap from retailer to Stan’s farms = 250/2 mi = 125 mi

Equally, when Frank drives to Louisa’s farm and again, he makes use of 1/3 of a tank.

So, for 1/3 tank of gasoline tank he can journey = 600 × 1/3 = 200 × 1 = 200 mi

Due to this fact, the gap from retailer to Stan’s farms = 200/2 mi = 100 mi

Distance from Stan’s farm to Louisa’s farm is 120 mi.

Loop distance = Retailer to Stan’s farm to Louisa’s farm to Retailer

= 125 mi + 120 mi + 100 mi

= 345 mi

Due to this fact, Loop distance = 345 mi

Frank can inform by taking a look at his gas gauge that he has 5/8 of a tank of gasoline.

So, for five/8 tank of gasoline tank he can journey = 600 × 5/8 = 75 × 5 = 375 mi

Due to this fact, 5/8 tank of gasoline tank Frank can journey = 375 mi

345 mi < 375 mi

Thus, Frank drive this loop with out having to cease for gas.

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