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3 years ago

The complete factorization of -12x^3 + 14x^2 +6x is -2x(ax + 1)(2x-3). What is the value of a?

Mathematics

1 answer:

tester [92]3 years ago

4 0

Answer:

a = 3

Step-by-step explanation:

-12x³+14x²+6x = -2x(ax+1)(2x-3)

Divide both sides by -2x(2x-3)

$\frac{-2x(ax+1)(2x-3)}{-2x(2x-3)} = - \frac{12x^{3} }{-2x(2x-3)} + \frac{14x^{2} }{-2x(2x-3)} +\frac{6x}{-2x(2x-3)}$

ax+1=3x+1

Subtract 1 from both sides

ax=3x

Divide both sides by x

a=3

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Karo-lina-s [1.5K]

The answer is 27
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7 0

3 years ago

Read 2 more answers

1. When professional golfer Jordan Spieth hits his driver, the distance the ball travels can be modeled by

Doss [256]

Answer:

a. About 96% of Spieth's drives travel at least 290 yards

b. The ball has to travel about 314.24 yards

Step-by-step explanation:

* Let us explain how to solve the problem

- The distance the ball travels can be modeled by distribution with

mean 304 yards and standard deviation 8 yards

- Jordan would need to hit the ball at least 290 yards to have a clear

second shot that avoids a large group of trees

- We need to find the percent of Spieth's drives travel at least

290 yards

∵ The mean μ = 304 yards

∵ The standard deviation σ = 8 yards

∵ The distance x = 290

∵ P(x ≥ 290) = P(z ≥ z)

- We need to find z score

∵ z-score = (x - μ)/σ

∴ z = $\frac{290-304}{8}$ = -1.75

* Let us use the normal distribution table to find the corresponding

area of z = -1.75

∵ P(-z) = 1 - P(z)

∵ P(z ≥ -1.75) = 1 - 0.04006 = 0.95994

∴ P(x ≥ 290) = 0.96 = 96%

* About 96% of Spieth's drives travel at least 290 yards

- On another golf hole, Spieth has the opportunity to drive the ball

onto the green if he hits the ball a distance in the top 10% of all

his drives

- We need to find how far the ball has to travel

- Let us find the z-score from the normal distribution table for the 10%

to the right or 90% to the left

∵ The area which equivalent to 0.9 ≅ 0.89973

∴ z = 1.28

∵ z-score = (x - μ)/σ

∴ 1.28 = $\frac{x-304}{8}$

- Multiply both sides by 8

∴ 10.24 = x - 304

- Add 304 for both sides

∴ x = 314.24 yards

* The ball has to travel about 314.24 yards

8 0

3 years ago

5 yrs ago, Nuri was thrice as old as Sonu. 10 yrs later, Nuri will be twice as old Sonu. How old are Nuri n Sonu?

Papessa [141]

Answer:

Answer will be 50

Step-by-step explanation:

Let us suppose, present age of Nuri be ‘x’ years and present age of Sonu be ‘y’ years.

Now, it is given that five years ago, Nuri was thrice old as Sonu. Hence,

Five years ago,

Nuri’s age = x-5 years

Sonu’s age = y-5 years

And relation between ages can be given as

Nuri’s age = 3×sonu’s age or

x-5 = 3(y-5)

x-5 = 3y-15

x-3y+10 = 0 ………..(i)

Another relation is given in the problem that ten years later, Nuri is twice as old as Sonu.

So, ten years ago,

Nuri’s Age = x+10

Sonu’s Age = y+10

And relation between ages can be written as

x+10 = 2(y+10)

x+10 = 2y+20

x-2y-10 = 0 …………..(ii)

Now we can solve the equation (i) and (ii) to get values of x and ‘y’ or present ages of Nuri and Sonu.

Value of ‘x’ from equation (i) be

x = 3y-10 ……….(iii)

Putting value of ‘x’ from equation (iii) in equation (ii) we get,

3y-10-2y-10 = 0

y = 20

Now, from equation (iii) value of ’x’ can be given as,

x= 3(20)-10

x = 50

Hence, the present ages of Nuri and Sonu are 50 years and 20 years respectively.

7 0

2 years ago

Laura rode her bike 3.5 miles. Shanay rode her bike 4 miles. How many more feet did Shanay ride her bike then Laura?

g100num [7]

Answer:

I am pretty sure the answer is 2640 feet.

Step-by-step explanation:

8 0

3 years ago

Help me please with numbers 1-8 I'm stuck!!

siniylev [52]

Hopefully this helps, and sorry I didn't do 8 I'm limited on time

5 0

3 years ago