what’s the total area of a converter box buildings of 4 feet, width of 3 feet,and a height of 6 feet?

Which function has exactly three distinct real zeros?

quester [9]

H(X) = (x - 2)²(x + 4)(x - 1) has 3 zeroes, they are -4,2 and 1

7 0

3 years ago

What are the solutions to the equation 2(x-3)^2=54 ?

erastova [34]

Answer:

x =(6-√108)/2=3-3√ 3 = -2.196

x =(6+√108)/2=3+3√ 3 = 8.196

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

2 • (x - 3)2 - 54 = 0

Step 2 :

2.1 Evaluate : (x-3)2 = x2-6x+9

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

2x2 - 12x - 36 = 2 • (x2 - 6x - 18)

Adding 9 has completed the left hand side into a perfect square :

x2-6x+9 =

(x-3) • (x-3) =

(x-3)2 (x-3)1 =

x-3

Now, applying the Square Root Principle to Eq. #4.3.1 we get:

x-3 = √ 27

Add 3 to both sides to obtain:

x = 3 + √ 27

Since a square root has two values, one positive and the other negative

x2 - 6x - 18 = 0

has two solutions:

x = 3 + √ 27

or

x = 3 - √ 27

Solve Quadratic Equation using the Quadratic Formula

4.4 Solving x2-6x-18 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -6

C = -18

Accordingly, B2 - 4AC =

36 - (-72) =

108

Applying the quadratic formula :

6 ± √ 108

x = —————

2

Can √ 108 be simplified ?

Yes! The prime factorization of 108 is

2•2•3•3•3

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 108 = √ 2•2•3•3•3 =2•3•√ 3 =

± 6 • √ 3

√ 3 , rounded to 4 decimal digits, is 1.7321

So now we are looking at:

x = ( 6 ± 6 • 1.732 ) / 2

Two real solutions:

x =(6+√108)/2=3+3√ 3 = 8.196

or:

x =(6-√108)/2=3-3√ 3 = -2.196

7 0

2 years ago

A welder requires 18 hours to do a job. After the welder and an apprentice work on a job for 6 hours, the welder moves to anothe

Dafna1 [17]

Answer:

the apprentice can complete the job in 30 hours by working alone.

Step-by-step explanation:

Given:

Number of hours required to complete a job by welder = 18 hours

Number of hours welder work on job = 6 hours.

Number of hours required by apprentice to complete the job = 14 hours

We need to find Number of hours required to complete a job by apprentice alone.

Solution:

Let Number of hours required to complete a job by apprentice alone be 'a'.

Also let the job completed be = 1

Now we know that ;

Time required on job is equal to sum of Number of hours welder work on job and Number of hours required by apprentice to complete the job.

framing in equation form we get

Time required on job = $6+14 =20\ hrs$

Now we can say that;

each has done a fraction of the work so we will add to two fraction as number of hours of work done by Total number of hours required to do the work to complete 1 job.

so we can frame the equation as;

$\frac{6}{18}+\frac{20}{a}=1$

By reducing the fraction we get;

$\frac{1}{3}+\frac{20}{a}=1$

Now we will make the denominator common to solve the fraction we get;

$\frac{1\times a}{3\times a}+\frac{20\times3}{a\times3}=1\\\\\frac{a}{3a}+\frac{60}{3a}=1$

Now denominators are same so we will solve the numerator we get;

$\frac{a+60}{3a}=1$

Multiplying both side by 3a we get;

$\frac{a+60}{3a}\times3a=1\times 3a\\\\a+60=3a$

Combining the like terms we get;

$3a-a=60\\\\2a=60$

Dividing both side by 2 we get;

$\frac{2a}{2}=\frac{60}{2}\\\\a=30\ hrs$

Hence the apprentice can complete the job in 30 hours by working alone.

4 0

2 years ago

Please help me with this problem thank you soo much

olya-2409 [2.1K]

Answer:

A, 12:47

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Which of the following shows the prime factorization of 72 using exponential notation?

Luba_88 [7]

Answer:

2^3 .3^2

Step-by-step explanation:

if 2×2×2 = 8

and 3×3=9 then 8×9=72

6 0

3 years ago

Read 2 more answers