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lorasvet [3.4K]
2 years ago
5

I am thinking of a positive number. If I square it, double the result, take half of that result, and then add 12, I get 21. What

is my number?
Mathematics
1 answer:
Margarita [4]2 years ago
8 0

Answer:

3

Step-by-step explanation:

work backwards.

x^2*2/2+12=21

x^2+12=21

x^2=9

x=3

You might be interested in
each of 4 family members uses 175 minutes or fewer of their combined family cell phone plan. at the end of the month, the family
Mamont248 [21]

Answer:

 

x = ± ∜175 = ± 3.6371

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    x^4-(175)=0

Step by step solution :

STEP

1

:

Trying to factor as a Difference of Squares:

1.1      Factoring:  x4-175

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 175 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Polynomial Roots Calculator :

1.2    Find roots (zeroes) of :       F(x) = x4-175

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers. The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -175.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,5 ,7 ,25 ,35 ,175

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -174.00    

     -5       1        -5.00        450.00    

     -7       1        -7.00        2226.00    

     -25       1       -25.00       390450.00    

     -35       1       -35.00       1500450.00    

     -175       1       -175.00       937890450.00    

     1       1        1.00        -174.00    

     5       1        5.00        450.00    

     7       1        7.00        2226.00    

     25       1        25.00       390450.00    

     35       1        35.00       1500450.00    

     175       1       175.00       937890450.00    

Polynomial Roots Calculator found no rational roots

Equation at the end of step

1

:

 x4 - 175  = 0

STEP

2

:

Solving a Single Variable Equation:

2.1      Solve  :    x4-175 = 0

Add  175  to both sides of the equation :

                     x4 = 175

                    x  =  ∜ 175  

The equation has two real solutions  

These solutions are  x = ± ∜175 = ± 3.6371  

Two solutions were found :

x = ± ∜175 = ± 3.6371

4 0
2 years ago
Read 2 more answers
The sum of 444 consecutive integers is 326326326.<br> What is the second number in this sequence?
Nookie1986 [14]

Answer:

82

Step-by-step explanation:

Let's first figure out what the first number is and use that to solve for the next. The problem states that the numbers are consecutive. So the 2nd number word be 1 plus the first.

The sum of 4 consecutive numbers:

1st = x

2nd = x + 1

3rd = x + 2

4th = x + 3

The sum of 4 consecutive number is 326.

1st + 2nd + 3rd + 4th = 326

x + (x + 1) + (x + 2) + (x + 3)  = 326

Combine like terms:

4x + 6 = 326

Then we subtract 6 from both sides to isolate 4x:

4x + 6 - 6 = 326 - 6

4x = 320

Then we divide both sides by 4 to isolate x:

4x/4 = 320/4

x = 80

So the first number is 79

Now to get the second, let's just add 1.

80 + 1 = 81

Let's check if our answer would be correct:

80 + 81 + 82 + 83

= 326

5 0
3 years ago
Read 3 more answers
Need help ASAP thankyou sorry if u can’t see the picture but u can zoom in :)
Andrej [43]

Answer:

a)Volume 390ft3. Surface area 450ft2

b)surface area

c)volume

Step-by-step explanation:

2*15*13=390

2*15*2=60+15*13*2=390

7 0
2 years ago
If m&lt;6=85° what is the measure of &lt;3
777dan777 [17]

Answer:

I am not sure , but my answer would be 42.5° .

3 0
3 years ago
X2 + 45x = -200 Using the quadratic formual and the discirimnat
dybincka [34]

Answer:

Positive discriminant = 2 real solution

x= -5,-40

Step-by-step explanation:

The discriminant is used to see how many solutions an equation has. If it is negative, the equation has no real solutions, if =0 the equation has 1, and if it is positive, the equation has two real solutions.

The discriminant is the part of the quadratic formula inside the square root:

b^{2}-4ac

Every quadratic formula has the structure:

ax^{2} +bx+c=0

So first, in order to meet this structure we need to add 200 to both sides so the equation is equal to 0. This gives us:

x^{2} +45x+200=0

Our a=1, b=45 and c=200

Now we can substitute these values into the discriminant:

(45)^{2} -4(1)(200)

Solve:

2025-800=1225

The discriminant is a positive number which means this equation will have 2 real solution. Now we just need to plug in our values into the quadratic formula to solve this equation. Quadratic formula:

x=\frac{-+/-\sqrt{b^{2}-4ac} }{2a} \\x=\frac{-45+/-\sqrt{1225} }{2}

(Same discriminant value)

x=\frac{-45+/-35}{2}

Now to find the two solutions, we use both signs in the equation. Solution 1:

x=\frac{-45+35}{2}

x=\frac{-10}{2}=-5

Our first solution is -5, now for the second:

x=\frac{-45-35}{2}\\\\ x=\frac{-80}{2}=-40

The two solution to this equation are -5 and -40.

Hope this helped!

7 0
3 years ago
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