What is the square unit of 5,469

<em>Find a quadratic polynomial with integer coefficients which has the following real zeros: </em> $x = \frac{2}{9}\pm \frac{\sqrt{23}}{9}$ <em>. </em>

Let be $r_{1} = \frac{2}{9}+\frac{\sqrt{23}}{9}$ and $r_{2} = \frac{2}{9}-\frac{\sqrt{23}}{9}$ roots of the quadratic function. By Algebra we know that:

$y = (x-r_{1})\cdot (x-r_{2}) = x^{2}-(r_{1}+r_{2})\cdot x +r_{1}\cdot r_{2}$ (1)

Then, the quadratic polynomial is:

$y = x^{2}-\frac{4}{9}\cdot x -\frac{19}{81}$

$y = 81\cdot x^{2}-36\cdot x -19$

The quadratic polynomial with integer coefficients is $y = 81\cdot x^{2}-36\cdot x -19$ .

5 0

3 years ago

Divide $800 between kofi and kweku so that kofi gets three times what kweku gets

AfilCa [17]

Answer:

600 and 200

Step-by-step explanation:

kofi : kweku is 3 :1

so Kofi gets 3 out of ( 3 +1) = 3/4 of 800 = 3/4 * 800 = 600

kweku get s the rest 800- 600 = 200

6 0

1 year ago

0.45m-9=0.9m, what is the least power of ten you could multiply by to write an equivalent equation with integer coefficients?

tia_tia [17]

Answer:

m = -20

Step-by-step explanation:

Step 1 :

9

Simplify ——

10

Equation at the end of step 1 :

45 9

((——— • m) - 9) - (—— • m) = 0

100 10

Step 2 :

9

Simplify ——

20

Equation at the end of step 2 :

9 9m

((—— • m) - 9) - —— = 0

20 10

Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 20 as the denominator :

9 9 • 20

9 = — = ——————

1 20

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

9m - (9 • 20) 9m - 180

————————————— = ————————

20 20

Equation at the end of step 3 :

(9m - 180) 9m

—————————— - —— = 0

20 10

Step 4 :

Step 5 :

Pulling out like terms :

5.1 Pull out like factors :

9m - 180 = 9 • (m - 20)

Calculating the Least Common Multiple :

5.2 Find the Least Common Multiple

The left denominator is : 20

The right denominator is : 10

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

2 2 1 2

5 1 1 1

Product of all

Prime Factors 20 10 20

Least Common Multiple:

20

Calculating Multipliers :

5.3 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 1

Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

5.4 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 9 • (m-20)

—————————————————— = ——————————

L.C.M 20

R. Mult. • R. Num. 9m • 2

—————————————————— = ——————

L.C.M 20

Adding fractions that have a common denominator :

5.5 Adding up the two equivalent fractions

9 • (m-20) - (9m • 2) -9m - 180

————————————————————— = —————————

20 20

Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

-9m - 180 = -9 • (m + 20)

Equation at the end of step 6 :

-9 • (m + 20)

————————————— = 0

20

Step 7 :

When a fraction equals zero :

7.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

-9•(m+20)

————————— • 20 = 0 • 20

20

Now, on the left hand side, the 20 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

-9 • (m+20) = 0

Equations which are never true :

7.2 Solve : -9 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

7.3 Solve : m+20 = 0

Subtract 20 from both sides of the equation :

m = -20

One solution was found :

m = -20

6 0

3 years ago