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marissa [1.9K]
2 years ago
7

Simplify (4x^2+2)÷(2x^2-9x-5)​

Mathematics
1 answer:
frosja888 [35]2 years ago
5 0

Answer:

4.1     Pull out like factors :

   4x2 + 2  =   2 • (2x2 + 1) 

Polynomial Roots Calculator :

 4.2    Find roots (zeroes) of :       F(x) = 2x2 + 1

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  2  and the Trailing Constant is  1.

 The factor(s) are:

of the Leading Coefficient :  1,2

 of the Trailing Constant :  1

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      3.00        -1     2      -0.50      1.50        1     1      1.00      3.00        1     2      0.50      1.50   

Polynomial Roots Calculator found no rational roots

Trying to factor by splitting the middle term

 4.3     Factoring  2x2 - 9x - 5 

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -9x  its coefficient is  -9 .

The last term, "the constant", is  -5 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -5 = -10 

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   -9 .

     -10   +   1   =   -9   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  1 

                     2x2 - 10x + 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

                    2x • (x-5)

              Add up the last 2 terms, pulling out common factors :

                     1 • (x-5)

Step-5 : Add up the four terms of step 4 :

                    (2x+1)  •  (x-5)

             Which is the desired factorization

Final result :

2 • (2x2 + 1) —————————————————— (x - 5) • (2x + 1)

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27(2+1)

Step-by-step explanation:

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Let $P$ and $Q$ be constants. The graphs of the lines $x + 5y = 7$ and $15x + Py = Q$ are perpendicular and intersect at the poi
Marta_Voda [28]

Answer:

<em>(-3, -129)</em>

<em></em>

Step-by-step explanation:

Given

Two lines:

$x + 5y = 7$

$15x + Py = Q$

are perpendicular to each other and intersect at point (-8,3).

To find: (P, Q)

Solution:

The two lines intersect at (-8,3).

It means, the equation of line will be satisfied when we put value of x = -8 and y = 3

Putting in the second equation, we will get an equation in P and Q:

15\times (-8) + P \times 3 = Q\\\Rightarrow 3P = Q +120 ..... (1)

Given that two lines are perpendicular.

It means the product of their slopes will be equal to -1.

i.e. m_1\times m_2=-1

Slope of a line of the form ax+by+c=0 is given as:

m=-\dfrac{a}{b}

So, slopes of given lines are:

m_1=-\dfrac{1}{5}\\m_2=-\dfrac{15}{P}

Using the condition:

-\dfrac{1}{5}\times \dfrac{-15}{P}=-1\\\Rightarrow P = -3

Putting the value of P in equation (1):

\Rightarrow 3\times (-3) = Q +120 \\\Rightarrow Q = -9-120 = -129

So, answer is <em>(-3, -129)</em>

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3 years ago
find the product with the exponent in the simplest form. Then, identify the values of x and y. 6^1/3 * 6^1/4 = 6^x/y
mr Goodwill [35]
<span>6^1/3 * 6^1/4 = 6^x/y

The key to solving this problem is understanding properties of exponents:
If you are multiplying two powers with the same base (in this case the base is 6), the result is the base raised to the power of the two exponents added together.

6^1/3+1/4 = 6^x/y
6^7/12 = 6^x/y
 
So the product would be 6^7/12
x = 7
y = 12</span>
6 0
2 years ago
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