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Mrrafil [7]
3 years ago
7

Make sure all solutions are in lowest terms. 5/6 • 1/3

Mathematics
1 answer:
stiks02 [169]3 years ago
3 0
1/3=2/6
5/6x2/6= 10/36
10/36 simplified is 5/18
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What is 6(3x - 4) = -8
Ludmilka [50]

Answer:

x = 8/9

Step-by-step explanation:

6(3x - 4) = -8

Distribute the 6

18x -24 = -8

Add 24 to each side

18x -24+24 = -8+24

18x = 16

Divide each side by 18

18x/18 =16/18

Simplify the fraction by dividing top and bottom by 2

x = 8/9

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Find the vertex and x-intercepts for 39x^2+38x+8.
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What is the sum of the first 5 prime numbers?
JulijaS [17]

Answer:

Prime numbers are the number that are divisible only by two whole numbers : 1 and itself. The first five prime numbers are : 2,3,5,7 and 11. The sum of the first five prime numbers is 2+3+5+7+11 = 28.

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Factorise 2x^3+9x^2+10x+3​
Advocard [28]

In order to factor a polynomial p(x), we have to find all its roots x_1,\ x_2,\ldots x_n so that we can rewrite the polynomial as

p(x)=(x-x_1)(x-x_2)\ldots(x-x_n)

This is exactly the same idea we apply when we factor numbers: we look for all the primes that divide the number, and then we write

n = p_1^{e_1}\cdot p_2^{e_2}\ldots p_n^{e_n}

When talking about polynomials, the idea of prime numbers is represented by irreducible polynomials, i.e. polynomials with no roots.

So, we have to find a root of our polynomial. Using the rational root theorem, we can check that x=-1 is a solution:

p(-1)=2(-1)^3+9(-1)^2+10(-1)+3 = -2+9-10+3=0

So, our polynomial is divisible by (x+1). The long division yields

\dfrac{2x^3+9x^2+10x+3​}{x+1} = 2x^2+7x+3

Which is the same as

2x^3+9x^2+10x+3=(x+1)(2x^2+7x+3)

We can complete the factorization by breaking the quadratic equation: using the standard quadratic formula we can find the solutions

2x^2+7x+3=0 \iff x=-\dfrac{1}{3}\text{ or }x=-3

Which implies

2x^2+7x+3=\left(x+\dfrac{1}{2}\right)(x+3)

And finally

2x^3+9x^2+10x+3=(x+1)\left(x+\dfrac{1}{2}\right)(x+3)

8 0
3 years ago
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