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3 years ago

Please help me answer and explain number 55

Mathematics

1 answer:

melamori03 [73]3 years ago

6 0

Answer:

Step-by-step explanation:

An operation of two real numbers is defined by the rule

$a\bigotimes b=b^a+2ab$

Calculate $2\bigotimes (1\bigotimes 3).$ First evaluate the expression in brackets:

$1\bigotimes 3=1^3+2\cdot 1\cdot 3=1+6=7$

Now,

$2\bigotimes (1\bigotimes 3)=2\bigotimes 7=2^7+2\cdot 2\cdot 7=128+28=156$

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Find all roots: x^3 + 7x^2 + 12x = 0 Show all work and check your answer.

Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

Solution:

We have been given a cubic polynomial.

$x^{3}+7 x^{2}+12 x=0$

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

$x^{3}+7 x^{2}+12 x=0$

$x\left(x^{2}+7 x+12\right)=0$ ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

$x^{2}+7 x+12=0$

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

$\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}$

Therefore, the two roots are:

$\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}$

And,

$\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}$

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

4 0

3 years ago

How do you answer the picture below?

3241004551 [841]

Answer:

42cm²

Step-by-step explanation:

because if the perimeter of the rectangle is 28 then the length is 5, 5 - 11 = 6, the formula for finding the trapezium is to add the 2 parallel sides, half them, then times them with the length so your sum will look like this, 5+9=14, (i knew the other side was 9 as the length of AB is the same as the length of FC, which is the one of the parallel sides of the trapezium) then we do 14÷2=7, finally we times 7 by 6 which is 42cm²

3 0

3 years ago

Question 2 of 10

Delvig [45]

The answer is B i think

5 0

2 years ago

Read 2 more answers

Solve the exponential equation:

seraphim [82]

Step-by-step explanation:

2⁵ˣ = 8ˣ⁺²