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Mathematics

1 answer:

bija089 [108]3 years ago

6 0

Answer:

-103

243

Step-by-step explanation:

(q•r)(5) = q(r(5))

r(5) = 2(5²) + 1 = 51

q(51) = -2(51) - 1 = -103

(r•q)(5) = r(q(5))

q(5) = -2(5) - 1 = -11

r(-11) = 2(-11)² + 1 = 243

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Factorise x squared + 4x + 3

olganol [36]

<h3>Answer: (x+1)(x+3)</h3>

===================================================

Explanation:

Let's assume it factors into (x+a)(x+b)

The goal is to find the two numbers a and b.

FOIL out (x+a)(x+b) to get x^2+(a+b)x+ab

Note how a+b is the middle term and ab is the last term.

In the original expression, 4 is the middle term and 3 is the last term.

So we need to find two numbers that

add to 4
multiply to 3

There are two ways to multiply to 3 and they are

1 times 3 = 3
-1 times -3 = -3

But only the first way has the factors add to 4. So that means a = 1 and b = 3.

Therefore (x+a)(x+b) = (x+1)(x+3)

And x^2+4x+3 = (x+1)(x+3)

8 0

3 years ago

I NEED HELP PLEASE, THANKS! :)

Afina-wow [57]

Answer:

Third option is the right choice.

Step-by-step explanation:

Manipulate the right hand side.

$\sec \left(x\right)\\\\=\frac{1}{\cos \left(x\right)}\\\\\mathrm{Use\:the\:following\:identity}:\quad \:1=\cos ^2\left(x\right)+\sin ^2\left(x\right)\\\\=\frac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)}\\\\\Rightarrow \mathrm{True}$