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3 years ago

If f(x) = 3x + 2 and g(x) = x^2 + 1, which expression is equivalent to (g(f(x))?

1 answer:

7 0

<span>Whenever we are given one function and must calculate a funciton of the funciton, such as g(f(x)) in this case, we simply substitute the second function, f(x) in this case, in the first function, g(x) in this case, wherever the first function has a variable. Therefore, g(f(x)) = (3x + 2)^2 + 1 g(f(x)) = 9x^2 + 12x + 4 + 1 g(f(x)) = 9x^2 + 12x + 5</span>

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The symbol ⊕ is used to denote exclusive or, so p ⊕ q ≡ (p v q) ^ ~ (p ^ q).

Elan Coil [88]

I'll use text forms of the logical symbols because copying/pasting on mobile is annoying.

⊕ = XOR

∨ = OR

∧ = AND

~ = NOT

↔ = IFF (meaning "if and only if")

→ = IMP (short for "implies")

and for logical equivalence I'll use a regular equal sign.

Then

p XOR q = (p OR q) AND NOT (p AND q)

(a) By definition of XOR, we have

p XOR p = (p OR p) AND NOT (p AND p)

= p AND NOT p

and this is tautologically FALSE.

(b) To rewrite XOR, first distribute the NOT over the AND using DeMorgan's law:

NOT (p AND q) = NOT p OR NOT q

Then we can interchange the AND and ORs using their respective distributive properties. That is,

p XOR q = (p OR q) AND (NOT p OR NOT q)

= (p AND (NOT p OR NOT q)) OR (q AND (NOT p OR NOT q))

= ((p AND NOT p) OR (p AND NOT q)) OR ((q AND NOT p) OR (q AND NOT q))

Both (p AND NOT p) and (q AND NOT q) are tautologically FALSE, so the truth value of either OR depends only on the other statements, so we have

p XOR q = (p AND NOT q) OR (q AND NOT p)

Recall the definition of IFF:

p IFF q = (p IMP q) AND (q IMP p)

Also recall that IMP is logically equivalent to

p IMP q = p OR NOT q

Then we have

p IFF q = (p OR NOT q) AND (q OR NOT p)

so that its negation is

NOT (p IFF q) = NOT ((p OR NOT q) AND (q OR NOT p))

= NOT (p OR NOT q) OR NOT (q OR NOT p)

= (NOT p AND q) OR (NOT q AND p)

The statements in bold match, so p XOR q is indeed equivalent to NOT (p IFF q).

3 0

3 years ago

Write 4/14 in simplest form

kondaur [170]

Answer:

2/7

Step-by-step explanation:

14/2=7. 4/2=2 .2/7 is the answer

7 0

3 years ago

Read 2 more answers

Find the value of x.

olchik [2.2K]

Answer:

x = 4

Step-by-step explanation:

In $\triangle BAC, \: DE || AC$

Hence, by basic proportionality theorem:

$\frac{x + 2}{x} = \frac{3}{2} \\ \\ \therefore \: 2(x + 2) = 3x \\ \therefore \:2x + 4 = 3x \\ \therefore \:4 = 3x - 2x \\ \therefore \:4 = x \\ \huge \red { \boxed{\therefore \:x = 4}}$

7 0

3 years ago

This is a polygon and I need help finding the missing angle ?

allsm [11]

First, you need to know that the total (degrees) of the interior angles is 360 because this is a quadrilateral.

The unnumbered angle is 109 degrees. We know this because the angle labeled 71 degrees and the unnumbered angle are supplementary. So you subtract 180 from 71 to get 109.
$180-71=109$

To solve for x, we need to realize the other numbers playing into the angles' values. To make solving this easier, I'm gonna assign letters to the angles.

(10x+6) is angle A.

(13x-2) is angle B.

(8x-1) is angle C.

and 109 (the one we solved) is angle D.

We know that the total of the interior angles is 360, so we can add the 2 from angle B and the 1 from angle C to 360. This is because these numbers are subtracted from the other values.
$360+2+1=363$

Now, we have to subtract the 6 from angle A from 363, because the 6 is added to the other values.
$363-6=357$

Now we have to subtract 109 from 357 because you want to get the x's by themselves. Since you're solving for x.
$357-109=248$

That leaves you with 248. Now you add all the x's up to get the total number of x's. You have 10x from angle A, 13x from angle B, and 8x from angle C.
$10x+13x+8x=31x$

You get 31x. To get what x is, you divide 248 by 31.
$\frac{248}{31} =8$

That equals 8. So now that you know that x equals 8, if you need to find the values of the angles, you just plug in the numbers into the formulas.

$(10(8))+6= 86$
$(13(8))-2=102$
$(8(8))-1=63$
$109$

Check your work by plugging your answers in and seeing if they add up to 360.
$86+102+63+109=360$

Which they should:)

So...
angle A= 86
angle B=102
angle C=63
angle D=109

and x=8

Hope this helped!!!

4 0

3 years ago

What’s 4/5 times 2/3

maxonik [38]

Answer:

8/15

Step-by-step explanation:

When multiplying fractions, simply multiply the numbers straight across. First, multiply the numerators to get 8. Then, multiply the denominators and you'll get 15.

6 0

3 years ago

Read 2 more answers