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serg [7]
3 years ago
7

Which polynomials are prime? Check all that apply. x2 + 4 x2 – 5x + 2 x2 + 10x – 24 x2 – x + 27 2x3 – 4x + 5x2 – 10

Mathematics
2 answers:
KengaRu [80]3 years ago
8 0

Answer:

X2+4, x2-5x+2, x2-x+27

Step-by-step explanation:

ed2020 i got them right

bekas [8.4K]3 years ago
3 0
A prime polynomial is a polynomial that can be further dissected into factored into factors while an even polynomial, on the other <span>hand,cannot</span> be factored out. In this case, the equations that are factorable are:
<span>x2 + 10x – 24 = (x+12)(x-2) 
</span>All the other polynomials cannot be factored. 

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What are all of the powers of 3 in range 3 to 1000
Agata [3.3K]
3*1 = 3
3*2 = 9
3*3 = 27
3*4 = 81
3*5 = 243
3*6 = 729
6 0
3 years ago
HELPPP!!!!! Plzzzz!!
Lina20 [59]

Given:

Cards labelled 1, 3, 5, 6, 8 and 9.

A card is drawn and not replaced. Then a second card is drawn at random.

To find:

The probability of drawing 2 even numbers.

Solution:

We have,

Even number cards = 6, 8

Odd numbers cards = 1, 3, 5, 9

Total cards =  1, 3, 5, 6, 8 and 9

Number of even cards = 2

Number of total cards = 6

So, the probability of getting an even card in first draw is:

P_1=\dfrac{\text{Number of even cards}}{\text{Number of total cards}}

P_1=\dfrac{2}{6}

P_1=\dfrac{1}{3}

Now,

Number of remaining even cards = 1

Number of remaining cards = 5

So, the probability of getting an even card in second draw is:

P_2=\dfrac{\text{Number of remaining even cards}}{\text{Number of remaining total cards}}

P_2=\dfrac{1}{5}

The probability of drawing 2 even numbers is:

P=P_1\times P_2

P=\dfrac{1}{3}\times \dfrac{1}{5}

P=\dfrac{1}{15}

Therefore, the probability of drawing 2 even numbers is \dfrac{1}{15}. Hence, the correct option is (b).

5 0
2 years ago
James is 8 years old. Last year, his father was 4 times as old as he was. In how many years' time will their combined age be 51?
Snowcat [4.5K]

Last year He was 7 years old.

His father is 4 times the age 7 x 4 = 28

Last year his dad was 28, so this year he is 29.

Combined age this year = 29 + 8 = 37

51 - 37 = 14 years

14/ 2 people = 7 years

8 + 7 = 15

29 + 7 = 36

15 + 36 = 51

It will take 7 years.

7 0
3 years ago
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
A rental car company is running two specials. Customers can pay $40 to rent a compact car for the first day plus $6 for each add
Flura [38]

Answer: she wants to rent the car for 11 days.

Step-by-step explanation:

Let x represent the number of additional days that Pamela wants to rent the car for.

Customers can pay $40 to rent a compact car for the first day plus $6 for each additional day. This means that the total cost of using this special for x days would be

40 + 6(x - 1) = 40 + 6x - 6

= 34 + 6x

Also, they can rent the same car for $30 the first day and $7 for every additional day beyond that. This means that the total cost of using this special for x days would be

30 + 7(x - 1) = 30 + 7x - 7

= 23 + 7x

Since she found out that the two specials are equivalent for x days, then

34 + 6x = 23 + 7x

7x - 6x = 34 - 23

x = 11

4 0
3 years ago
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