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klio [65]
3 years ago
15

Which trinomials are prime?Choose all answers that are correct.

Mathematics
1 answer:
lbvjy [14]3 years ago
7 0

Answer:

x^2+11x+18 is prime

Step-by-step explanation:

<u>Prime Trinomials</u>

A given trinomial is prime if it cannot be factored. The general expression for a trinomial is

ax^2+bx+c

Another useful expression is

a(x-x_1)(x-x_2)

where x1 and x2 are the zeroes of the trinomial.

The zeroes can be computed by using the known formula

\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

The trinomial has two zeroes if the root can be found as a real number, that is if d is positive or zero, where

d=b^2-4ac

Let's test the four options

x^2-8x+2

a=1,b=-8,c=2

d=(-8)^2-4\cdot 1\cdot 2=56

Since d is positive, the trinomial can be factored and therefore is not prime

x^2+4x+5

a=1,b=4,c=5

d=4^2-4\cdot 1\cdot 5=-4

Since d is negative, the trinomial is prime

x^2+11x+18

a=1,b=11,c=18

d=11^2-4\cdot 1\cdot 18=49

Since d is positive, the trinomial can be factored and therefore is not prime

x^2-3x-2

a=1,b=-3,c=-2

d=(-3)^2-4\cdot 1\cdot (-2)=17

Since d is positive, the trinomial can be factored and therefore is not prime

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Answer:

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Step-by-step explanation:

We see the relationship is closer to linear in the interval 30 to 40

<u>Approximate points:</u>

  • (30, 34) and (34, 54)

<u>The slope of the line:</u>

  • m = (54 - 34)/(34- 30) = 20/4 = 5

<u>The line is:</u>

  • y - 34 = 5(x - 30)
  • y = 5x - 116

<u>At x = 40, the value of y would be:</u>

  • y = 5*40 - 116 = 84

The closet option is B

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3 years ago
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Answer:

118.75

Step-by-step explanation:

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How do I do this problem?
Vikentia [17]
You use the distributive property and multiple everything inside of the parentheses by 2x^2 then everything in the parentheses by y to get 2x^4y-6x^3y^2+16x^2y^3. I think that’s the answer and I hope that helped!
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3 years ago
Three rectangular tables are placed end to end to form one long table 7.8 meters long. The lengths of two of the tables are 3.5
NeTakaya

It's a 3rd grade problem in addition and subtraction, or number lines. As a college-level problem, it might be described as ...

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3 years ago
Brian has saved five dollars in dimes quarters and half dollars she finds that she has 30 coins all together and there are four
Thepotemich [5.8K]

9514 1404 393

Answer:

  • 20 dimes
  • 8 quarters
  • 2 half-dollars

Step-by-step explanation:

Let d, q, h represent the numbers of dimes, quarters, and halves Brian has. We can write 3 equations in these 3 variables:

  10d +25q +50h = 500 . . . . value of the coins, in cents

  d + q + h = 30 . . . . . . . . . . . total number of coins

  4h = q . . . . . . . . . . . . . . . . . four times as many quarters as halves

Using the last equation to substitute into the other two, we get ...

  10d + 150h = 500

  d +5h = 30

The second equation can be written as ...

  5h = 30 -d

and the first can be written to facilitate substitution:

  10d +30(5h) = 500

  10d +30(30-d) = 500 . . . . . substitute for 5h

  900 -20d = 500 . . . . . . . . . simplify

  400 = 20d . . . . . . . . . . . . . add 20d-500 to both sides

  d = 20 . . . . . . . . . . . . . . . . divide by 20

Brian has 20 dimes.

5 0
3 years ago
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