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Maurinko [17]
3 years ago
7

Can someone pls help me on the last three!

Mathematics
1 answer:
Solnce55 [7]3 years ago
4 0
Red to total I believe is 12/23
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what is the polynomial function of lowest degree with leading coefficient of 1 and roots 2 and 1 + square root2
Marta_Voda [28]
If the roots to such a polynomial are 2 and 1+\sqrt2, then we can write it as

(x-2)(x-(1+\sqrt2))

courtesy of the fundamental theorem of algebra. Now expanding yields

(x-2)(x-1-\sqrt2)=x^2-2x-(1+\sqrt2)x+2(1+\sqrt2)=x^2-(3+\sqrt2)x+2+2\sqrt2

which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.

So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use 1-\sqrt2 as a root. In this case, that would make our polynomial

(x-2)(x-(1+\sqrt2))(x-(1-\sqrt2))=x^3-4x^2+3x+2

so that the answer is (probably) the third choice.

Whoever originally wrote this question should reevaluate their word choice...
5 0
3 years ago
What value of $k$ will make $4x^2 - 20x + k$ the square of a binomial?
Arisa [49]

Answer:

k = 25

Step-by-step explanation:

(2x  - sqrt(k) )^2              Expand this as a binomial                          

4x^2 - 4x*sqrt(k) + k      The middle term must be -20x Solve for k so it is

-4xsqrt(k) = - 20x            Divide by -4x

sqrt(k) = -20x/-4x             Do the division

sqrt(k) = 5                         Square both sides

k = 25


5 0
3 years ago
an online movie streaming plan has no annual fee but charges $4.25 per movie watched. Another plan charges an annual fee of $36
Juli2301 [7.4K]
X is the number of movies for the cost of the plan to be the same.

4.25x=36+3.5x
4.25x-3.5=36
0.75x=36
x=36/0.75
x=48
3 0
3 years ago
Read 2 more answers
Which of the following relations is a function?
ale4655 [162]

Answer:

{(5, –4), (–4, 5), (–5, 4), (4, –5)}

5 0
3 years ago
Read 2 more answers
The product of two consecutive positive integers is 18 more than eight times the smaller number. Find the two numbers.
olga2289 [7]

Let , smallest integer is x.

So , other one is x + 1.

By , given conditions :

x( x + 1 ) = 8x + 18\\\\x^2+x=8x+18\\\\x^2-7x-18=0\\\\x^2-9x+2x-18=0\\\\x(x-9)+2(x-9)=0\\\\x=-2 \  ,\ x = 9

Since, the numbers are positive so, x = -2 is ignored.

Therefore, the numbers are 9 and 10.

Hence, this is the required solution.

6 0
3 years ago
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