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Pie
3 years ago
7

Find two values for k such that the trinomial x2 – 7x + k can be factored over the integers. Explain your reasoning.

Mathematics
1 answer:
vova2212 [387]3 years ago
6 0

Answer:

1) For a = 1: b = 6 and k = 6, 2) For a = 3: b = 4 and k = 12

Step-by-step explanation:

The polynomial y = x^{2} - 7\cdot x + k is a second-order polynomial of the form (x-a)\cdot (x-b) = x^{2}-(a+b)\cdot x + a\cdot b. By direct comparison, we construct the following system of equations:

a + b = 7 (1)

a\cdot b = k (2)

By (1) we know that there are a family of pairs such that the system of equations is satisfied. Let suppose that both a and b are integers. We assume two arbitrary integers for a:

1) a = 1

b = 7 - a

b = 6

a\cdot b = k

k = (6)\cdot (1)

k = 6

2) a = 3

b = 7 - a

b = 4

a\cdot b = k

k = (3)\cdot (4)

k = 12

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How do I solve this problem?
Liono4ka [1.6K]

Answer:

10100

Step-by-step explanation:

Use this formula,

\frac{n}{2} (2 {a} + d(n - 1)

where n is the amount of even intergers, a is the starting term, d is the common difference.

  • the amount of even intergers from 2 to 200 is 100
  • The starting number is 2
  • The common difference is 2

\frac{100}{2} (4 + 2(99)

50(4 + 198)

50(202)

10100

3 0
2 years ago
Which situation has a unit rate of $7?
cupoosta [38]

Answer:

C is the answer.

Step-by-step explanation:

4 0
3 years ago
A random sample of 121 automobiles traveling on an interstate showed an average speed of 73 mph. from past information, it is kn
tatiyna

121 is big enough to assume normality and not worry about the t distribution. By the 68-95-99.7 rule a 95% confidence interval includes plus or minus two standard deviations. So 95% of the cars will be in the mph range


(73 - 2 \cdot 11, 73 + 2 \cdot 11) = (51,95)


The question is a bit vague, but it seems we're being asked for the 95% confidence interval on the average of 121 cars. The 121 is a hint of course.


The standard deviation of the average is in general the standard deviation of the individual samples divided by the square root of n:


\sigma = \dfrac{ 11}{\sqrt{121}} = 1


So repeating our experiment of taking the average 121 cars over and over, we expect 95% of the averages to be in the mph range


(73 - 2 \cdot 1, 73 + 2 \cdot 1) = (71,75)


That's probably the answer they're looking for.



4 0
3 years ago
Which expression is equivalent
Artist 52 [7]
I would say c
Ccccccccccccccccccccccc
8 0
2 years ago
Work out the size of the angle marked t
tiny-mole [99]

Answer:

<h2>35°</h2>

Step-by-step explanation:

This is an isoceles triangle

And as we all know an isoceles triangle has two equal base angles.

And we also know that the sum of all interior angles of the triangle is 180°

So based on this we can form an algebraic equation of solve for angke t (Let's do it :))

110 + 2t = 180 \\ 2t = 180 - 110 \\ 2t = 70 \\ t  =  \frac{70}{2}  \\ t = 35

So the base angle is 35°

3 0
3 years ago
Read 2 more answers
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