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Vikki [24]
3 years ago
11

QUESTION 9

Mathematics
1 answer:
Ratling [72]3 years ago
8 0
The first one is (v+6)(v-6)
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Find the set of values of k for which the line y=kx-4 intersects the curve y=x²-2x at 2 distinct points?
Sonbull [250]

Answer:

-6 < k < 2

Step-by-step explanation:

Given

y = x^2 - 2x

y =kx -4

Required

Possible values of k

The general quadratic equation is:

ax^2 + bx + c = 0

Subtract y = x^2 - 2x and y =kx -4

y - y = x^2 - 2x - kx +4

0 = x^2 - 2x - kx +4

Factorize:

0 = x^2 +x(-2 - k) +4

Rewrite as:

x^2 +x(-2 - k) +4=0

Compare the above equation to: ax^2 + bx + c = 0

a = 1

b= -2-k

c =4

For the equation to have two distinct solution, the following must be true:

b^2 - 4ac > 0

So, we have:

(-2-k)^2 -4*1*4>0

(-2-k)^2 -16>0

Expand

4 +4k+k^2-16>0

Rewrite as:

k^2 + 4k - 16 + 4 >0

k^2 + 4k - 12 >0

Expand

k^2 + 6k-2k - 12 >0

Factorize

k(k + 6)-2(k + 6) >0

Factor out k + 6

(k -2)(k + 6) >0

Split:

k -2 > 0 or k + 6> 0

So:

k > 2 or k > -6

To make the above inequality true, we set:

k < 2 or k >-6

So, the set of values of k is:

-6 < k < 2

3 0
3 years ago
9 9/25 in decimal form
Serhud [2]

Answer:

9.36

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
What is a multiple of 7 and is also a factor of 7
olga2289 [7]
28 is a multiple of 7 and also a factor of seven!
4 0
3 years ago
Rename 24 ten thousands
NemiM [27]
I'm not sure what you mean by rename
4 0
3 years ago
Is my answer and graph correct?
PIT_PIT [208]
Yes it is correct. You plotted the slope and initial rate value correctly and found the
point of intersection.



7 0
2 years ago
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