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Gre4nikov [31]
3 years ago
10

The line y = 2x – 3 touches the curve y = x^2 + kx + 6. Find the possible values of k.

Mathematics
1 answer:
Ugo [173]3 years ago
8 0

The value of "k" will be a value greater than 4 or less than -8

If the line y = 2x – 3 touches the curve y = x^2 + kx + 6, this means that both equations will be equal as shown:

2x - 3 = x^2 + kx + 6

Rewrite in the form ax^2+bx+c=0

2x - 3 = x^2 + kx + 6\\x^2+kx-2x+6+3 =0\\x^2+(k-2)x+9=0\\

The roots has a distinct solution if b² - 4ac > 0

From the equation

a = 1

b = k-2

c = 9

Substitute into the formula:

(k-2)^2-4(1)(9) > 0\\k^2-4k+4-36>0\\k^2-4k-32>0

Factorize

k^2+8k-4k-32 >0\\k(k+8)-4(k+8)>0\\(k-4)(k+8)>0\\k>4 and k>-8

Hence the value of "k" will be value greater than 4 or less than -8

Learn more here: brainly.com/question/24896483

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A backyard pool has a concrete walkway around it that is 3 feet wide on all sides. The total area of the pool and the walkway is
Sloan [31]

Answer:

x \approx 21.080\,ft, y = 29.080\,ft

Step-by-step explanation:

The total area of the pool and the walkway is:

(x + 6\,ft)\cdot (y + 6\,ft) = 950\,ft^{2}

(x + 6\,ft)\cdot (x + 14\,ft) = 950\,ft^{2}

x^{2} + 20\cdot x + 84\,ft^{2} = 950\,ft^{2}

x^{2} + 20\cdot x - 866\,ft^{2} = 0

The roots of the second-order polynomial is:

x_{1} \approx 21.080\,ft and x_{2} \approx -41.081\,ft

The only possible root is:

x \approx 21.080\,ft

The other dimension of the pool is:

y = x + 8\,ft

y = 21.080\,ft + 8\,ft

y = 29.080\,ft

3 0
4 years ago
Rewrite 10 + 12 using the GCF and factoring.
Airida [17]

Answer:

1st option

Step-by-step explanation:

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= 2(5 + 6)

5 0
2 years ago
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Lynn paid $12.21 for ribbon. The cost per yard was $1.48.
just olya [345]

Answer:

D

Step-by-step explanation:

All we need to do is divide the values we are given.

12.21 / 1.48 = 8.25

Best of Luck!

7 0
3 years ago
Read 2 more answers
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Answer:

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Step-by-step explanation:

7 0
3 years ago
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