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2 years ago

8

Express 5 as a fraction. A) 1/5 B) 30/6 C) 42/6 D) 5/5

2 answers:

nataly862011 [7]2 years ago

8 0

The answer is B

Explanation:

30 divided by 6 is 5
5 times 6 is 30

Fiesta28 [93]2 years ago

3 0

Answer:

B) 30/6

Step-by-step explanation: 30 divided by 6 is 5 :)

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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:

$-6 < k < 2$

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2 years ago

N + 9 >_ 13 (with the “_” under the “>”

Step2247 [10]

Answer:

n >_ 4

Step-by-step explanation:

move 9 to the other side

n >_ 13 - 9

n >_ 4

8 0

3 years ago

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Mademuasel [1]

Answer:

a + c = 80

a = 2c - 8

Step-by-step explanation:

Topic: Algebra

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2 years ago

Find two consecutive integers whose sum is 123

Helen [10]

I believe it is 61 and 62 I'm not 100% positive tho

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3 years ago

Give the equation of the horizontal asymptote shown below.

Oxana [17]

Polynomial division yields

$\dfrac{7x^2}{x^2+5}=7-\dfrac{35}{x^2+5}$

As $x\to\pm\infty$ , you have the remainder term approaching $0$ , so the horizontal asymptote is the line $y=7$ .

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3 years ago

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