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s344n2d4d5 [400]

2 years ago

14

Hep help help help hell

1 answer:

Taya2010 [7]2 years ago

6 0

Answer:

$\frac{2x + 4}{2} < 6 \\ 2x + 4 < 2 \times 6 \\ 2x + 4 < 12 \\ 2x < 12 - 4 \\ 2x < 8 \\ x < \frac{8}{2} \\ \color{blue} \boxed{x < 4}$

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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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3 years ago

When you convert 100ft per second to inches per second will there be more or less than 100 inches

Firlakuza [10]

It would be more than 100 inches because in one foot is 12 inches, so take 100 x 12 = 1200 inches

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4 years ago

John runs a computer software store. Yesterday he counted 127 people who walked by his store, 58 of whom came into the store. Of

Delicious77 [7]

The answer is 3/4. All you need to do is make proportion and simplify! Hope it helps!

3 0

3 years ago

|-5| |-9| <br> is it greater, less than, or equal to<br> <, >, = ??!?!

Katyanochek1 [597]

Answer:

< (less than)

Step-by-step explanation:

since abs value changes it to positive it would be

5 and 9

5 < 9

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3 years ago

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What does x equal ?<br> quick answer!!!

Anna35 [415]

136 should be your answer

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3 years ago