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3 years ago

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Whats it asking and how to solve it

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kotegsom [21]3 years ago

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Whats the value of x and y

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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

Write a few sentences summarizing how to solve word problems that involve square roots

Snowcat [4.5K]

Answer:

Square both sides of the equation given in order to remove the square root.

8 0

3 years ago

Assuming that Samir is equally likely to hit each of the 10 targets, what is the probability that he will miss at least one of t

hammer [34]

Answer:40%

Step-by-step explanation:

7 0

3 years ago

Also this question tooo pleease, PS: what topic is this <br> Solve for x.

MrRissso [65]

This falls under geometry. The two labeled angles are congruent, which means the line segment between them (AD in the image) is a bisector of the angle at vertex A. Use the angle bisector theorem, which says that

$\dfrac{BD}{DC}=\dfrac{AB}{AC}\iff\dfrac{12}{(5+9x)-12}=\dfrac{15}{25}$

$\dfrac{12}{9x-7}=\dfrac35$

$20=9x-7$

$x=3$

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3 years ago

Louisa needs 3 liters of lemonade and punch for a picnic she has 1800 milliliters of lemonade. How much punch does she need expl

8090 [49]

There are 1000 millimetres in a litre, so 1800 ml is 1.8 litres. 3-1.8 is 1.2.

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3 years ago

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