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3 years ago

15

Which expression is equivalent to the fraction below?

1 answer:

iragen [17]3 years ago

6 0

5/8=expression is equivalent to

5 8

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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

2 years ago

Find the area of the composite figure. <br><br>A=36cm<br><br>A=40cm<br><br>A=48cm<br><br>A=64cm

MissTica

Check the picture below.

so the shape is really 4 triangles with a base of 2 and a height of 4 each, and 2 squares tha are 4x4.

$\bf \stackrel{\textit{area of the 4 triangles}}{4\left[\cfrac{1}{2}(2)(4) \right]}~~+~~\stackrel{\textit{area of the two squares}}{2(4\cdot 4)}\implies 16+32\implies 48$

8 0

2 years ago

Answer these four questions. Giving BRAINLIEST.

Alina [70]

Answer:

24

Step-by-step explanation:

because i said so

5 0

2 years ago

What is the measure of the secant AB

cricket20 [7]

A secant is a line that intersects a circle in exactly two points. When a tangent and a secant, two secants, or two tangents intersect outside a circle than the measure of the angle is formed is one-half the positive difference of the measures of the intercepted arcs.

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2 years ago

1,200 students chose meat lasagna and 400 chose vegetable and spinach lasagna, what percent of students chose vegetable and spin

gladu [14]

400/1600 =25%

Explanation:

Total=1,200+400=1,600

5 0

3 years ago

Read 2 more answers