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If the equation y² - (K-<br>2y + 2k +1 = 0<br>with equal roots find the value of k

777dan777 [17]

Answer:

y² - (K- 2)y + 2k +1 = 0

equal roots means D=0

D= b^2 - 4ac

a=1, b= (k-2), c= 2k+1

so,

(k-2)^2 - 4(1)(2k+1) = 0

=> k^2 +4 - 8k -4 = 0

=> k^2 -8k = 0

=> k^2 = 8k

=> k= 8k/k

=> k = 8

Therefore the answer is k= 8

Hope it helps........

8 0

2 years ago

If a system of linear equations has no solution, what do you know about the slopes and y-intercepts of the graphs of the equatio

Nata [24]

Answer:

B. The slopes of the graphs are the same and the y-intercepts of the graphs are different

Step-by-step explanation:

The lines will also be parallel

7 0

2 years ago

How many feet tall is the building

Fantom [35]

Answer:

Height of the building = 77 ft.

Step-by-step explanation:

Let the height of the building (AB) = h feet

It's given that height of a woman (ED) = 5 feet 3 inches

≈ 5 feet + $\frac{3}{12}$ ft

≈ 5.25 ft

Length of the shadow (BC) of the building = 55 ft

Length of the shadow (DC) of the woman = 45 in ≈ 3.75 ft

Since, both the triangles ABC and EDC are similar, their corresponding sides will be proportional.

By the property of similar triangles,

$\frac{AB}{ED}= \frac{BC}{DC}$

$\frac{h}{5.25}=\frac{55}{3.75}$

h = $\frac{55\times 5.25}{3.75}$

h = 77 ft

Therefore, height of the building will be 77 ft.

6 0

2 years ago

Let us have four distinct collinear points $a,$ $b,$ $c,$ and $d$ on the cartesian plane. the point $c$ is such that $\dfrac{ab}

Deffense [45]

Start with a line segment connecting two points, A and B. $\dfrac{DA}{BA}=3$ means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with $\dfrac{DB}{BA}=2$ , or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, $\dfrac{AB}{CB}=\dfrac12$ , so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let $d$ be the length of AB. Then the length of CD in terms of $d$ is $4d$ . We have the coordinates of C and D, and the distance between them is $\sqrt{(4-0)^2+(0-4)^2}=4\sqrt2$ . So

$4d=4\sqrt2\implies d=\sqrt2$

The slope of the line through C and D is

$\dfrac{0-4}{4-0}=-1$

and so the equation of the line through these points is

$y-4=-(x-0)\implies x+y=4$

So the coordinates of A are $(x,y)=(x,4-x)$ . The distance between C and A is $d=\sqrt2$ , so we have

$\sqrt{(x-0)^2+(4-x-4)^2}=\sqrt{2x^2}=|x|\sqrt2=\sqrt2\implies|x|=1$

Since A falls to the right of C (in the $x,y$ plane, not just in the sketch), we know to take the positive value $x=1$ . Then the $y$ coordinate is $y=4-1=3$ .