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kirill115 [55]
2 years ago
15

Solve for x. LMN ~ LEF

Mathematics
1 answer:
shutvik [7]2 years ago
8 0

Answer:

  x = 9

Step-by-step explanation:

Corresponding sides of similar triangles are proportional.

  FL/NL = EL/ML

  (2x -5)/78 = 12/72 . . . . . . fill in given values

  2x -5 = 78(12/72) = 13 . . . multiply by 78

  2x = 18 . . . . add 5

  x = 9 . . . . . . divide by 2

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Can u guys help me please
stich3 [128]

Step-by-step explanation:

zidufhehkcsyjodbjd r

7 0
2 years ago
The line y = hx - 2 where h > 0 meets the curve 3y² = 9x² - 6x + 1.
I am Lyosha [343]

Answer:

h=6

Step-by-step explanation:

since y =hx -2 is an equation for a line which intersects with the curve 3y^2 = 9x^2 - 6x +1. The point of intersection, let's say (x_1,y_1), should satisfy the two equations. As a result, the value of y in the second equation can be replaced with the value of y in the first equation as the following,

3y^2 = 3(hx-2)^2 = 9x^2 - 6x +1\\3(h^2x^2 -4hx + 4) = 9x^2 - 6x + 1\\3h^2 x^2 -12hx +12 = 9x^2 - 6x +1

therefore, the latter equation can be rewritten in a quadratic equation form as the following,

(9 - 3h^2) x^2 + (12h-6)x + (1-12) = (9 - 3h^2) x^2 + (12h-6)x -11 = 0

if the line is tangent to the curve, it means that the line touches the curve at one point, therefore the discernment of the second order equation will be equal to zero for the famous quadratic equation solution.

b^2 -4ac =0

where a=9-3h^2, b=12h-6 and c=-11, as a result, the following equations can be deduced,

(12h-6)^2 - 4*(9-3h^2)*(-11) = (144h^2 -144h +36) - (36 -12h^2)*(-11)=\\(144-(-12)*(-11)h^2 )  -144h +36 -(36*(-11)) =\\12 h^2 -144h +432 =0

therefore, dividing both sides by 12

h^2 -12 +36 =0\\(h-6)^2 =0\\h=6

8 0
2 years ago
I need help pls! A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they
statuscvo [17]

Answer:

Look down below ;)

Step-by-step explanation:

How far is the campsite from their car?

4 miles

(0,4)

Write an equation that describes the relationship between d and h.

d = 3h + 4

After how many hours will the hikers be 16 miles from their car?

16 = 3h + 4

12 = 3h

4 = h

After 4 hours

5 0
3 years ago
Helppp!!!!
-Dominant- [34]

Answer:

30

Step-by-step explanation:

Let's say x is the number of friends he has

4 · x = 121 - 1

4x = 120

Divide by 4 on each side

x = 30

7 0
3 years ago
Identify the equation of the circle that has its center at (9, 12) and passes through the origin.
katrin [286]

The circle has center at (9, 12) and passes through the origin.

Equation of the circle in center and radius form is given by

(x-h)^2+(y-k)^2=r^2

where r is the radius and center at (h,k)

Now substitute the value of the center we get

(x-9)^2+(y-12)^2=r^2

As it passes through the origin so we can write

(0-9)^2+(0-12)^2=r^2\\ \\ 81+144=r^2\\ \\ 225=r^2\\ \\ r=15\\

Hence the equation of the circle is

(x-9)^2+(y-12)^2=15^2

4 0
2 years ago
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