All categories

3 years ago

Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589.

1 answer:

4 0

Given:

segment AU = 20x + 108,
UB = 273,
BC = 703,
UV = 444,
AV = 372 and
AC = 589.

Point U lies on AB and V lies on AC.

UV is perpendicular to AC.

Therefore, the similar triangles are AUV and ABC

So the similarity is: segment AU / segment UV = segment AB / segment BC

20x + 108 20X + 381
--------- = ---------------
372 589

(20x + 108)* 589 = (20X + 381)*372

11780 X + 63612 = 7440X + 141732

4340 X - 78120 = 0

4340 X = 78120

X = 78120/4340 = 18


Answer: x = 18

To check:

AU = 20*18 + 108 = 360 + 108 = 468

AB = 741

468/372 = 741/589

Which the two are equal ratios

You might be interested in

Help please I need to answer this question

djverab [1.8K]

Answer:

Step-by-step explanation:

first find the perimeter of both triangles

Original perimeter: 72 in

scaled perimeter: 24 in

A is wrong since the scaled perimeter is actually smaller.

B is wrong because its not 6 times smaller

C is wrong since it's not 1/9 of the original

D is correct since the scaled is a 1/3 of the original perimeter (72*1/3 = 24)

6 0

3 years ago

A wildlife service wanted to estimate the number of alligators in a river so they tagged 90 alligators and released them back in

lilavasa [31]

You can solve this with a proportion. If you know that 23 tagged alligators were in a 200 alligator sample, there are 90 tagged alligators in the entire river. Written otherwise:

23/200 = 90/x

and solve for x:

x = 782.608...

So the "best estimate" would be around 783 alligators. Hope that helps! If you liked this answer please rate it as brainliest!! thank you!!!

5 0

3 years ago

Find the vertex: -4x² + 16x - 7

guapka [62]

Find the vertex: -4x^2 + 16x - 7

Vertex = ( x, f(x)).

x = -b/2a

x = -16/2(-4)

x = -16/-8

x = 2

f(x) = -4x^2 + 16x - 7

Let x = 2

f(2) = -4(2)^2 + 16(2) - 7

f(2) = -4(4) + 32 - 7

f(2) = -16 + 32 - 7

f(2) = 16 - 7

f(2) = 9

Vertex = (2, 9)

7 0

3 years ago

Which expression is equivalent to the expression 1/4 (x- 2) + 1/3x HELP

Law Incorporation [45]

The answer is 7x/12 - 1/2. Its the first option in your picture. Hope this helps .

3 0

2 years ago

M is the centroid (center of gravity) of △ABC, line k goes thru M and intersects AB and AC . The distances of the vertices B and

lana [24]

Answer:

Step-by-step explanation:

The midpoint of BC will be a distance from line k that is the average of the distances of B and C: (17+13)/2 = 15. Call that midpoint P. We know distance MP is half of distance MA. This same relationship will hold with respect to the distances from P and A to any line through M. That is, the distance from line k (through M) is twice the distance from P to line k: 30 units.

5 0

3 years ago