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

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n200080 [17]

Answer:

1) $m\angle x = 35^{\circ}$ , 2) $m\angle x = 60^{\circ}$ , 3) $m \angle x = 40^{\circ}$

Step-by-step explanation:

1) Triangle is a right triangle since tangent line is perpendicular to the radius of the circle. Based on the fact that the sum of internal angles in triangles equals 180°, we find the value of the angle $x$ :

$m\angle x = 180^{\circ} - 90^{\circ} - 55^{\circ}$

$m\angle x = 35^{\circ}$

2) Both triangles are symmetrical right triangles since tangent lines are perpendicular to the two radii and common side is parallel to the third radius. Based on the fact that the sum of internal angles in triangles equals 180°, we find the value of the angle $x$ :

$m \angle x = 180^{\circ} - 90^{\circ} - 30^{\circ}$

$m\angle x = 60^{\circ}$

3) The figure is formed by two symmetrical right triangles. These triangles are right-angled and symmetrical since tangent lines are perpendicular to the two radii and common side is parallel to the third radius. Based on the fact that the sum of internal angles in quadrilaterals equals 360°, we find the value of the angle $x$ :

$m\angle x = 360^{\circ} - 180^{\circ} - 140^{\circ}$

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3 years ago

A farmer sells 8.3 kg of apples and pears at the farmers market this way is apples and Restless Paris how many kilograms of Pari

Serga [27]

Answer:

She sell 2.075 kilograms of pears at the farmer's market.

Step-by-step explanation:

There is a mistake in the question some data is missing, so the correct question is below:

A farmer sells 8.3 kg of apples and pears at the farmer's market. 3 /4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?

Now, to find the kilograms of pears.

Total weight of apples and pears = 8.3 kg.

Weight of apples = $\frac{3}{4}$ of 8.3 kg.