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2 years ago

1. ΔEFG ~ ΔLMN. Find LN.

Mathematics

1 answer:

Dafna11 [192]2 years ago

5 0

Part 1:

Given that triangle EFG is similar to triangle LMN, this means that the ratio of the measures of any two sides of triangle EFG is equal to the ratio of the measures of the corresponding sides of triangle LMN.

From the figure shown

FG / EG = MN / LN
⇒ 4 / 7 = 2 / LN
⇒ LN = 7 * 2 / 4 = 14 / 4 = 3.5

Therefore, LN = 3.5

Part 2:

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Thus, if m∠A = m∠D. The other fact that would guarantee that the triangles are similar is that m∠C = m∠F.

This is because if m∠A = m∠D and m∠C = m∠F, then m∠B = m∠E and thus satisfies the triangle similarity condition.

Part 3:

Given that the two triangles shown are congruent, one way to verify that the corresponding angles of the two triangles are congruent is to place one of the triangle on top of the other to see if the corresponding angles of both triangles coincide.

This can be achieved by translating triangle 2 up by 2 units, and to the left by 6 units.

Part 4:

Given that trapezoid ABCD and trapezoid JKLM are similar.

From the naming of the trapezoids, the order of the naming of any similar object corresponds to the order of their similarity.

Thus, side AB corresponds to side JK, side AC corresponds to side JL and so on.

Therefore, the side that corresponds to side AB is side JK.

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2 years ago

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Find the distance from (4, −7, 6) to each of the following.

LenKa [72]

Answer:

(a) 6 units

(b) 4 units

(d) 9.22 units

(e) 7.21 units

(f) 8.06 units

Step-by-step explanation:

The distance d from one point (x₁, y₁, z₁) to another point (x₂, y₂, z₂) is given by;

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Now from the question;

(a) The distance from (4, -7, 6) to the xy-plane

The xy-plane is the point where z is 0. i.e

xy-plane = (4, -7, 0).

Therefore, the distance d is from (4, -7, 6) to (4, -7, 0)

d = √[(4 - 4)² + (-7 - (-7))² + (0 - 6)²]

d = √[(0)² + (0)² + (-6)²]

d = √(-6)²

d = √36

d = 6

Hence, the distance to the xy plane is 6 units

(b) The distance from (4, -7, 6) to the yz-plane

The yz-plane is the point where x is 0. i.e

yz-plane = (0, -7, 6).

Therefore, the distance d is from (4, -7, 6) to (0, -7, 6)

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 6)²]

d = √[(4)² + (0)² + (0)²]

d = √(4)²

d = √16

d = 4

Hence, the distance to the yz plane is 4 units

(c) The distance from (4, -7, 6) to the xz-plane

The xz-plane is the point where y is 0. i.e

xz-plane = (4, 0, 6).

Therefore, the distance d is from (4, -7, 6) to (4, 0, 6)

d = √[(4 - 4)² + (-7 - 0)² + (6 - 6)²]

d = √[(0)² + (-7)² + (0)²]

d = √[(-7)²]

d = √49

d = 7

Hence, the distance to the xz plane is 7 units

(d) The distance from (4, -7, 6) to the x axis

The x axis is the point where y and z are 0. i.e

x-axis = (4, 0, 0).

Therefore, the distance d is from (4, -7, 6) to (4, 0, 0)

d = √[(4 - 4)² + (-7 - 0)² + (6 - 0)²]

d = √[(0)² + (-7)² + (6)²]

d = √[(-7)² + (6)²]

d = √[(49 + 36)]

d = √(85)

d = 9.22

Hence, the distance to the x axis is 9.22 units

(e) The distance from (4, -7, 6) to the y axis

The x axis is the point where x and z are 0. i.e

y-axis = (0, -7, 0).

Therefore, the distance d is from (4, -7, 6) to (0, -7, 0)

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 0)²]

d = √[(4)² + (0)² + (6)²]

d = √[(4)² + (6)²]

d = √[(16 + 36)]

d = √(52)

d = 7.22

Hence, the distance to the y axis is 7.21 units

(f) The distance from (4, -7, 6) to the z axis

The z axis is the point where x and y are 0. i.e

z-axis = (0, 0, 6).

Therefore, the distance d is from (4, -7, 6) to (0, 0 6)

d = √[(4 - 0)² + (-7 - (0))² + (6 - 6)²]

d = √[(4)² + (-7)² + (0)²]

d = √[(4)² + (-7)²]

d = √[(16 + 49)]

d = √(65)

d = 8.06

Hence, the distance to the z axis is 8.06 units

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The price per night for a hotel room is different at three different hotels.

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I think you meant it to be not repeating 3 times so
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Then it’s 300/5 which is 60
455/7. So first see, if I multiply 7 by 60 is it over or under. If it’s over then B is the least and if it is less then C is the least. So 7 *60 is 420
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2 years ago

point M with coordinates (3,4) is the midpoint of the line AB and A has the point (-1,6). what is the point of B?

irina [24]

Answer:

B = (7, 2)

Step-by-step explanation:

B = 2M -A

B = 2(3, 4) -(-1, 6) = (2·3-(-1), 2·4-6)

B = (7, 2)

_____

The expression for the other end point, B, comes from the equation for the midpoint.

M = (A +B)/2

2M = A + B . . . . . multiply by 2

2M -A = B . . . . . . subtract A to get an expression for B

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2 years ago

How is the graph of y = negative RootIndex 3 StartRoot x minus 4 EndRoot transformed to produce the graph of y = negative RootIn

SVEN [57.7K]

Answer:

Multiply by ∛2 and translate the graph to left by 4 units.

Step-by-step explanation:

The initial function given is:

y = -∛(x - 4)

The transformed function is:

y = -∛(2x - 4)

Consider the initial function.

y = -∛(x - 4)

(Represented by Black line in the graph)

Multiply the function by ∛2. The function becomes:

y = -∛(x - 4) × ∛2

y = -∛(2)(x-4)

y = -∛(2x-8)

(Represented by Red line in the graph represents this function)

Translate the graph 4 units to the left by adding 4 to the x component:

y = -∛(2x-8+4)

y= -∛(2x - 4)

(Represented by Blue line in the graph)

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2 years ago

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