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3 years ago

Isosceles trapezoid FGHJ has base angles that measure (8x+14) and (14x-15). Find x and the measure of each base angle.

Mathematics

1 answer:

lisov135 [29]3 years ago

7 0

Answer:

See below

Step-by-step explanation:

Remark

Base angles of Isosceles triangles are equal.

Equation

That means that 8x + 14 = 14x - 15

Solution

8x + 14 = 14x - 15 Add 15 to both sides

8x + 14+15 = 14x Combine

8x + 29 = 14x Subtract 8x from both sides

8x - 8x + 29 = 14x - 8x Combine

29 = 6x Divide by 6

x = 29/6

x = 4 5/6

Answer

x = 4 5/6 or 4.833

8x + 14 = 8 * (4 5/6) + 14

8x + 14 = 38 2/3 + 14

8x + 14 = 52 2/3 or 52.6666

14x - 15 = 14 *(4 5/6) - 15

14x - 15 = 67 2/3 -15

14x - 15 = 52 2/3 or 52.666

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Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m calculate the volume of the

sammy [17]

Answer:

1. The volume of the pile is 4,399.7719 m^3

2. The number of sanders to be filled from a pile is 638

Step-by-step explanation:

Here, we firstly would calculate the volume of the pile

Mathematically, that will be;

V = 1/3 * pi * r^2 * h

from the question, h = 14.2

Mathematically, r = d/2

r = 34.4/2 = 17.2 m

So the volume will be:

V = 1/3 * 3.142 * 17.2^2 * 14.2

V = 4,399.7719 m^3

To find the number of sanders to be filled,

we simply divide the volume obtained by the volume a sander can take

That will be;

4,399.7719/6.9

= 637.6 which is 638

4 0

3 years ago

Find the acute angle between the sides of a rhombus whose diagonals are 8cm and 12cm long

Sergeu [11.5K]

Answer:

67.38°

Step-by-step explanation:

The diagonals of a rhombus intersect at their midpoints and make a right angle. They also divide the angles of the rhombus in two equal angles.

So, to find the acute angle of the rhombus, we can use the tangent relation of half this angle in the small triangle made when drawing the diagonals:

tan(angle/2) = 4 / 6

tan(angle/2) = 0.666

angle/2 = 33.69

angle = 67.38°

So the acute angle of the rhombus is 67.38 degrees.

Please check the image attached for better comprehension.

4 0

3 years ago

Solve each equation (Polynomial equations)

lesya [120]

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8 0

4 years ago

Solve for g. 3/16 = (-5/4) + g

Ierofanga [76]

Answer:

g = 23/16

Step-by-step explanation:

3/16 = (-5/4) + g

Add 5/4 on both sides.

3/16 + 5/4 = g

Make denominators equal and add.

3/16 + 20/16 = g

23/16 = g

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3 years ago

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makvit [3.9K]

Answer:

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Step-by-step explanation:

3 0

3 years ago

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