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Slav-nsk [51]
2 years ago
11

In the following diagram \overline{DE} \parallel \overline{FG}

Mathematics
1 answer:
Gnesinka [82]2 years ago
7 0

Answer:

<x = 31°

Step-by-step explanation:

m<BCA = m<GCJ (vertical angles)

m<BCA = 59° (substitution)

Since line KL is perpendicular to line FG, the angle formed at point B is 90°.

Therefore, m<ABC = 90°

m<BAC + m<ABC + m<BCA = 180° (sum of triangle)

m<BAC + 90° + 59° = 180° (Substitution)

m<BAC + 149° = 180°

m<BAC = 180° - 149°

m<BAC = 31°

<x = <BAC (vertical angles)

m<x = 31° (substitution)

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The base of a solid right pyramid is a regular hexagon with
cupoosta [38]

Answer: Last option.

Step-by-step explanation:

Observe the base of the pyramid, which is a regular hexagon. You can see that there is a right triangle.

The area of the triangle can be calculated with this formula:

A_t=\frac{bh}{2}

Where "b" is the base and "h" is the height.

You can say that the apothem is the height of the right triangle, then, you need to find the base applying the Pythagorean Theorem:

(2x)^2=(x\sqrt{3})^2+b^2\\\\b=\sqrt{(2x)^2-(x\sqrt{3})^2} \\\\b=\sqrt{4x^2-3x^2}\\\\b=\sqrt{x^2}\\\\b=x

Then, the area of the triangle is:

 A_t=\frac{x(x\sqrt{3})}{2}=\frac{x^2\sqrt{3})}{2}

Since the base of the pyramid is a regular hexagon, then you can multiply by 12 the area of the right triangle calculated above, in order to find the area of the hexagon. Then you get:

A_h=12(\frac{x^2\sqrt{3})}{2})=6x^2\sqrt{3}\ units^2

5 0
2 years ago
Read 2 more answers
A rectangular table is positioned in a 10-foot by 10-foot room as shown.
makkiz [27]

Answer:

40 and 20

Step-by-step explanation:

3 0
2 years ago
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If sin theta = sqrt(2/2), which could not be the value of theta?
Nataliya [291]

The solution would be like this for this specific problem:

sin(θ°) = √(2)/2 

θ° = 360°n + sin⁻¹(√(2)/2) and θ° = 360°n + 180° − sin⁻¹(√(2)/2)
θ° = 360°n + 45° and θ° = 360°n + 135° where n∈ℤ 

360°*0 + 45° = 45° 
360°*0 + 135° = 135° 
360°*1 + 45° = 405° 

<span>sin(225°) = -√(2)/2

</span>225 has an angle where sin theta= -(sqrt2)/2 therefore, the value of theta cannot be 225 degrees.

4 0
2 years ago
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A rectangular board is 1.6 meters long and 1.2 meters wide. What is the area of the board in square millimeters? Do not round yo
Arisa [49]
<h2>Area of rectangular board is 1920000 square millimeters</h2>

Step-by-step explanation:

A rectangular board is 1.6 meters long and 1.2 meters wide.

Here we need to find the area of the board in square millimeters.

Length = 1.6 m= 1.6 x 1000 = 1600 mm

Width = 1.2 m= 1.2 x 1000 = 1200 mm

Area = Length x Width

Area = 1600 x 1200

Area = 1920000 square millimeters

Area of rectangular board is 1920000 square millimeters

6 0
2 years ago
The store sells a 9 ounce jar of mustard for $1.53 and a 15 ounce for $2.55 explain whether the cost of the mustards have the sa
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Answer:

same amount of money

Step-by-step explanation:

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