All categories

3 years ago

The figure is a parallelogram. Solve for x.

Mathematics

1 answer:

lions [1.4K]3 years ago

4 0

Answer:

x = 7

Step-by-step explanation:

Adjacent angles of a parallelogram are supplementary.

$\therefore \: (14x + 2) \degree + 80 \degree = 180 \degree \\ \\ \therefore \: (14x + 2) \degree = 180 \degree - 80 \degree \\ \\ \therefore \: (14x + 2) \degree = 100 \degree \\ \\ 14x + 2 = 100 \\ 14x = 100 - 2 \\ \\ 14x = 98 \\ \\ x = \frac{98}{14} \\ \\ x = 7$

You might be interested in

Joe read 140 pages of his 300 page book what percent of his book has he read

kaheart [24]

Answer:

Step-by-step explanation:

8 0

3 years ago

Write 0.000673 in scientific notation

WINSTONCH [101]

Answer:

6.17

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Suppose you have an equal sided spinner that is numbered 1 thru 5 and another spinner with 4 equal sections with the colors red,

DanielleElmas [232]

Answer:6

778

Step-by-step explanation:

hh8yyyyyyyyyyyyyy

8 0

3 years ago

Read 2 more answers

Keith works 8 hours per day for 5 per week. melba works 2,250 minutes each week. who spends more time at work

Orlov [11]

Answer:

Keith does.

Step-by-step explanation:

2250/60=37.5

8*5=40

Keith spends 40 hrs at work Melba spends 37.5 hrs.

6 0

4 years ago

The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.

MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle = $3\times\ side$

$3\times\ side$ $=[tex]81\sqrt{3}$

$Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm$

Thus from the diagram , Side $AB=BC=AC= 27\sqrt{3} \ cm$

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus $\angle OBC = 30$ °

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

$tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2} } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\$

Thus ,apothem OE= 13.5 cm

Now for radius,

We consider ΔOBE

$cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB} \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm$

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

4 0

3 years ago