All categories

3 years ago

If ABCD is a parallelogram, mZA = x° and mZD = (2x - 3)º, find the value of 'x'.

Mathematics

1 answer:

patriot [66]3 years ago

6 0

Answer:

x = 61

Step-by-step explanation:

Angles A and D are consecutive interior angles of a parallelogram.

Consecutive interior angles of a parallelogram are supplementary.

m<A + m<D = 180

x + 2x - 3 = 180

3x - 3 = 180

3x = 183

x = 61

You might be interested in

Of the 465 sophomores at eastside high school, exactly 13 are taking french ii or chemistry i or both. there are 40 sophomores t

gizmo_the_mogwai [7]

352 I think hope this helps

8 0

3 years ago

Read 2 more answers

A board measures 19.5 meters in length is cut into two pieces. One piece measures 7.2 meters. Write and solve an equation to fin

Naddik [55]

Answer:

7.2+x=19.5

x=19.5-7.2

x=12.2

Step-by-step explanation:

4 0

3 years ago

The expression 3280(1.0117)^12t models the future population of wolves in a park after T years.

Dvinal [7]

The answer is c I think I hope you get it right

7 0

3 years ago

Read 2 more answers

find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long. round your answer to the nearest te

irakobra [83]

The answer is 374.4 yards.

There are 2 ways to calculate the area of a a regular hexagon.
It is given:
apothem: b = 10.4 yards
side: a = 12 yards

1. The direct way is to use the formula for the regular hexagon without using an apothem:
 $A= \frac{3 \sqrt{3} }{2} a^{2}$
where
A - the area of the hexagon
a - the side of the hexagon

Therefore:
 $A= \frac{3 \sqrt{3} }{2} 12^{2}$
 $A= \frac{3 \sqrt{3} }{2} 144$
 $A= 374.4$

2. The indirect way is to sketch the hexagon with 3 diagonals and create 6 triangles. Then, it is necessary to calculate the area of one triangle and multiply it by 6. In this triangle, apothem is actually the height.
The area of the hexagon is:
A = 6 · A₁
where:
A - the area of the hexagon,
A₁ - the area of the triangle

$A_{1}= \frac{a*h}{2}$

where
h - height of the triangle.


Since apothem (b) of the hexagon is the height (h) of the triangle, then:
$A_{1}= \frac{a*h}{2}$
 $A_{1}= \frac{12*10.4}{2}$
 $A_{1}= 62.4$

Thus, the area of one triangle is 62.4 yards.

To calculate the area of the hexagon, we will multiply it by 6:
A = 6 · A₁
A = 6 · 62.4
A = 374.4 yards

In both cases, the result is 374.4 yards.The answer is

5 0

3 years ago

What is the 30th term of the arithmetic series 4, 7, 10, … ?

Irina18 [472]

$a_1=4;\ a_2=7;\ a_3=10\\\\d=a_2-a_1\to d=7-4=3\\\\a_n=a_1+(n-1)d\to a_n=4+(n-1)\cdot3=4+3n-3=3n+1\\\\\boxed{a_n=3n+1}\\\\a_{30}=3\cdot30+1=90+1=91\\\\Answer:\boxed{a_{30}=91}$

3 0

3 years ago

Read 2 more answers