A health food store makes trail mix using dried fruit and nuts. The cost of the dried fruit is $2.50 per

A rhombus ABCD has AB = 10 and m∠A = 60°. Find the lengths of the diagonals of ABCD.

melisa1 [442]

Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus

First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.

Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.

For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.

$\overline{OB}:\overline{AB} = 1:2$
$\overline {OB}:10 = 1:2$
$\overline{OB} = \frac{1}{2}(10) = 5$

Similarly, we have

$\overline{AO}:\overline{AB} = \sqrt{3}:2$
$\overline {AO}:10 = \sqrt{3}:2$
$\overline{AO} = \frac{\sqrt{3}}{2}(10) = 5\sqrt{3}$

Now, to find the lengths of the diagonals,

$\overline{AD} = 2(\overline{AO}) = 10\sqrt{3}$
$\overline{BC} = 2(\overline{OB}) = 10$

So, the lengths of the diagonals are 10 and 10√3.

Answer: 10 and 10√3 units

8 0

3 years ago

Select all of the names of this polygon

babunello [35]

Answer: i believe its rhombus rectangle quadrilateral

Step-by-step explanation:

4 0

2 years ago

1. Oceanside Bike Rental Shop charges 13 dollars plus 6 dollars an

umka21 [38]

It cost 3$ per hour

3 0

3 years ago

Find the area of the shaded region.

lbvjy [14]

Answer:

$48\pi\\\approx 150.796$

Step-by-step explanation:

1.Approach

To solve this problem, find the area of the larger circle, and the area of the smaller circle. Then subtract the area of the smaller circle from the larger circle to find the area of the shaded region.

2.Find the area of the larger circle

The formula to find the area of a circle is the following,

$A=(\pi)(r^2)$

Where (r) is the radius, the distance from the center of the circle to the circumference, the outer edge of the circle. ( $\pi$ ) represents the numerical constant (3.1415...). One is given that the radius of (8), substitute this into the formula and solve for the area,

$A_l=(\pi)(r^2)\\A_l=(\pi)(8^2)\\A_l=(\pi)(64)$

3.Find the area of the smaller circle

To find the area of the smaller circle, one must use a very similar technique. One is given the diameter, the distance from one end to the opposite end of a circle. Divide this by two to find the radius of the circle.

8 ÷2 = 4

Radius = 4

Substitute into the formula,

$A_s=(\pi)(r^2)\\A_s=(\pi)(4^2)\\A_s=(\pi)(16)$

4.Find the area of the shaded region

Subtract the area of the smaller circle from the area of the larger circle.

$A_l-A_s\\=64\pi - 16\pi\\=48\pi$

$\approx150.796$

5 0

2 years ago

nk, Inc. has 40,000 shares of stock outstanding. The company declares dividends of $120,000. What is the dividend per share of s

Angelina_Jolie [31]

To find the he dividend per share of stock,we can divide the dividends by the total amount of
share:

120000÷40000
=$3

If Tim Worker owns 45 shares of stock, his share of the declared dividends would be:

3×45
=$135

Hope it helps!

5 0

3 years ago