1. Check the drawing of the rhombus ABCD in the picture attached.
2. m(CDA)=60°, and AC and BD be the diagonals and let their intersection point be O.
3. The diagonals:
i) bisect the angles so m(ODC)=60°/2=30°
ii) are perpendicular to each other, so m(DOC)=90°
4. In a right triangle, the length of the side opposite to the 30° angle is half of the hypothenuse, so OC=3 in.
5. By the pythagorean theorem,

6. The 4 triangles formed by the diagonal are congruent, so the area of the rhombus ABCD = 4 Area (triangle DOC)=4*

=

(

)
Hello,
I suppose equations are:
x+y=3 (1)
x+2y=9 (2)
(2)-(1)==>y=6
(1)==>x=3-6
x=-3, y=6
Sol={(-3,6)}
Answer:
30 mph
Step-by-step explanation:
Let d = distance (in miles)
Let t = time (in hours)
Let v = average speed driving <u>to</u> the airport (in mph)
⇒ v + 15 = average speed driving <u>from</u> the airport (in mph)
Using: distance = speed x time

Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:

We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:

Now all we have to do is solve the equation for v:







As v is positive, v = 30 only
So the average speed driving to the airport was 30 mph
(and the average speed driving from the airport was 45 mph)
Answer:

Step-by-step explanation:
Given
-- total
--- defective
--- selected
Required
The probability of rejecting the batch
This means that at least one of the selected piece is defected.
So, we first calculate the probability that all the selected piece are accepted.
So, we have:

The denominator decreases by 1 because it is a probability without replacement; 180 is subtracted from the numerator to represent the number of non-defective CDs
So, we have:


Using the complement rule, the probability that the batch will be rejected is:

