Answer:
(-6, -3)
Step-by-step explanation:
The coordinate is at (2, -1), when using a dilation with a scale factor of 3, multiply the coordinates by 3.
(2, -1) ------> (2 x 3, -1 x 3) ----------> (6, -3)
When reflecting the point over the y-axis, take the opposite of the x coordinate.
(6, -3) ------> (-6, -3)
To solve this problem, let us recall that the formula for
probability is:
Probability = total number of successful events / total
events
Where in this case, an event is considered to be successful
if the sum is 3 on the pair of six sided dice.
First, let us calculate for the total number of events. There
are 6 numbers per dice, therefore the total number of combinations is:
total events = 6 * 6 = 36
Next, we calculate for the total number of combinations
that result in a sum of 3. We can identify that there are only two cases that
result in sum of 3. That is:
1st case: first dice rolls 1, second dice
rolls 2
2nd case: first dice rolls 2, second dice
rolls 1
Hence, total number of successful events = 2. Therefore the
probability is:
Probability = 2 / 36 = 1 / 18 = 0.0556 = 5.56%
Answer:
Step-by-step explanation:
We are asked to represent 
as the product of the GCF and another sum.
First of all, we will find the greatest common factor of 18 and 24.
Factors of 18: 1, 2, 3, 6, 9, 18.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
We can see that greatest common factor of 18 and 24 is 6. Let us write our given expression as product.
Factor our 6:
Therefore, our required expression would be .
There are 7000 ones in 7 thousands
Answer:
x = 60
Step-by-step explanation:
Vertical opposite angles are formed when two straight lines intersect each other.
Given that AD and CD are two straight lines intersecting at O, the two vertical opposite formed are, ∠AOD and ∠COB. Therefore:
∠AOD = ∠COB (Vertical opposite angles are congruent)
∠AOE = 90° (right angle)
∠DOE = x
∠COF = 30°
∠BOF = 2x
m∠AOE + m∠DOE = m∠AOD (angle addition postulate)
90 + x = ∠AOD (Substitution)
m∠COF + m∠BOF = m∠COB (Angle addition postulate)
30 + 2x = ∠COB
m∠AOD = m∠COB (vertical opposite angles)
90 + x = 30 + 2x (Substitution)
Collect like terms
90 - 30 = 2x - x
60 = x
x = 60
