Answer:
Step-by-step explanation:
To prove Δ ABC similar to ΔDBE we can consider
Segments AC and DE are parallel.
⇒ DE intersects AB and BC in same ratio.
AB is a transversal line passing AC and DE.
⇒∠BAC=∠BDE [corresponding angles]
Angle B is congruent to itself due to the reflexive property.
All of them are telling a relation of parts of ΔABC to ΔDBE.
The only option which is not used to prove that ΔABC is similar to ΔDBE is the first option ,"The sum of angles A and B are supplementary to angle C".
Hello!
The problem has asked that we write a
point-slope
equation of the line in the image above.
Point-Slope Form uses the following formula:
y –

= m(x –

)
In this case, M represents the
slope while

and

represent the
corresponding X and Y values of any given point on the line.
We are given that the slope of the line is -

. We also know that any given point on a graph takes the form (x,y). Based on the single point provided in the image above, we can determine that

is equal to
6 and

is equal to
2. Now insert all known values into the point-slope formula above:
y – 2 = -

(x – 6)
We have now successfully created an equation based on the information given in the problem above. Looking at the four possible options, we can now come to the conclusion that
the answer is C.
I hope this helps!
Answer: The answer is F.
Step-by-step explanation:
1.) The first equation represents how the spiral notebook has 30 more pages than the the memo book, and how subtracting the memo book's pages would result with 30.
2.) The second equation represents how the total number of pages in 3 spiral notebooks plus 5 memo books would result in 810 total pages.
Answer:
a) S = {1, 2, 3}
b) P(odd number) = 
c) No
d) Yes
Step-by-step explanation:
a) The sample space is the set of all possible outcomes. By definition, the elements of a set should not be repeated. Hence, the sample space S = {1, 2, 3}
However, the sample is not equiprobable because each element has different probabilities.
b) P(odd number) = 
Note that the odd numbers are 1 (on three faces) and 3 (on one face).
c) The fact the die has been biased does not change the possible outcomes. It only changes the probability of getting any given number.
d) Because the 3-face has been loaded, this probability changes. In fact, it is calculated thus:
Let's assume the probability for 1 or 2 is
. Then that of 3 is
(because it is twice the others). The sum of probabilities must be 1.



P(odd number) =
Prob(1) + Prob(3)
=
= 
The geometric mean of 32 and 2 is 8