Answer:
Step-by-step explanation:
So we have the trinomial:
First, factor out a 2:
Now, factor within the parentheses.
To do so, we want to find two numbers. When multiplied, these two numbers must equal (a)(c) and when added, they must equal b
(a)(c) is 2(-5) or -10 and b is -3. So, we want two numbers that when multiplied together gives -10 and when added gives -3.
-5 and 2 works. Therefore:
Replace -3x with 2x and -5x:
Factor out a 2x for the first two terms. And factor out a negative 5 for the remaining two:
Grouping:
And we're done!
3. <u>Two angles and included side (ASA congruence theorem)</u>.
<u>Reason:</u> This is because, it is given that angle Q is congruent to angle T and line QR is congruent to line TR. Also, we proved in step 2 that 
. Thus, we have two angles and the side included as congruent and thus, the two triangles are congruent.
4. <u>CSCT (Corresponding Sides of a Congruent Triangle)</u>
<u>Reason:</u> PR and SR are the corresponding sides of the congruent triangles 
and 
, therefore, by the CSCT these corresponding sides have to be congruent.
Answer:
4 weekdays and 2 weekends.
Step-by-step explanation:
6 days.
x = weekdays
y = weekends
7x = amount with weekdays
12y = amount with weekends
7x + 12y = 52, total
x + y = 6, amount of days
solve double variable equation
x = 6 - y, plug in to 1st equation
7(6 - y) + 12y = 52
42 - 7y + 12y = 52
5y = 10
y = 2 weekends
2 + x = 6
x = 4 weekdays
Answer:
The probability that Pete passes his test given that he studied = (8/10) = (4/5) = 0.80
Step-by-step explanation:
Let the event that Pete studies be S.
Let the event that Pete passes the test be P.
The probability that he studies for his test and then passes it is P(S n P) = 7/10
The probability that Pete studies is P(S) = 7/8
The probability that Pete passes his test given that he studied = P(P|S)
The conditional probability, P(A|B) is given mathematically as
P(A|B) = P(A n B) ÷ P(B)
So, the required probability, P(P|S) will be
P(P|S) = P(P n S) ÷ P(S)
P(P n S) = P(S n P) = (7/10)
P(S) = (7/8)
P(P|S) = P(P n S) ÷ P(S)
= (7/10) ÷ (7/8)
= (7/10) × (8/7)
= (8/10) = (4/5) = 0.80
The probability that Pete passes his test given that he studied = (8/10) = (4/5) = 0.80
Hope this Helps!!!
