Answer:
-1
Step-by-step explanation:
-5-15+4+15
=-20+19
=-1
Answer:
Statement: angle QAU congruent to angle KAC
Reasoning: vert. angle congruenct thm
S: angle U congruent to angle C
R: Alt. Int. Angle Thm
S: Triangle QUA similar to Triangle KCA
R: AA Sim. Thm
Step-by-step explanation:
Practice a lot of proofs and you'll start seeing a pattern in them and it will become way easier.
The diagonal of a rectangle = sqrt(w^2 + l^2)
w = width
l = length
In this problem,
The diagonal = 20 in
w = x
l = 2x + 8
Let's plug our numbers into the formula above.
20in = sqrt((x)^2 + (2x + 8)^2)
Let's simplify the inside of the sqrt
20 in = sqrt(5x^2 + 32x + 64)
Now, let's square both sides.
400 = 5x^2 + 32x + 64
Subtract 400 from both sides.
0 = 5x^2 + 32x - 336
Factor
0 = (5x - 28)(x + 12)
Set both terms equal to zero and solve.
x + 12 = 0
Subtract 12 from both sides.
x = -12
5x - 28 = 0
Add 28 to both sides.
5x = 28
Divide both sides by 5
x = 28/5
The width cant be a negative number so now we know that the only real solution is 28/5
Let's plug 28/5 into our length equation.
Length = 2(28/5) + 8 = 56/5 + 8 = 96/5
In conclusion,
Length = 96/5 inches
Width = 28/5
Answer:
t2 = 52.8 hours
it will take 52.8 hours if its flow is reduced to 5 litres per minute.
Step-by-step explanation:
The volume of the swimming pool can be written as;
Volume V = flow rate × time
V = R×t
V = R1×t1 = R2×t2
R1×t1 = R2×t2
t2 = R1×t1/R2 ........1
Given;
Flow rate R1 = 12 litres per minute
Flow rate R2 = 5 litres per minute
time t1 = 22 hours
Substituting the given values into equation 1;
t2 = R1×t1/R2 = 12×22/5
t2 = 52.8 hours
it will take 52.8 hours if its flow is reduced to 5 litres per minute.
Answer:
R=7
Step-by-step explanation:
R=1+3w
This is a classic substitution question.
Just replace the w with 2.
R = 1+3(2)
You only need to multiply 3 with 2.
R = 1 + 6
R= 7
