Answer:
The answer is below
Step-by-step explanation:
The equation of a straight line is given by:
y = mx + b
where m is the slope of the line and b is the y intercept (value of y when x = 0).
Given the equation of two lines as 
, the two lines are parallel to each other if 
. Also the lines are perpendicular if
Given line BC:
3x + 2y = 8
2y = -3x + 8
y = -3x/2 + 4
Hence the slope of the line BC = -3/2
For line AD:
-3x - 2y = 6
-2y =3x + 6
y = -3x/2 - 3
Hence the slope of line AD is -3/2
Since both line BC and AD have equal slope (-3/2), hence both lines are parallel to each other
<span>0*60=2,400 ft^2 is the area of the pool.
(40+2x)(60+2x)=2*2,400
2400+120x+80x+4x^2=4,800
4x^2+200x+2,400-4,800=0
4x^2+200x-2,400=0
4(x^2+50x-600)=0
</span><span>4(x-10)(x+60)=0
x-10=0
x=10 ans. for the width of the patio.
Proof:
(40+2*10)(60+2*10)=2*2,400
(40+20)(60+20)=4,800
60*80=4,800
4,800=4,800</span>
Answer:
A) c = 16.5h
B) $74.25
C) 7 hours
Step-by-step explanation:
Bazinga charges $16.50 per hour to dog sit.
Therefore, to calculate the total charge, multiply the number of hours by the charge per hour:
<h3><u>Part A</u></h3>
As explained above, to calculate the total charge, multiply the number of hours worked by the charge per hour of $16.50
⇒ c = 16.5h
where:
- h = number of hours worked
- c = total charge (in dollars)
<h3><u>Part B</u></h3>
To calculate how much Bazinga will earn if they dog sit for 4.5 hours, substitute h = 4.5 into the equation and solve for c:
⇒ c = 16.5h
⇒ c = 16.5(4.5)
⇒ c = $74.25
<h3><u>Part C</u></h3>
To calculate how long it will take Bazinga to earn $115.50, substitute c = 115.5 into the equation and solve for h:
⇒ c = 16.5h
⇒ 115.5 = 16.5h
⇒ h = 115.5 ÷ 16.5
⇒ h = 7 hours
X/7-4 = - 2
x = 14
i am a mathematics teacher. if anything to ask please pm me
Answer:
B) 21
Step-by-step explanation:
There are 7 cars total and 5 slots to fill for the showroom selections. Put another way, there are 7-5 = 2 cars that don't make it to the showroom floor. Since this value (2) is smaller than the previous number of slots (5), it makes it easier to ask the question "how many ways are there to pick 2 cars that don't make it to the show room floor?" instead of "how many ways are there to pick 5 cars that make it to the showroom floor?". We'll get the same answer either way.
So we have 7 total to pick from for slot 1, and then 6 left over for slot 2. Making 7*6 = 42 permutations. Order does not matter, meaning that picking a red car and then a blue car is the same as picking a blue and then red. The count 42 has double counted, so we divide by 2 to sort this out
42/2 = 21 represents the number of combinations. We can see this if we use the nCr combination formula with n = 7 and r = 2
nCr = (n!)/(r!*(n-r)!)
7C2 = (7!)/(2!*(7-2)!)
7C2 = (7!)/(2!*5!)
7C2 = (7*6*5!)/(2*5!)
7C2 = (7*6)/2
7C2 = 42/2
7C2 = 21
a similar computation happens if you use n = 7 and r = 5.
