Answer:
A. 5
Step-by-step explanation:
The triangle will be a right triangle when the side lengths satisfy the Pythagorean theorem: the sum of the squares of the legs is equal to the square of the hypotenuse.
(x +1)^2 +x^2 = (√61)^2
x^2 +2x +1 +x^2 = 61 . . . eliminate parentheses
2x^2 +2x = 60 . . . . . . .subtract 1, collect terms
x^2 +x -30 = 0 . . . . . divide by 2, subtract 30
(x +6)(x -5) = 0 . . . . factor the quadratic
x = -6 or +5
The solution is x = 5.
_____
Side lengths cannot be negative. Solution values are values of x that make the factors zero. x+6=0 when x=-6, for example.
The first thing we should know in this case is that by definition the flow of liquid is given by:
Q = V / t
Where,
V: volume
t: time
The volume of the cone is given by:
V = (pi * r ^ 2 * h) / (3)
Where,
r: radio
h: height
Substituting the values we have:
V = (3.14 * ((3) ^ 2) * 7) / (3)
V = 65.94 in ^ 3
We now turn off the time of the flow equation:
t = V / Q
Substituting values:
t = (65.94) / (14)
t = 4.71 minutes
Answer:
It will take for all the liquid in the funnel to pass through the nozzle about:
t = 4.71 minutes
Answer: 65
Step-by-step explanation:
All those angles added up have to equal 360 degrees.
The little square on the angle to the left of x means that it's a right angle, or 90 degrees.
360
- 180
= 180 <--- this is the bottom half,
180
- 90 <--- the right angle on the left
= 90
90
-25
= 65 <--- that's x
There are total 10 juice boxes
P(grape) first pick:
2/10=1/5
P(grape) second pick:
1/9
As a result, the probability that, when Jill reaches into the cooler to grab two juice boxes without replacing them, she grabs two that are grape is 1/45. Hope it help!
Answer: The car has to sell for $20000
Step-by-step explanation:
Let x represent the price that the car would have to sell for in order for these two job opportunities to pay Jim the same amount.
Ace Cars says they will pay Jim a 10% commission on the sale price of each car. It means that his pay would be
10/100 × x = 0.1x
Budget Cars says they will pay him $500 per week plus a 7.5% commission on the sale price of each car. It means that his pay would be
500 + 0.075x
For boths pays to be the same, it means that
0.1x = 500 + 0.075x
0.1x - 0.075x = 500
0.025x = 500
x = 500/0.025
x = 20000
The car has to sell for $20000
