The coordinate will be (5, 12). Then the number of balloons that a group of 5 people pops will be 12.
<h3>What is coordinate geometry?</h3>
Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Rami works at a carnival dart game where groups of people try to pop balloons taped to a wall by throwing darts.
He records the number of people in each group and the total number of balloons they pop.
This graph represents Rami’s data.
Then the number of the balloons that a group of 5 people pops will be
The coordinate will be given as
⇒ (5, 12)
More about the coordinate geometry link is given below.
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Answer:
4
Step-by-step explanation:
Since the base angles are the same, the side have to be the same
ML = MN
4x = x+3
Subtract x from each side
4x-x = x+3-x
3x= 3
Divide by 3
3x/3 = 3/3
x = 1
We want the length of MN
MN = x+3 = 1+3 = 4
Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.
Step-by-step explanation:
Salt in the tank is modelled by the Principle of Mass Conservation, which states:
(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)
Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

By expanding the previous equation:

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

Since there is no accumulation within the tank, expression is simplified to this:

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:
, where
.

The solution of this equation is:

The salt concentration after 8 minutes is:

The instantaneous amount of salt in the tank is:
Answr:
p=−7/2
Step-by-step explanation:
Simplify both sides of the equation.
p+
1
2
=−3
Step 2: Subtract 1/2 from both sides.
p+
1
2
−
1
2
=−3−
1
2
p=
−7
2