is so that AP:BP=1:3 and point M is the midpoint of segment
CP
. Find the area of △ABC if the area of △BMP is equal to 21m2.
56 m²
A diagram can be helpful.
Triangles with the same altitude will have areas proportional to the length of their bases.
The altitude from B to PC is the same for triangles BMP and BMC, so they have areas that are in the same proportion as MP : MC. Since M is the midpoint of CP, MP = MC and ABMP = ABMC = 21 m². Then ...
... ACPB = 21 m² + 21 m² = 42 m²
The altitude from C to AB is the same for triangles CPA and CPB, so those triangles have areas in the sampe proportion as AP : BP = 1 : 3. Then ...
... ACPA : ACPB = PA : PB = 1 : 3
... ACPA : 42 m² = 1 : 3
So, the area of ∆CPA is 1/3 of 42 m², or 14 m². The area of ABC is the sum of the areas of CPA and CPB, so is ...
... AABC = ACPA + ACPB = 14 m² + 42 m²
... AABC = 56 m²
Answer:$20250
Step-by-step explanation:
6.5% of 30000
6.5/100 x 30000
(6.5 x 30000)/100
195000/100=1950
First year depreciation 30000-1950=28050
Second year=28050-1950=26100
Third year=26100-1950=24150
Fourth year=24150-1950=22200
Fifth year=22200-1950=20250
The equation −3x − y² = −1 is not a function because it violates the definition of a function where each input should have a unique output.
To determine whether the equation −3x − y² = −1 represents a function, we need to check if there is a unique output (y) for every input (x) or if there are multiple outputs for the same input. In other words, we need to ensure that each x-value maps to only one y-value.
First, let's rearrange the equation to isolate y²:
−3x − y² = −1
y² = 3x - 1
Now, it's evident that for a single value of x, there could be two possible values of y due to the square root. This means that for some values of x, there would be multiple outputs (y-values). Therefore, the equation −3x − y² = −1 is not a function because it violates the definition of a function where each input should have a unique output.
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Answer:
No (not a function)
Step-by-step explanation:
Begin by isolating the y-term to find
−3x−y2−y2y2=−1=3x−1=−3x+1
For each value of x, we multiply it by −3, add 1, and then take the square root to get the y-value. For example, if x=−8, we have
y2y2y2y=5=−3x+1=−3(−8)+1=25ory=−5
We have that if x=−8, then y=5 or y=−5. In other words, a single value of x results in more than one value of y. Since some value of x corresponds to more than one value of y, the equation does not define a function.
b. you add 6000 kilograms of water to the pool. what is the depth of the water in the pool? write your answer as a fraction. the water is about meters deep.
Answer:
1). Mass of water present= 18000 kg
2).4/3 meters deep
Step-by-step explanation:
Area of the rectangle= 6*3= 18m²
Volume of water in the pool
= Deepness of water*area of rectangle
= 1*18
= 18 m³
density of water is about 1 gram per cubic centimeter
In kg per m³= 1000 kg/me
Mass of water present= density*volume
Mass of water present= 1000*18
Mass of water present= 18000 kg
2)6000 kilograms of water is added to 18000 of
Total mass present= 6000+18000
Total mass present=24000 kg
If density= 1000kg/m³
Volume present= mass/density
Volume present= 24000/1000
Volume present= 24 m³
Area of the rectangle= 18 m²
deepness of the pool= volume/area
deepness of the pool= 24/18
deepness of the pool= 4/3 meters deep
G. V = 36h cubic units
H. V = 18h cubic units
J. V = 12h cubic units
Answer:
J. V = 12h cubic units
Step-by-step explanation:
Volume if a square pyramid = ⅓*a²*h
Where,
h = height = ?
a = edge = 6 in.
Plug in the values
Volume = ⅓*6²*h
V = ⅓*36*h
V = 12*h
V = 12h cubic units
B) Survey several more random samples of 25 people each from people in the town who are registered to vote
C) Survey serveral more random samples of 25 people each from the Republican voters in town
D) Survey a random sample of 25 people who are registered to vote in another town