Answers
A third alternative to the formulas I suggested in a comment is to use the vector cross product. Recast the three given points as points in 3D space with 0 z-coordinate:
A(20, 21, 0), B(8, 29, 0), and C(13, 1, 0)
Now consider two vectors,
u = B - A = 〈8, 29, 0〉 - 〈20, 21, 0〉 = 〈-12, 8, 0〉
v = C - A = 〈13, 1, 0〉 - 〈20, 21, 0〉 = 〈-7, -20, 0〉
Then recall the cross product identity,
||u × v|| = ||u|| ||v|| |sin(θ)|
where θ is the angle between the two vectors. The magnitude of u × v is equal to the area of the parallelogram spanned by u and v, and hence twice the area of the triangle of interest.
So we have
area = ||1/2 〈-12, 8, 0〉 × 〈-7, -20, 0〉||
area = 1/2 ||〈-12, 8, 0〉 × 〈-7, -20, 0〉||
area = 1/2 ||〈0, 0, 296〉||
area = 296/2
area = 148
Related Questions
Evaluate the algebraic expression for the given value of the variable.
x2 + 7x; x = 5
Answers
25+35
Answer is 60
Mike sold H hats. Nate sold three times as many hats as Mike. Write an expression for the number of hats Nate sold.
Answers
Answer:
3 times Mike's amount = 3h
A train travels 625 kiy north in 15 hours. What is the bus's velocity?
Answers
41.6666667
Step-by-step explanation:
Velocity = distance/time
Velocity = 625/15
Velocity = 41.6666667
Write 0.8 as a fraction in simplest form.
Answers
Answer:
Step-by-step explanation:
[tex]0.8 = \dfrac{8}{10}=\dfrac{2*4}{2*5}=\dfrac{4}{5}[/tex]
describe two ways 100 and 10 are related
Answers
Answer:
YES WE CAN SAY THAT 100 AND 10 ARE RELATED AS 10×10=100 AND 100÷10=10
the complement of an angle is 32 more than three times the angle. what are the angles
Answers
Answer:
Let 3x+32 - be the complement angle
x - be the angle
Therefore,
3x+32+x = 90
4x = 58
x = 14.5°
and the compliment is, 75.5°
Hope that helps!
Plz answer it's important
Answers
Answer:
AB = 4
Step-by-step explanation:
Since the line is horizontal then its length is the difference of the x- coordinates, that is
AB = | 8 - 4 | = 4 , or
AB = | 4 - 8 | = | - 4 | = 4
third grade math answers
25+50=75
30+30=60
70+70=140
Answers
Answer:
What?
Step-by-step explanation:
please help me out on this problem!
the main floor of an auditorium ranges from 6 feet below the stage
to 8 feet above the stage. the floor of the balcony ranges from 26 to 37 feet above the stage. write the range of the floor levels relative to the stage in interval notation and in set-builder notation.
Answers
This is a simple problem of ranges, we will find that the ranges for the main floor and the balcony are:
[-6ft, 8ft] or {x ∈ R | -6ft ≤ x ≤ 8ft}
[26ft, 37ft] or {x ∈ R | 26ft ≤ x ≤ 37ft}
respectively.
We know that:
The main floor of the auditorium ranges from 6ft below the stage to 8 feet above the stage.
The floor of the balcony ranges from 26 to 37 feet above the stage
The ranges relative to the stage will be, in interval notation, the interval that contains the two extremes of the range.
For the main floor, it goes from -6ft to 8ft (the first one is negative because is 6ft below the stage) then this interval will be: [-6ft, 8ft]
While in set-builder notation we want to specify that the variable must be a real number, so we start with: {x ∈ R
And we need to specify that x can go from -6ft to 8ft, then we add the restriction:
{x ∈ R | -6ft ≤ x ≤ 8ft}
Notice that we use a close interval here.
While for the balcony, the minimum is 26ft and the maximum is 37ft, then the interval will be [26ft, 37ft]
For the set-builder notation we will have:
{x ∈ R | 26ft ≤ x ≤ 37ft}
If you want to learn more, you can read:
https://brainly.com/question/19159374
It take 5 minutes to help a restock an area. How much areas can you restock in 50 minutes?
Answers
Answer:
10 areas
Step-by-step explanation:
5 minutes = 1 area
→ Divide the 50 by the 5
50 ÷ 5 = 10
→ Multiply this by the area
10 × 1 = 10
Someone help please
1= 39 degrees
2: 40 degrees
3: 41 degrees
4: 42 degrees
Answers
Answer:
A
Step-by-step explanation:
This uses the sine law.
Sin(theta)/113 = sin(42)/120 Multiply both sides by 113
sin(theta) = 113*sin(42)/120
sin42 = 0.6691
sin(theta) = 113 * 0.6691 / 120
sin(theta) = 0.630008
theta = sin-1(0.63008)
theta = 39.1 Looks Like A
Claculus, whoever can answer ill give brainlyest
Answers
The table suggests that f(x) approaches a value of 6.5 as x approches 3, or in other words, that
[tex]\displaystyle \lim_{x\to3}f(x) = 6.5[/tex]
Answer:
they are proportional
Step-by-step explanation:
When one goes up so does the other
I really need help because I’m so confused where to start and it’s due tomorrow :(
Answers
Answer:
1. 8t+4v
A.9v+7t+6
S.14v+7t
3. At a local high school championship football game, 595 tickets were sold. A student
admission ticket costs $1.50 and an adult admission ticket costs $5. The sum of all ticket
receipts for the game was $1750. How many of each type of ticket were sold?
Answers
Because 595 tickets were sold, so 595 - x will be the tickets sold for adults
=> x*1,5 + (595 - x)*5 = 1750
<=> 1,5x + 2975 -5x = 1750
<=> -3,5x = -1225
<=> x = 350
We have 595 - 350 = 245
In conclusion, 350 tickets were sold for students
And 245 tickets were sold for adults
6x - 3
2x – 1
A
B
10x – 1
#11: X =
1 point
Your answer
#12: AB =
1 point
Your answer
Answers
Answer:
Step-by-step explanation:
6x-3+2x-1=10x-18
8x-4=10x-18
18-4=10x-8x
14=2x
X=7
AB = (6*7)-3=39
BC=13
AC=39+13=52 or
AC=(10*7)-18=52
Please answer in full
Answers
Answer:
1) 1/2 *bh
2) 2s+4
3) 35+2m
1. 1/2bh
2. 2(s) + 4
3. 2m + $35
Step-by-step explanation:
1. Explanation: half the product of the base times the height can be written as 1/2 bh because as base is being multiplied by the height it will soon be half the product
2. Explanation: Man’s age can be described as 4 MORE THAN (add) TWO times (multiply) his son’s age
3. Explanation: $35
Plus an extra $2 per mile
How many miles??
Miles represented by m
The side of a cube is 3^4 centimeters long. What is the volume of the cube?
Answers
Step-by-step explanation:
v=s^3 s=3^4=81
v=(81)^3
v=531,441 cm^3
Find the distance between the two numbers on a number line. Write your answer as a decimal.
-2.2, 8.4
Answers
Answer
10.6
Explanation
Logic
Which of the following set of points represents a function?
(4,3), (2, 1), (2, 9). (9, 4)
(3,5), (4,5), (5,9), (7.-2)
(-1,2). (-1, 4), (-1,8), (-1,9)
Answers
Answer:
Each of the domain values, x, should only output a single unique range value, y.
This example is a relation and not a function because the the domain value of -1 output 2 distinct range values.
-1 outputs a 3
and
-1 outputs a 5
If I were to draw a vertical line at the domain value of -1 that vertical line would intersect the points (-1,3) and (-1,5). Which indicates that the relation is not a function.
Answer:
None of the following set of points represents a function .
Gina rented a truck for one day there was a base fee of 1275 there was an additional charge of 20 cents for each mile driven the total cost c in dollars for driving in miles is given by the following function
Answers
Answer:
[tex]1275+0.2m=c[/tex]
m is the amount of miles driven, c is the total cost.
Step-by-step explanation:
Since she has a flat fee of 1275, that's the 1275 in the equation and since we don't know how many miles she drives, that's the m in the equation for miles driven. Since each mile costs 0.20, that's the 0.2 in the equation. And since c is the total cost in dollars, that's the c in the equation.
Points Z L and S are
Answers
Answer:
Question is?
Step-by-step explanation:
what's the que for Points Z L and S are
A ladder 13m long leans against a wall such that the top of the ladder is 12 m from the ground.how far is the foot of the ladder from the wall
Answers
Answer:
5
Step-by-step explanation:
The pythagorean theorem
A^2+B^2=C^2
A^2 =12^2
b^2 is what you need to find
C^2= 13^2
so it's
144+B^2=169
-144 -144
B^2=25
square root of 25 is 5 which is the answer
ITS NUMBER 10. THAT I NEED HELP WITH
Answers
Which One Does Not Belong? EXPLAIN your REASONING
Answers
Answer:
The last one
Step-by-step explanation:
0.3333..., 30%, 3/10 are parts.
The last one ( 3 circles) are 3 wholes.
(whole numbers)
I hope this helped:)...
:-)
Hey there! I'm happy to help!
30% is the same thing as 0.3, which is 30% of 1.
0.3 is what you multiply numbers if you want to see what 30% of that number is as 0.3 is 30% of 1, the whole number.
3/10 is the same value as 30% because 3 divided by 10 is equal to 0.3, which is 30%.
The dots in the boxes are also the same thing as 3/10. There are 10 boxes, and 3 out of the 10 have dots, which is 3/10 and 30%.
The one that does not belong is 0.333333...... This is equivalent to 1/3, which is greater than 30%, 0.3, and 3/10.
Have a wonderful day and keep on learning! :D
please answer this math
Answers
What was the result of John overdrawing his checking account?
Answers
Answer:
What do you mean
Step-by-step explanation:
please help ill mark brainliest and add explanation too pleas
Answers
Step-by-step explanation:
In A,
length=3units
width=2 units
area=length×width
area=3×2 sq.units
area=6 sq.units
In B,
length=1unit
width=4units
area=length × width
area=1unit × 4units
area= 4 sq.units
Note:if you need to ask any question please let me know.
what are the Properties of real numbers for 6425
Answers
Step-by-step explanation:
Properties of the number 6425
Factorization5 * 5 * 257Square root80.156097709407Natural logarithm8.7679519097634Decimal logarithm3.8078731320033Sine-0.42867294834975
Amir stands on a balcony and throws a ball to his dog, who is at ground level.
The ball's height (in meters above the ground), xxx seconds after Amir threw it, is modeled by:
h(x)=-(x-2)^2+16h(x)=−(x−2)
2
+16h, left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, minus, 2, right parenthesis, squared, plus, 16
How many seconds after being thrown will the ball hit the ground?
Answers
Answer:
6 seconds
Step-by-step explanation:
h(x)=-(x-2)^2+16
We want h(x) to be 0 ( that is when the ball hits the ground)
0 = -(x-2)^2+16
Subtract 16 from each side
-16 = -(x-2)^2+16-16
-16 = -(x-2)^2
Divide by -1
16 = (x-2)^2
Take the square root of each side
sqrt(16) = sqrt((x-2)^2)
±4 = x-2
Add 2 to each side
2±4 = x-2+2
2±4 =x
2+4 = x 2-4 = x
6 =x -2 =x
Time cannot be negative so x=6
Answer:
X = 6
Step-by-step explanation:
hope it will help you
How many decimal places does
0.005011
have please? :)
Answers
Answer:
6
Step-by-step explanation:
6 decimal places
0.005011 has six decimal places.
What is a decimal place?
'The place value of a decimal number is recognized according to the position of the dot or decimal point. The first digit to the right of the decimal point indicates the number of tenths and the second digit to the right indicates the number of hundreths.'
According to the given problem,
For the number 0.005011, after the decimal there are numbers up to the sixth place which is that there are six numbers.
For counting decimal places, we need to count the number of digits present to the right of decimal point.
Hence, we can conclude that 0.005011 has 6 decimal places.
Learn more about decimal places here:
https://brainly.com/question/26568840
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