Given ▲ABC with vertices A(2, -1), B(5, 6), and C(-1, 4) as shown. Find the number of square units in the area of ▲ABC in simplest form.
Answers
The area of the triangle of 18.
Area of triangle for coordinatesThe area of a triangle on a coordinate plane is given by the formula,
[tex]Area\ \triangle = \dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
where,
[tex](x_1, y_1)[/tex], [tex](x_2, y_2)[/tex], and [tex](x_3, y_3)[/tex] are the coordinates of the three points in the coordinate plane.
Given to us,A(2, -1) = [tex](x_1, y_1)[/tex]
B(5, 6) = [tex](x_2, y_2)[/tex]
C(-1, 4) = [tex](x_3, y_3)[/tex]
[tex]Area\ \triangle = \dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Substituting the values[tex]\begin{aligned}Area \triangle &= \dfrac{1}{2}\ |2[6-4]+5[4-(-1)]-1[-1-6]|\\\\& = \dfrac{1}{2}\ |2[2]+5[4+1]-1[-7]|\\\\& = \dfrac{1}{2}\ |2[2]+5[5]-1[-7]|\\\\& =\dfrac{1}{2}|4+25+7|\\\\& = \dfrac{1}{2}\times 36\\\\& = 18\end{aligned}[/tex]
Hence, the area of the triangle of 18.
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Related Questions
Steve is playing a carnival game. He wants to win a prize, but he thinks he has about a 20% chance of winning. He uses the expression 0.2t to calculate the number of games he will need to play in order to win a prize.
If he plays the game 12 times, about how many times can he expect to win?
Answers
Answer:50%
Step-by-step explanation:
Steve's expected times of winning in 12 trials is about 2 times.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
The winning chance of Steve is 20% or 0.2.
We know, We know The expected value, also known as the expectation, average, is a generalization of the weighted average in the field of probability theory.
Informally, the anticipated value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
Therefore, If he plays the game 12 times the number of times he is expected to win is,
= 12×0.2.
= 2.4 Or 2 times.
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Nora has a 12 ounce apple juice. She drinks 5 ounces. Enter the percentage of ounces Nora has left of her apple juice. Round your answer to the nearest hundredth.
Answers
Answer:
200% out of 1000% srry if im wrong
Step-by-step explanation:
Answer:
please answer this i need it too
Step-by-step explanation:
Find the slope of the line that passes through points (6,9) and (11,2)
Answers
Answer:
[tex]-1.4[/tex]
Step-by-step explanation:
The slope of a line is the change in the line. It can be found using the formula;
[tex]\frac{rise}{run}[/tex] or [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
Substitute in the given points, and solve for the slope;
[tex]\frac{y_2-y_1}{x_2-x_1}\\\\= \frac{2-9}{11-6}\\\\= \frac{-7}{5}\\\\= -1.4[/tex]
Answer:
-7/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-9)/(11-6)
m=-7/5
hey what's 3 3/8 + 3 3/8 + 3 3/8 as a proper fraction i need it right right now
Answers
Answer: 10.1
Step-by-step explanation:
The price of a T-shirt was $20. It was first increased by 20%. They did not
sell well the shop owner decreased the price by 20%. What is the new price
of the T-shirt?
Answers
Answer:
First S.P= 20$ + (20/100)×20
=24$
New price = 24- (20/100)×24
=19.2$
If it was increased to $20 it would originally be $16
Hopefully, this helped
ANSWER THESE AND YOU GET BRAINLIEST OH AND THESE ARE JUST PROBLEMS I MADE FOR YALL
5. Miley had a rope that was 5.5 meters in length. She cut 3 pieces, 1.25 meters each. How long, in meters, was the remaining rope?
6. Isaiah hiked 3 days.
On Monday, he hiked 314miles
On Tuesday, he hiked 134miles less than he hiked on Monday
On Wednesday, he hiked 212miles more than he hiked on Tuesday
How many miles did Isaiah hike on Wednesday?
Answers
What is the relationship between the two quantities in the table?
Х
у
25
1
50
IN
3
75
100
O The relationship between the quantities is: multiply by 25.
O The relationship between the quantities is: add 25.
The relationship between the quantities is: subtract 75.
The relationship between the quantities is: add 75.
Answers
Answer:
The answer is d
Step-by-step explanation:
Answer:
The Answer Is A.
Step-by-step explanation:
I Just Got It Correct, And Your Welcome.
please answer ill give brainliest
Answers
Answer:
71
Step-by-step explanation:
i think this is right
What is an equation of the line that passes through the points (3,1) and (-3, – 7)?
Put your answer in fully reduced form.
Answers
Answer:
y = 4/3x - 3
Step-by-step explanation:
Use rise over run to find the slope, (y2 - y1) / (x2 - x1)
Plug in the points:
(y2 - y1) / (x2 - x1)
(-7 - 1) / (-3 - 3)
-8 / -6
= 4/3
Now, plug in the slope and a point into y = mx + b to get the equation:
y = mx + b
1 = 4/3(3) + b
1 = 4 + b
-3 = b
Plug in the slope and y intercept into the equation:
y = 4/3x - 3
So, the equation is y = 4/3x - 3
which make an angle 45 degree with x axis in negative direction and passes through a point (- 3, 2)
Answers
9514 1404 393
Answer:
y = -x -1
Step-by-step explanation:
The slope of a line is the tangent of the angle it makes with the x-axis. If you want an angle of -45°, then you need a line with a slope of m = tan(-45°) = -1.
Then the y-intercept is ...
b = y -mx
b = 2 -(-1)(-3) = 2 -3 = -1
So, the slope-intercept equation is ...
y = mx + b
y = -x -1
The Points in the table lie on a line. Find the slope of the line.
The slope is —-???
Plz I need help
Answers
Answer:
The slope is 2/5
Step-by-step explanation:
1.) Do (y1-y2)/(x1-x2)
(4-2)-(7-2) which is 2/5
2.) 2/5 is the slope
what is the slope of line that is parallel to
y=2x+1
Answers
Answer:
2x
Step-by-step explanation:
Parallel lines have the same gradient
Therefore it would have the same gradient of 2x
On the map the scale is
inch = 25 miles. How many
1 /
miles would it be to travel 8 inches on the map?
Answers
Answer:
200 miles
Step-by-step explanation:
1 inch =25
8 inches=200
because 25*8=200
Which vertex in XYZ corresponds to vertex b in ABC
A. vertex Z
B. vertex A
C. vertex Y
D. vertex X
Answers
Answer:
C
Step-by-step explanation:
Answer:
C is the correct answer
Step-by-step explanation:
have a good day <3
A customer buys roses and carnations from a florist. The customer pays $1.50 for 2 roses and $2.70 for 3 carnations. How much would the customer pay for 1 rose and 1 carnation?
Answers
Answer:
1.11 for a carnation and 1.33 for a rose
Step-by-step explanation:
you divide 2 and 1.50 and 3 and 2.70 to get the amount for each flower.
Help me please I need it by tommrow
Answers
Answer:
Only answer is A
Answer:
The first and fourth one.
Step-by-step explanation:
A ratio of 5:2 is saying that for every 5 boys, there are 2 girls. Now, in the question, it says, "In a school" so it must be within the whole school, hence #4. Hope this helps!
You pay no Federal taxes up to $9525, 12%
Answers
Answer:
1143
Step-by-step explanation:
one thousand one hundred fourty three
Solve for x. Round all answers to the nearest tenth
Please help
Answers
Answer:
36.9
Step-by-step explanation:
PLEASE HURRY 10 POINTS FOR ALL OF YOU
And why is hannajackson so rood
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Answer:
288cm
Step-by-step explanation: She is a beach..Thats why shes rude
A home building company purchases 24 acres of land and divides it into 1/2-acre plots for sale. How many 1/2-acre plots will be for sale?
Answers
Answer:
48
Step-by-step explanation:
This is a division problem.
You need to divide 24 by 1/2.
24 / 1/2 = 24/1 / 1/2 = 24/1 * 2/1 = 48/1 = 48
Answer: 48
You can also do it this way.
Each acre is the same size as 2 half-acres.
1 acre = 2 half-acres
Multiply both sides of the equation above by 24.
24 * 1 acre = 24 * 2 half-acres
24 acres = 48 half acres
Answer: 48
Use the table to write a quadratic function in vertex form. Then rewrite the function in standard form.
Answers
Answer:
Step-by-step explanation:
The graph decreases at first, then changes direction at (2, 5).
y = a(x-2)^2 + 5
Plug in (1,11) and solve for a:
11 = a(1-2)^2 + 5
a = 6
Equation in vertex form:
y = 6(x-2)^2 + 5
A number tripled and tripled again is 576. What is the number?
Answers
Answer:
192
Step-by-step explanation:
Answer:
It is either 64 or 96. Thank u for ur time
Step-by-step explanation:
I literally used a calculater... and thats the truth...
is 3(x + 2) and 5x + 6 both the answer 6 , which one is not 6 or are they both not 6
giving brainliest if correct
Answers
3(x+2)
Distribute
3x+6
This cannot be simplified any further
5x+6
This cannot be simplified any further
help please!
Which of the following is required to construct the inscribed circle of a triangle?
A. the perpendicular bisectors of the sides of the triangle
B. the circumcenter of the triangle
C. the orthocenter of the triangle
D. the incenter
Answers
Answer:
D. the incenter
Step-by-step explanation:
Hope this helps
Answer:
D. the incenter
Step-by-step explanation:
Because it is the "Correct Answer"
please fill all 3 of them
Answers
Answer:
Median: 36 and 1/7
Mode: 45
Range: 25
Step-by-step explanation:
33 + 45 + 38 + 27 + 45 + 20 + 45
253 ÷ 7 = 36 and 1/7
1 33
3 45s
1 38
1 27
1 20
The mode is 45.
Largest number: 45
Smallest number: 20
45 - 20 = 25
how much is 3570 cg
Answers
Answer:
357,000 Centigrams
Step-by-step explanation:
Answer:
3 Grams = 300 Centigrams
I WILL GIVE YOU BRAINLIEST TO THE FIRST PERSON THAT ANSWERS
D'(4,4), E'(3,0), F'(0,3)
Write a rule to describe this transformations
Answers
A monument casts a shadow 215-ft long when the angle of elevation of the sun is 52º. Find
the height of the monument.
Answers
I don’t have a calculator on hand but this is how it’s done so just type the final equation in:
SOH
sin (52) x 215 = your answer
Which of the following is the solution set of the given equation?
(x - 3) - 2(x + 6) = -5
{-10}
{-4}
{8}
Answers
(x-3)-2(x+6)= -5
x-3-2x-12= -5
-x= -5+12+3
-x=10
x= -10
Answer:
x = -10
Step-by-step explanation:
Sizwe bought a table for R200 and sold it for 240. Calculate his percentage profit