Answer:
The answer should be "B" (The area of △RST is equal to the area of △LMN.)
The area of ΔRST is equal to the area of ΔLMN.
How to find the area of a triangle from its vertices ?We know that, if the vertices of a triangle are [tex](x_{1},y_{1}), (x_{2} ,y_{2} ), (x_{3} ,y_{3} )[/tex],
then the area of the triangle is [tex]\frac{1}{2}[/tex] | [tex]x_{1} (y_{2} -y_{3} )+x_{2} (y_{3} -y_{1} )+x_{3} (y_{1} -y_{2} )[/tex] |
What is the result of comparing area of two given triangles ?In ΔRST, Vertices are R=(5,5), S=(2,1), T=(1,3)
In ΔLMN, Vertices are L=(0,-1), M=(2,-4), N=(-2,-3)
Area of ΔRST = [tex]\frac{1}{2}[/tex] | [tex]x_{1} (y_{2} -y_{3} )+x_{2} (y_{3} -y_{1} )+x_{3} (y_{1} -y_{2} )[/tex] |
= [tex]\frac{1}{2}[/tex] | 5(1-3)+2(3-5)+1(5-1) |
= [tex]\frac{1}{2}[/tex] | 5×(-2)+2×(-2)+4 |
= [tex]\frac{1}{2}[/tex] | -10-4+4 |
= [tex]\frac{1}{2}[/tex] | -10 |
Removing the absolute sign, we get,
Area of ΔRST = [tex]\frac{1}{2}[/tex] ×10 = 5 square unit
Again, Area of ΔLMN = [tex]\frac{1}{2}[/tex] | [tex]x_{1} (y_{2} -y_{3} )+x_{2} (y_{3} -y_{1} )+x_{3} (y_{1} -y_{2} )[/tex] |
= [tex]\frac{1}{2}[/tex] | 0(-4+3)+2(-3+1)-2(-1+4) |
= [tex]\frac{1}{2}[/tex] | 0+2(-2)-2(3) |
= [tex]\frac{1}{2}[/tex] | -4-6 |
= [tex]\frac{1}{2}[/tex] | -10 |
Removing the absolute sign, we get,
Area of ΔLMN = [tex]\frac{1}{2}[/tex] ×10 = 5 square unit
Hence, we can say that, the area of ΔRST = the area of ΔLMN
Learn more about area of a triangle from its vertices here :
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What do cos and sin mean?
Answer and Step-by-step explanation:
These two terms (pronounced as Sine and Cosine) are used to solve for the sides and angles of a triangle in Trigonometry.
They are functions revealing the shape of a right triangle.
Sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle.
Cosine is also a trigonometric function of an angle. The cosine of an angle is the relation of the length of the side that is adjacent that angle, to the length of the longest side of the triangle.
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help me please (Math)
Answer:
x = 7
Step-by-step explanation:
Exterior angle thm:
4x + 12 + 7x + 12 = 101
11x + 24 = 101
11x = 101 - 24
11x = 77
x = 7
[tex]\frac{3}{4}- \frac{2}{3}[/tex]
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
We require the fractions to have the same common denominator
The LCM of 4 and 3 is 12 , then
[tex]\frac{3(3)}{4(3)}[/tex] - [tex]\frac{2(4)}{3(4)}[/tex]
= [tex]\frac{9}{12}[/tex] - [tex]\frac{8}{12}[/tex]
= [tex]\frac{1}{12}[/tex]
HELP PLSS
Write the percent as a fraction and as a decimal.
3/15%
Answer:
0.2% and 1/5%
Step-by-step explanation:
Hope this helps
Answer:
0.2% is the answer as decimal.
3/15/100
3/15*1/100
3/1500
1/500( as fraction)
Step-by-step explanation:
Find the exact value of sin (8x) cos (3x) – cos (8x) sin (3x).
Answer:
answer is 11 x
Step-by-step explanation:
Mark brainliest
T^T T^T T^T T^T T^T HELP please?
Applying the Pythagorean theorem, solve this triangle.
Answer:
Step-by-step explanation:
using pythagoras theorem
h^2=p^2+b^2
3^2=q^2+2^2
9=q^2+4
9-4=q^2
5=q^2
[tex]\sqrt{5}[/tex] =q
6 inches is cut from a piece of wood measuring 15 yards. How long is the
remaining piece of wood, in inches?
Answer:
there are 534 inches pieces of remaining wood left.
Step-by-step explanation:
If we convert 15 yards into inches. it would be 540 so you just have to subtract 540 - 6 and that will give you 534.
find the missing sides of the triangle
Answer:
b. u=13√2 , v=13
Step-by-step explanation:
________
Answer:
u=13[tex]\sqrt{2}[/tex] and v=13[tex]\sqrt{2}[/tex]/2
Step-by-step explanation:
Solve the equation.
5x + 6 = 2x – 3
Answer:
x = -3
Step-by-step explanation:
5x + 6 = 2x – 3
5x-2x+6=-3
3x=-9
x=-9/3
x=-3
Which of the following best estimate the sum 1/2+1/3
Answer:
5/6
Step-by-step explanation:
what you do first is find the common denominator
so that would be:
3/6 + 2/6
then you would add them
so that would be:
3/6 + 2/6 = 5/6
and 5/6 is your answer
Which is greater 5.97 or 5.946????
Answer:
5.97
Step-by-step explanation:
Answer:
5.97
Step-by-step explanation:
5.946 = 5.94
5.97>5.94
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
equilateral acute
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
C. Equilateral acute
Step-by-step explanation:
The triangle is less than 90 degrees so it's an acute
Simplify this for me thanks u
[tex]4n + 3(n - 5) + 2 \\ \\ = 4n + 3n - 15 + 2\\ \\ = 7n - 13[/tex]
Option BHope This Helps You ❤️Solve the equation below 8x - 2 (x + 5) = 2 (x - 1)
Answer:
x = -3
i explained it in the picture
Which equations are equivalent to his weekly addition of 0.5 km and would correctly determine how many weeks it will take Hector to reach 10 km if he starts at 2.5 km and adds 0.5 km every week? Select all that apply. 0.5x + 2.5 = 10 0.5 – 2.5 = 10x 10 = 2.5 + 0.5x 2.5x + 0.5 = 10 2.5x – 0.5 = 10
Answer:
C. 10 = 2.5 + 0.5x
Step-by-step explanation:
A. 0.5x + 2.5 = 10
B. 0.5 – 2.5 = 10x
C. 10 = 2.5 + 0.5x
D. 2.5x + 0.5 = 10
E. 2.5x – 0.5 = 10
Total distance Hector covers = 10 km
Distance he has covered = 2.5 km
Distance he covers per week = 0.5 km
Let
x = number of weeks
The equation is given by
2.5 + 0.5x = 10
It can also be written as:
10 = 2.5 + 0.5x
10 - 2.5 = 0.5x
7.5 = 0.5x
x = 7.5/0.5
x = 15 weeks
Answer:
A and C
0.5x + 2.5 = 10
10 = 2.5 + 0.5x
Step-by-step explanation:
hope this helps!
Draco and his friends bought Bertie Bott's Every Flavor Beans for $3 per packet and chocolate frogs for $1 per packet at Honeydukes. They spent a total of $54 to buy a total of 36 packets of Beans and frogs.
Part A: Write a system of equations that Draco can solve to find the number of packets of Bertie Bott's Every Flavor Beans and the number of packets of chocolate frogs that he and his friends bought at Honeydukes. Tell what the variables used in the equations represent. (5 points)
Part B: Solve the system of equations from Part A to find out how many packets of chocolate frogs and Bertie Bott's Every Flavor Beans Draco and his friends bought and write the answer in (x, y) form. Tell which method you used to get the answer, and explain why you selected that particular method to get the answer.
Answer:
Part A: x + y = 36, 3x + y = 54
Part B: (9, 27), I used subtraction to solve the system, because it eliminated the "y" value, so it would be easiest to solve.
Step-by-step explanation:
Amount of Bean Packets: x
Amount of Frogs: y
We are given that:
x + y = 36
3x + y = 54
This is the answer to answer A.
To solve, use subtraction. Subtract:
3x + y - (x + y) = 54 - 36
3x - x + y - y = 18
2x = 18
x = 9
Substituting x = 9 into x + y = 36, we find that y = 27
In (x, y) form, substitute x = 9 and y = 27 to get (9, 27)
I used subtraction to solve the system, because it eliminated the "y" value, so it would be easiest to solve.
Which of the following measurements must be accurate when used in a grocery store? Check all that apply.
i am little bit confused
but according to me
C and D must be right
hope this is helpful
pls help someone !!!!!!!
Answer:
Has a slope of [tex]\frac{3}{4}[/tex] and passes through the point (0,1)
Step-by-step explanation:
We can eliminate half the answer choices by finding whether the line passes through (1,0) or (0,1). Coordinates are read as (x,y), therefore the line passes through (0,1). The slope of the line y=x has a slope of 1. Looking at the graph, we can see that the increasing interval of the line is tilted down ever so slightly, therefore the slope must be less than one.
Therefore, the answer is has a slope of [tex]\frac{3}{4}[/tex] and passes through the point (0,1).
Answer:
Its C, or the third option.
Step-by-step explanation:
Rise/run on this graph is 3/4
and y-intercept is (0, 1)
so C, or third option is correct.
Help pls
Bshdndbrjdhbdbdhdjd
Answer:
just function A
A is, for every 2x (2 steps) the value of y increased linearly by 2.5
B isn't, for every 10x (10 steps), the increase of y varies
Marking brainliest
Please help!
Answer:
[tex]AB\approx 24.22[/tex]
Step-by-step explanation:
In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse of the triangle.
In this case, in order to form the ratio, we're looking for the angle to the bottom right of the triangle. Notice how this angle is the supplement to the angle marked [tex]130.8^{\circ}[/tex]. Since the two angles form one side of the line, we can solve for this angle.
Let's call the angle [tex]\theta[/tex]:
[tex]130.8+\theta=180,\\\theta=49.2^{\circ}[/tex]
From basic. trig for right triangles (refer to first paragraph in answer):
[tex]\sin 49.2^{\circ}=\frac{AB}{32},\\AB=32\sin 49.2^{\circ}=24.2238417809\approx \boxed{24.22}[/tex]
in a fruit basket there were 24 oranges and the rest were lemos if 20% of fruits were lemons how many fruits were there altogether
FAST
Answer:30
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the side length of the base is 17 in and the height of the pyramid is 9 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
The volume of the pyramid is 867 inch^3
Step-by-step explanation:
Here in this question, we are interested in calculating the volume of a square based pyramid.
Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.
V = a^2h/3
where a represents the length of the side of the square and h is the height of the pyramid
From the question, the length of the side of the square is 17 in while the height is 9 in
Plugging these values, we have ;
V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch
can you answere this please? i will give brainleyest
Step-by-step explanation:
Bestie there is nothing attached
Find all the zeroes of 2x⁴-3x³-3x²+6x-2, if you know that two of its zeroes are √2 and -√2.
Answer:
nose es algo q no se puede saber
Megan runs a bakery in which she can sell cakes for $12.95. Write a function for the amount of profit, in dollars, she makes for selling n amount of cakes.
I NEED HELP! I'll make brainliest!
The ages of 10 boys are listed below.
7, 6, 8, 6, 8, 7, 8, 7, 8, 6
Which of the following best describes the data?
1.The data have range 2, and are otherwise unrelated.
2.The data are evenly distributed, with mean 7.1.
3.The data contain outliers, so the mean is not the best measure.
4.The data have no mode.
Answer:
the data has 2 range
Step-by-step explanation:
you can subtract the largest number with the smallest
Answer:
Step-by-step explanation:
The data are evenly distributed with a mean of 7.1
Which statement correctly uses limits to determine an asymptote of g(x)?
Answer:
Step-by-step explanation:
When a limit has the x value approaching infinity, we are talking about end behavior of functions which implies horizontal asymptotes. As x approaches both positive and negative infinity, the tails of each branch of this function approaches 0; therefore, the correct choice for this the third one down.
Answer: c
Step-by-step explanation: got it right
What happens when we have two lines that are
NOT parallel to each other?
They will meet at a point.
They will never meet.
Hi there!
»»————- ★ ————-««
I believe your answer is:
"They will meet at a point."
»»————- ★ ————-««
Here’s why:
For any set of parallel lines given, they will never intercept because of the same slope that they share. This means that if the slopes are different (if the lines are not parallel), they will eventually have a point of intersection.»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
7. George has some quarters and some dimes. He has 6 more dimes than quarters and all of
the coins he has are worth $3.05. How many dimes and quarters does George have?
Answer:
the answer will be 18 ohkay but they will eill have more dimes than quarters
Answer:
Please the answer from the other user is completely wrong, the real answer is 7 quarters and 13 dimes
Step-by-step explanation:
0.1 (x+6) + 0.25x = 3.05
0.35x = 2.45
x = 7
therefore,
7 quarters
x+6 dimes = 13 dimes
PLEASE GIVE BRAINLIEST
sam has a rope that is 38 feet long. He cuts the rope into 2 pieces. One piece is 1.5 feet long .
How long is the other piece?
Answer:
36.5 feet long.
Step-by-step explanation:
38-1.5 is equal to 36.5, you subtract to find the other number, therefor one piece is 1.5 feet long and the other is 36.5 feet long.
Answer:
36.5 feet long
Step-by-step explanation:
38 - 1.5
= 36.5