Please Help! Answer full step by step.
Triangle ABC has vertices A(- 3, - 4), B(16, - 2) and C(13, - 10) . Show algebraically that ABC is a right angled triangle.
Answers
Triangle ABC has the three sides AB, BC, and AC.
Let's find the slope of each line. We'll use the slope formula
Let's start with the slope of line AB.
A = (-3, -4) = (x1,y1)
B = (16, -2) = (x2,y2)
m = slope
m = (y2-y1)/(x2-x1)
m = (-2-(-4))/(16-(-3))
m = (-2+4)/(16+3)
m = 2/19
The slope of line AB is 2/19. I'll keep it in fraction form.
We'll use this later, so let p = 2/19.
---------------
Repeat those steps to find the slope of BC
B = (16, -2) = (x1,y1)
C = (13, -10) = (x2,y2)
m = (y2-y1)/(x2-x1)
m = (-10-(-2))/(13-16)
m = (-10+2)/(13-16)
m = -8/(-3)
m = 8/3
The slope of line BC is 8/3.
Let q = 8/3 so we can use it later.
---------------
Now find the slope of line AC.
A = (-3, -4) = (x1,y1)
C = (13, -10) = (x2,y2)
m = (y2-y1)/(x2-x1)
m = (-10-(-4))/(13-(-3))
m = (-10+4)/(13+3)
m = -6/16
m = -3/8
The slope of line AC is -3/8
Let r = -3/8.
---------------
To recap everything so far, we have
p = slope of line AB = 2/19q = slope of line BC = 8/3r = slope of line AC = -3/8We can see that,
p*q = (2/19)*(8/3) = 16/57q*r = (8/3)*(-3/8) = -1p*r = (2/19)*(-3/8) = -6/152 = -3/76Of those slope multiplications, q and r multiply to -1 is what we should focus on. If two slopes multiply to -1, then their lines are perpendicular. This applies to any perpendicular lines where neither line is vertical, and neither is horizontal.
The fractions 8/3 and -3/8 are negative reciprocals of one another. We flip the fraction and flip the sign from positive to negative, or vice versa. This is another way to see we have perpendicular slopes.
So in short, we've shown that BC and AC are perpendicular, and therefore triangle ABC is a right triangle.
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To solve this problem a completely different way, we could follow this outline:
Step 1) Find the length of each side AB, BC, and AC. Use the distance formula. Step 2) Apply the pythagorean theorem converse. If you can show a^2+b^2 = c^2 is true, then the triangle with sides a,b,c is a right triangle, where c is the longest side (hypotenuse) opposite the right angle.Through step 1, you should find that,
AB = sqrt(365)BC = sqrt(73)AC = sqrt(292)Let a = sqrt(73), b = sqrt(292), c = sqrt(365). You should find that a^2+b^2 = c^2 is a true statement based on those values, and therefore we have a right triangle. The longest side is AB = sqrt(365), making angle C to be the 90 degree angle. The diagram is shown below. I used GeoGebra to make the diagram.
Related Questions
Which of the following is equivalent to the expression below?
(– 3m + 5) + (m – 11)
A: – 2m – 6
B: 2m – 16
C: 4m – 16
D: – 4m – 6
Answers
What is the amplitude of the graph of y = 2 sin (4x – 1) + 3?
A. 1
B. 3
C. 2
D. 4
Answers
Answer: 2 is the answer
Step-by-step explanation:
what is the value of (-35) divided by (5/7)?
Answers
Answer:
-49
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Linear Equation
24 + 6a = 6 - 4a
Please help me with this ASAP
Answers
Answer:
Step-by-step explanation:
1. Combine Like Terms
24 + 6a = 6 - 4a
+4a +4a
24 + 10a = 6
-24 -24
10a = -18
___ ___
10 10
a= -1.8
Divide $81 in ratio 4:5
Answers
Answer:
36:45
Step-by-step explanation:
$81. u add the ratios 4+5=9
$81/9=9
9*4=36
9*5=45
Whats 9+10?? HELPPPPP
Answers
Answer:
19
Step-by-step explanation:
9+10=19
add the ones place (0+9) then the tens place (1+0).
A picture called a mosaic was made
from 172,435 small clay tiles. What is
the value of the digit 2 in 172,435?
Answers
Sandra has a bag of animal cookies. The bag contains the cookies below. What is the probability that Sandra chooses a tiger cookie first, eats it, and then
selects an elephant cookie?
Answers
Answer:
3/26
Step-by-step explanation:
Add 9+9+5+3 = 26
Total of 3 Tiger Cookies
3/26
help pleasee!!!! math
Answers
Answer:
its 90
m(PZR)=PR )
Hopefully its helpful and correct
Can someone help me with this
Answers
Answer:
∡J and ∡K are complementary
Step-by-step explanation:
since ∡L is a right angle, that means it measures 90 degrees
since there are a total of 180 degrees inside a triangle, angles J and K must add up to 90 which means they are complementary
permudahkan. 1. 3/4m (4m+16n) +m/n.
Answers
3/4m(4m+16n) + m/n open the bracket of equation,
3/4m(4m+16n) + m/n = 3+ 12n/m + m/n
now multiply and devide by mn on RHS,
3/4m(4m+16n) + m/n = (3mn+12n²+m²)/mn
PLZ PLZ HELP I DONT UNDER STAND THIS!!
Many games involve chance and they usually involved either dice or cards. For this activity, we will look
at a common game called 7‐11 where two dice are rolled. If the roll adds up to 7 or 11, the player wins.
If the roll adds up to 2, 3, or 12, the player loses. If there is any other sum, it is a draw (no winner or
loser). Use this two‐dice roll scenario to complete the problems below.
. What is the probability for each of the sums below? NOT A MULTIPLE CHOICE.
2=
3=
7=
11=
12=
Answers
Answer:
See below.
Step-by-step explanation:
See the attached chart that shows all outcomes for two dice.
There are 36 possible outcomes, all equally likely (if the dice are fair!).
The probability of getting a sum of 2 is 1/36 (only one way to get 2: both dice show 1).
The probability of getting a sum of 3 is 2/36 = 1/18.
The probability of getting a sum of 7 is 6/36 = 1/6 (the most likely sum!)
(Notice how all the sum = 7 outcomes like on a diagonal in the chart?)
The probability of getting a sum of 11 is 2/36 = 1/18.
The probability of getting a sum of 12 is 1/36.
In a survey of 100 students of Surkhet, 65 like to play football, 55 like
to play cricket and 35 like to play both football as well as cricket. How
many students did not like both events? Illustrate the above information
in Venn diagram.
Answers
Answer:
15 students do not like either sport
Step-by-step explanation:
See the attached image.
Step 1: put 35 in the "like to play both" (intersection) area.
Step 2: subtract those 35 from the 65 football players. 65 - 35 = 30 players like football but not cricket. Put 35 in the football but not cricket area.
Step 3: subtract 35 from the 55 cricket players. 55 - 35 = 20 players like cricket but not football. Put 20 in the cricket but not football area.
Step 4: Add the 30 + 35 + 20 = 85 together. So 85 players are accounted for as players of one or more sports.
Step 5: 100 - 85 = 15 must be the number of students who did not like either sport. Put 15 in the area outside both circles.
HELP . I'm not sure what the range is.
Answers
Answer:
y<-1
Step-by-step explanation:
This exponential function will never approach y=-1, but it goes "under" the line of -1, so it is y<-1
The art department at a school sold 323 tickets
to an art show, for a total of $790. Students paid
$2 for tickets, and non-students paid $3.50. The
principal asked how many non-students
attended the art show.
Answers
Answer:
96 students
Step-by-step explanation:
x + y = 323
2x + 3.5y = 790
=> by elimination
2x+3.5y=790
2x+ 2y = 646
__________-
1.5y = 144
y = 144/1.5 = 96
The system of equations are
x + y = 323
2x + 3.5y = 790
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the system of equations be A and B
Now , the number of tickets sold = 323 tickets
Let the number of students be = x
Let the number of non students = y
So , x + y = 323 be equation (1)
The cost for students = $ 2
The cost for non students = $ 3.50
The total cost of all the tickets = $ 790
So , 2x + 3.5y = 790 be equation (2)
On simplifying the equations , we get
Multiply equation (1) by 2 , we get
2x + 2y = 646 be equation (3)
Subtracting equation (3) from equation (4) , we get
1.5y = 144
Divide by 1.5 on both sides of the equation , we get
y = 96
So , the number of non students be y = 96
Substituting the values of y in equation (1) , we get
x = 323 - 96 = 227 students
Now , the graph of the equations is plotted and the point of intersection is the solution ( 227 , 96 )
Hence , the equations are solved
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
What is the length of the hypotenuse?
Answers
Answer:
h=15feet.
Step-by-step explanation:
using Pythagoras theorem
h²=p²+b²
h²=12²+9²h²=144+81h=√225h=15feet.hope it helps.
stay safe healthy and happy.[tex]\huge\bold{To\:find:}[/tex]
✎ The length of the hypotenuse.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\sf\purple{The\:length\:of\:the\:hypotenuse \:"c"\:is\:15\:feet.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
Using Pythagoras theorem, we have
[tex]( {perpendicular})^{2} + ( {base})^{2} = ( {hypotenuse})^{2} \\⇢ ({12 \: ft})^{2} + ( {9 \: ft})^{2} = {c}^{2} \\ ⇢ 144 \: {ft}^{2} + 81 \: {ft}^{2} = {c}^{2} \\ ⇢ 225 \: {ft}^{2} = {c}^{2} \\ ⇢ \sqrt{225 \: {ft}^{2} } = c \\ ⇢ \sqrt{15 \times 15 \: {ft}^{2} } = c \\ ⇢ 15 \: ft = c[/tex]
[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:hypotenuse\:is\:15\:feet.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex]( {12 \: ft})^{2} + ( {9 \: ft})^{2} = ( {15 \: ft})^{2} \\⇝144 \: {ft}^{2} + 81 \: {ft}^{2} = 225 \: {ft}^{2} \\ ⇝225 \: {ft}^{2} = 225 \: {ft}^{2} \\ ⇝L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Nancy is going to do some painting in her room. The paint she is using costs $12.34 per gallon. It measures 11 feet by 13 feet and has an 8-foot tall ceiling. What is the total area she will paint
Answers
Answer: [tex]527\ ft^2[/tex]
Step-by-step explanation:
Given
Cost of paint is [tex]\$12.34\ \text{per gallon}[/tex]
Dimension of room is [tex]11\times 13\times 8\ ft^3[/tex]
There are five side of wall to be painted leaving only the floor
Area is given by
[tex]\Rightarrow 2[8\times 11+8\times 13]+11\times 13\\\Rightarrow 2\times 8[24]+143\\\Rightarrow 384+143\\\Rightarrow 527\ ft^2[/tex]
what is 2 1/4% of 400
Answers
Answer:
900
Step-by-step explanation:
2 ¼% is equal to 225%
Doubled 400 to get 200% Then divide 400 by 4 to find 25% After that add these together to get 225%.225% = 900Help pls Help pls Help pls Help pls Help pls
Answers
Answer: The ansswer is B
Step-by-step explanation:
Answer: The answer is D
Step-by-step explanation: hope this helps
Expand 2x(5x-2)
PLEASEEEEEEEE!!!!!!!!!!!!
Answers
Answer:
2x(5x-2) = 10(x^2) - 4x
PLEASE GIVE BRAINLIEST
Evaluate 4 - 2 f when f =1
Answers
Answer:2
Step-by-step explanation:because 2f= 2 so 4-2=2 i am so sorry if its wrong
Answer:
2
Step-by-step explanation:
4-2f
4-2(1)
4-2=
2
A group of market women sell at least one of yam, plantain and maize.12 of them sell maize,10 sell yam and 14 sell plantain,5 sell plantain and maize,4 sell yam and maize,2 sell yam and plantain only ,while 3 sell all the three items.How many women are in the group?
Answers
Let the three items be M, Y and P.
n{M ∩ Y} only = 4-3 = 1
n{M ∩ P) only = 5-3 = 2
n{ Y ∩ P} only = 2
n{M} only = 12-(1+3+2) = 6
n{Y} only = 10-(1+2+3) = 4
n{P} only = 14-(2+3+2) = 7
n{M∩P∩Y} = 3
Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.
Lilly bought strawberries and blueberries for a picnic. Strawberries were on sale for $2.50 per pound, and blueberries were on sale for $4.00 per pound. She bought a total of 8 pounds of berries and spent $26.75 altogether. How many pounds of strawberries and blueberries did she purchase for the picnic?
A. 4.0 pounds of strawberries and 1.6 pounds of blueberries
B. 4.5 pounds of strawberries and 3.5 pounds of blueberries
C. 1.6 pounds of strawberries and 4.0 pounds of blueberries
D. 3.5 pounds of strawberries and 4.5 pounds of blueberries
Answers
Answer: a
Step-by-step explanation:pls brainly me
If a movie begins at 5:10 p.m. and runs for 1 hour and 45 minutes, what time will the movie end?
(Answer:_:__p.m.)
Answers
Answer:
6:55 p.m
Step-by-step explanation:
Hour connects with hour therefore, 5 + 1 = 6
Minutes connects with minutes thus, 10 + 45 = 55
Hence it being 6:55 p.m when the movie finishes if it starts at 5:10 p.m.
[tex]solve \: 15 {}^{2} + 20 {}^{2} = {?} [/tex]
Answers
Answer:
I hope this helps YOUUU hehe
Answer:
may be 625
Step-by-step explanation:
15×15 225
20×20 400
225+400
625
answer correctly please !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
Answer:
7.18
Step-by-step explanation
4* COS(23) = 3.682
3.5+3.682 = 7.182
help fr now i am in danger x_x
Answers
Answer:
B, it's a reflection over the y-axis
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
It's B because all your doing is flipping the image over the y-axis
Based on the areas of the squares determine whether the triangle shown is a right triangle
Answers
Answer:
The answer is "triangle ABC is not a right triangle".
Step-by-step explanation:
For a right-angle triangle:
Its square upon on longest or triangular edges is equivalent to the total of the other two squares
Its parameters indicated throughout the question are;
Square of lateral length [tex]A = 7 \ inch^2[/tex]
The square of lateral length [tex]B = 18 \ inch^2[/tex]
The square of lateral length [tex]C=27\ inch^2[/tex]
Thus, the longest side is C, as well as the size [tex]inch^2[/tex] of the squares of its two sides, is[tex]7 + 18 = 25 \ inch^2[/tex], lower than square [tex]C = 27\ inch^2[/tex], hence, the ABC triangle is not correct. Its longest edge is consequently C.
You bought a new water glass. The glass is cone-shaped and has a circular base. It has a
diameter of 3 inches and a height of 7.5 inches. What is the volume of the glass? Use 3.14 to
approximate pi. Round your answer to the nearest tenth.
Answers
Answer:
TO find the answer, first you have to find the formula for volume of a cone-
The formula is
V= 1/3 times base times height
So V= (1/3) (pi3^2) (12)
V= 113.04
By the way for the base you have to find the volume of a circle. I divided the diameter by 2 to find the radius.
and pi is 3.14
GIVING BRAINLIEST!!!!
If <3 Is 110 degrees find the degrees of
<4
<5
<6
Answers
Step-by-step explanation:
angle 4
110-180
=70
angle 5
angle = 110
angle 6
110-180=
70
HOPE IT HELPEDAnswer:
Step-by-step explanation:
angle 4+angle 3=180 degree(being linear pair)
angle 4+110=180
angle 4=180-110
angle 4=70 degree
angle 4=angle 5(being alternate interior angle)
70 degree=angle 5
angle 5+angle 6=180 degree(being linear pair)
70+angle 6=180
angle 6=180-70
angle 6=110 degree