A line passes through A( - 1 , 3) & B(0 , 2).
Prove:A , B , C(1 , 1) are collinear.
Proof:We know that,
Slope of a line passing through the co - ordinates (x₁, y₁) and (x₂ , y₂) is :
m = (y₂ - y₁)/(x₂ - x₁)
Let,
x₁ = - 1 x₂ = 0 y₁ = 3 y₂ = 2Hence,
→ m = (2 - 3)/( 0 - ( - 1))
→ m = - 1/1
→ m = - 1
Now,
Equation of a line ⟹ y - y₁ = m (x - x₁)
Putting the values we get,
→ y - 3 = - 1(x - ( - 1))
→ y - 3 = - x - 1
→ y + x = - 1 + 3
→ x + y = 2
Hence, the equation of the line is x + y = 2.
Now,
we have to prove that,
A , B , C are collinear.
If three points are collinear then the area of the triangle formed by them will be zero. Three points are collinear if the slope of line passing through the line segment are equal.i.e.,
Slope of AB should be equal to Slope of BC.
We have;
Slope of AB = - 1.
→ - 1 = ( 1 - 2)/(1 - 0)
→ - 1 = - 1/1
→ - 1 = - 1
Hence, A , B , C are collinear points.
I hope it will help you.
Regards.
30 POINTS!
Servers’ Collected Tips
Customers
54
46
34
67
52
22
49
64
55
80
38
42
Tips ($)
$92
$80
$76
$121
$109
$43
$87
$114
$99
$174
$88
$91
a) Create a scatterplot displaying the data in the table. Be sure to include a linear trend line.
Answer:
for A i do not know
B. 1.875x+12.25
C.50
B.track the number of customers served and the amount of tips collected per day
Step-by-step explanation:
Answer:
here is a
Step-by-step explanation:
sorry Im late
10 A man spends 88% of his salary. He now has £216 left.
What is the man's salary?
Answer:
£1,800
Step-by-step explanation:
passes through (8,-6) perpendicular to 2x+y=-4
Answer: y = 0.5x - 10
Step-by-step explanation:
2x + y = -4
y = -2x - 4
perpendicular, so slope = 1/2
y + 6 = (1/2)(x - 8)
y = (1/2)x - 10
Half a number increased by 4 is the same as six less than that number
Answer:
the number is 20
Step-by-step explanation:
Denote the number as "x",
write out the problem:
(1/2(x)) + 4 = x - 6
inverse operations
(1/2(x)) + 4 = x - 6
+6 +6
(1/2(x)) + 10 = x
-(1/2(x)) -(1/2(x))
10 = ((1/2)x)
*2 *2
20 = x
1. Henry is using a total of 40 ft. of lumber to make a bookcase. The left and right sides of the bookcase are each 8 ft. high. The top, bottom, and two shelves are all the same length, labeled .
Part A: Construct an equation to model the situation. (5 points)
Part B: Solve the equation. Show all your steps.
(5 points)
Part C: Use the solution to answer the question in a complete sentence. (5 points)
Answer:
Part A:
40 = 16 + 4·s
Part B:
The length of the top and bottom and the two shelves are each = 6 ft.
Part C:
The width of the bookshelf is 6 feet
Step-by-step explanation:
The given parameters are;
The length of the lumber Henry is using to make the book case = 40 ft.
The height of the left and right side of the book case = 8 ft. each
The length of the top and bottom and the two shelves are each = s
Therefore, we have;
Part A:
The equation is given as follows;
40 = 8 × 2 + 4·s = 16 + 4·s
40 = 16 + 4·s
Part B:
The solution of the equation is given as follows;
40 = 16 + 4·s
4·s= 40 - 16 = 24
s = 24/4 = 6 ft.
s = 6 ft.
The length of the top and bottom and the two shelves are each = 6 ft.
Part C:
The width of the bookshelf is 6 feet
Decimals Decimals Decimals
Answer:
b
Step-by-step explanation:
.7 is in the tenths place. so it is .70
Answer:
B. .7 is equal to .70 which is a C for her grade
The linear function y
2 + 3
Answer:
your answer is 5y
Step-by-step explanation:
could someone explain how to do this? i don't get it
Answer:
y=29x+5, I think that's the answer
please answer. i need help.
17. True (bc anything multiplied by 0 equals 0)
18. True (bc 13=13)
19. True (bc 6=6)
20. True (bc 7(x-3)=7x-21)
21. True (bc the negative sign cancels out the positive sign)
22. True (bc y=3 and 3=y are the same)
23. True (bc they are the same just rearranged)
24. True (because x and z both equal -1)
25. True (anything multiplied by 1 stays the same)
The ratio of two numbers is 2:5 and their difference is 63. The larger number is
Answer:
The larger number is 105
Step-by-step explanation:
When proportionally increased the numbers 2:5 can be multiplied by 21.
This gives you a ratio of 42:105
The difference of those numbers are 63
Hope that helps, let me know if this answer does or don't!
The school cafeteria orders 4 cartons of regular milk for every 5 cartons of chocolate milk. The ratio of cartons of regular milk to cartons of chocolate milk is 4 to 5. Type a ratio that is equivalent to 4 to 5
Answer:
20:25
Step-by-step explanation:
To find an equivilant Ratio is very simple. You only need to multiply both numbers by the same number. FOr example 3:6. To find an equivilant ratio for that you can multiply 3 by 4 and 6 by 4 to get 12:24 or 1:2
Hope this helps!
Divide 36 into two parts in such a way that 1/5 of one part is equal to 1/7 of the other.
Answer:
I think its going to be 1/6
Step-by-step explanation:
Add.
-7/2 + 5/4
PLS HELP
Answer:
-9/4 or -2 1/4 (it is the same amount)
Step-by-step explanation:
2 lbs. of halibut costs $16. what does it cost for 7 lbs. of halibut
Answer:$64
Step-by-step explanation:2x3=6 16x3=48 48+16=$64
Can someone help? I will mark brainlest whenever I get the option to!!
Answer:
8. x=18 9. x=33 10. x=65 11. x=19 12. x=59
Step-by-step explanation:
8. The angles are essentially vertical so they have to be equal to each other.
42=2x+6 subtract 6 from both sides 36=2x x=18
9. These angles are supplementary and equal 180 when added together.
98+(3x-17)=180 subtract 98 and add 17 to both sides 3x=99 x=33
10. Angles are essentially vertical so they are equal to each other.
2x+2=3x-63 add 63 to both sides subtract 2x from both sides 65=1x
11. Angles are supplementary so they equal 180 when added together.
112+(4x-8)=180 subtract 112 and add 8 to both sides 4x=76 x=19
12. Angles are vertical so they are equal to each other.
(3x-33)=(2x+26) add 33 to both sides and subtract 2x 59=1x
Can someone tell me the answer plz I’ll give you a brainlist and points NO WRONG ANSWERS
Answer:
x=43
Step-by-step explanation:
Subtract 61 from both sides giving:
x=43
Answer: x=43
Step-by-step explanation:
subtract 61 on both sides to isolate the variable. Divide 1x by 43 to get 43
Please look at the picture! Thank you I
Answer:
I think it’s the line before 0,
Step-by-step explanation: if it’s wrong I’m truly sorry Im just trying to help the best I can
Help Needed!! Find The Measure Of Angle A In The Triangle
Answer:
A=40°
Step-by-step explanation:
All angles in a triangle add up to 180°, so we take 60 away from 180 because we know that angle.
180-60=120
Next, we add up the number of x,
10x+20x=30x
Third, we need to find out what x is, so we divide 120 by 30, which gives us 4.
x=4
to find out what 10x is (A), we multiply 4 by 10
4×10=40
A=40
what is the range of the function?
a. 1,2,3,4
b. 2,4,9,16
c. 1,2
d. 1,2,3,4,9,16
Answer:
the answer is b
can someone please helpppp
what would be the perpendicular slope to 8
Answer:
-1/8
Step-by-step explanation:
perpendicular slope to 8 is -1/8
There were
32
3232 volunteers to donate blood. Unfortunately,
n
nn of the volunteers did not meet the health requirements, so they couldn't donate. The rest of the volunteers donated
470
470470 milliliters each.
How many milliliters of blood did the volunteers donate?
Answer:
470(32 - n)
Step-by-step explanation:
Here are the given:
> 32 volunteers
> n volunteers who didn't donate
> 470 mL each
So your expression is: 470(32 - n).
Why?
Subtract the 32 volunteers who want to donate blood from the volunteers who were not able to donate then multiply it by 470.
Answer:
dam just imagen that in real life
Step-by-step explanation:sorry haha ik its not about that but it had to be said
The temperature in
Kansas is 95°Fand the
temperature in Arizona is
14° cooler. What is the
temperature in Arizona?
Answer:
it is 81 degrees in Arizona
Step-by-step explanation:
95-14 is 81
Tenley is making a square frame for her painting. She is using 4 pieces of wood that are each 2.25 feet long.
How much wood will Tenley use to make the frame?
Tenley will use ____________ feet of wood.
Answer:
Tenley will use _9_ feet of wood.
Step-by-step explanation:
The key here is to multiply 4 by 2.25. If just adding 2.25 4 times is easier, go for that. Either way the correct answer will be 9 feet.
f(x) = -x2 – 10
Find f(-4)
Answer:
-2
Step-by-step explanation:
susitute for x and solve
PLEEASE help as soon as posible
factor 18x^2 - 98y^2
Answer:
(3x+7y)⋅(3x−7y)
Step-by-step explanation:
hopefully this helps!
please help me quickly!
Answer:
6xy+4
Step-by-step explanation:
What is 3/7 to the 2nd power?
Answer:
9/49
Step-by-step explanation:
(3/7) 2
(3/7)(3/7)=
3^2/7^2
=9/49
I hope this is right!
Write the equation of the line that contains the points (0, -5) and (3,-1).
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Can I get some help with this please?
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