Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation
box below.
M(0,6) N(6,0)
Answers
Answer:
\(y + x - 6 = 0\)
Step-by-step explanation:
Given
\(M(0,6) \ and \ N(6,0)\)
Required
Find the equation of the line
First, the slope of the line has to be calculated using the following formula;
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
\(where\ (x_1,y_1) = (0,6) \ and \ (x_2,y_2) = (6,0)\)
So, the equation becomes
\(m = \frac{0 - 6}{6 - 0}\)
\(m = \frac{-6}{6}\)
\(m = -1\)
The equation of the line can then be calculated using
\(m = \frac{y - y_1}{x - x_1} \ or \ m = \frac{y - y_2}{x - x_2}\)
\(Using \ m = \frac{y - y_1}{x - x_1}\)
\(-1 = \frac{y - 6}{x -0}\)
\(-1 = \frac{y - 6}{x}\)
Multiply both sides by x
\(-1 * x = \frac{y - 6}{x} * x\)
\(-x = y - 6\)
Add x to both sides
\(x -x = y - 6 + x\)
\(0 = y - 6 + x\)
Reorder
\(y + x- 6 = 0\)
\(Using \ m = \frac{y - y_2}{x - x_2}\)
\(-1 = \frac{y - 0}{x - 6}\)
\(-1 = \frac{y}{x - 6}\)
Multiply both sides by x - 6
\(-1 * (x-6) = \frac{y}{x - 6} * (x-6)\)
\(-1 * (x-6) = y\)
\(-x+6 = y\)
Add x - 6 to both sided
\(x - 6 -x+6 = y +x - 6\)
\(0 = y + x - 6\)
\(y + x - 6 = 0\)
Hence, the equation of the line is \(y + x - 6 = 0\)
Related Questions
Mackey invested some money in an account paying 6% interest for one year. She invested $1000 more than this amount in an account paying 8.5%. How much did she invest in total if the total interest earned in the year was $737.50?
Answers
Step-by-step explanation:
Let's assume the amount Mackey initially invested in the 6% account is x dollars.
According to the given information, Mackey invested $1000 more than x in the 8.5% account, which means she invested (x + $1000) dollars in that account.
The total interest earned from the 6% account would be 0.06x dollars, and the total interest earned from the 8.5% account would be 0.085(x + $1000) dollars.
The total interest earned in the year is given as $737.50, so we can set up the equation:
0.06x + 0.085(x + $1000) = $737.50
Simplifying the equation:
0.06x + 0.085x + 0.085($1000) = $737.50
Combining like terms:
0.145x + $85 = $737.50
Subtracting $85 from both sides:
0.145x = $737.50 - $85
0.145x = $652.50
Dividing both sides by 0.145:
x = $652.50 / 0.145
x ≈ $4500
Therefore, Mackey initially invested approximately $4500 in the 6% account, and she invested $1000 more, which means she invested a total of $5500.
$4500
$4500
$4500
$4500
Todd swam 10 laps around the pool and walked on the treadmill a total of 5.2 miles. It took him 2.3 minutes to swim each lap and 45.4 minutes to work on the treadmill. How long did it take him to swim and walk?
Answers
Answer:
Step-by-step explanation:
Was so she just wanted
Answer:
23 minutes in the pool
Step-by-step explanation:
please help! giving brainlest if explained
Answers
Answer:
Hello, Im Mack, | Hope your doing well :)
Here is the Answer Ive got for you:
Step-by-step explanation:
Here is the Table filled out with the correct Values:
Speed Equation: (Velocity=distance/time)
Distance: Distance traveled: Time traveled: Speed:
0-2 2 Meters 20 Secs 10secs/m
4-6 6 Meters 30 Secs 5secs/m
8-10 10 Meters 50 Secs 5secs/m
Comment if you need further help, and I will rely asap,
Hope I helped you out :)
Have a great day my friend and best of luck to your studies :)
can you help me please
Answers
Answer:
1,131 sq in.
Multiply length, times width, times height.
▬▬▬▬▬▬The math▬▬▬▬▬▬
8.7
13
10
1,131
▬▬▬▬▬The conclusion▬▬▬▬▬
Hope this helps!
Have a great day.
To test the safety of a car, crash tests will test different types of cars in collision situations. They want to determine in which car the crash test dummy receives the least amount of damage. What is the Dependent Variable?
A Amount of damage to the car
B Amount of collisions
C Amount of damage to the dummy
D Number of dummies
Answers
Answer:
C
Step-by-step explanation:
I think the safety on the car depends on the person inside it.
find the value of x
thank you in advance for your help!
Answers
Answer:
52
Step-by-step explanation:
Answer:
x= 12
Step-by-step explanation:
Please see attached picture for full solution.
Feel free to ask if you have any queries :)
the graph shows four ordered pairs that represent ratios. Which ordered pair represents a ratio that is not equivalent to the others
A.) (2, 12)
B.) (3, 18)
C.) (5, 24)
D.) (6, 36)
Answers
Answer:
C (I forgot the rule, but it is C because it is the only time when the division of both elements does not equal 6. And sorry for my English!)
a 2-quart carton of pineapple juice costs $5.28. what is the price per cup
Answers
Answer:
$0.66 per cup
Step-by-step explanation:
There are 8 cups in 2 quarts, so 5.28/8 is $0.66 per cup.
Answer:
0.66
Step-by-step explanation:
8 cups are in 2 quarts so you going to count 8 cups untill you get 5.28 and then you see how many cents that it is so its 0.66
which of the following rational functions is graphed below?
Answers
Answer:
C
Step-by-step explanation:
Vertical asymptotes= -2,1
Please hurry It's 4 my ixl diagnostic and all scores must be at 700+ my Friday this is 4 a test grade
Answers
Answer:
6.3
Step-by-step explanation:
\(c^{2} - a^{2} = b^{2} \\7^{2} = 49\\3^{2} = 9\\49-9 = 40\\\sqrt{40} = 6.32\)
rounded is 6.3
A fruit juice recipe calls for 2 parts orange juice and 8 parts pineapple juice. Which proportion can be used to find the amount of orange juice, j, that is needed to add to 18 L of pineapple juice?
2 over 8 equals j over 18
8 over 2 equals j over 18
8 over j equals 2 over 18
16 over 18 equals j over 100
Answers
The correct proportion to use to find the amount of orange juice, j, needed to add to 18 L of pineapple juice is:
2/8 = j/18
This proportion relates the ratio of orange juice to pineapple juice in the recipe (2:8) to the amount of orange juice needed to add to 18 L of pineapple juice. By cross-multiplying, we can solve for j as follows:
2/8 = j/18
218 = 8j
36 = 8*j
j = 36/8
j = 4.5
Therefore, you would need to add 4.5 L of orange juice to 18 L of pineapple juice to create the fruit juice recipe that calls for a ratio of 2 parts orange juice to 8 parts pineapple juice.
Answer:
2 over 8 equals j over 18Step-by-step explanation
2 over 8 equals j over 18
This proportion represents the ratio of orange juice to pineapple juice in the recipe. By setting up the proportion, we can solve for the value of 'j,' which represents the amount of orange juice needed.
So, the correct proportion is:
2 over 8 equals j over 18
Use the distributive property to remove the parentheses. Simplify your answer as much as possible. 2/3(5+9u)
Answers
Answer: 18u + 10/3
Step-by-step explanation: sorry if im wrong
Answer:
\(\boxed{\sf 6 u + \dfrac{10}{3}}\)
Explanation:
Given expression:
\(\sf \rightarrow \dfrac{2}{3} (5+9u)\)
distribute inside parenthesis
\(\sf \rightarrow \dfrac{2}{3} (5)+ \dfrac{2}{3} (9u)\)
multiply variables
\(\sf \rightarrow \dfrac{10}{3} + \dfrac{18}{3} u\)
simplify following
\(\sf \rightarrow 6 u + \dfrac{10}{3}\)
What is the surface area of this figure?
Enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
Area of a triangle: 1/2(B*H)
in this case, the triangle on the top has an area of 96 for both sides in the front
the two sides on the left and right of the triangle has an area of 240 square feet
and the rectangle on the bottom has an area of
216+324+108+240+96= 984 square ft
I did it
Halp meh p|z!!!!! I already asked this exact question but I accidentally put in the wrong screenshot.
People said that both of these equal the same answer but I don't think that the answers can be repeated...
I'm not sure. Maybe they can.
But I just need to double check.
Answers
Answer:
it's A/ m= -2.
PLEASE HELP ME WITH MATH LOL
Answers
Answer:
a
Step-by-step explanation:
it is a straight line coming out of the origin
Coming straight out of the orgin straight line
Which expression is equivalent to -1/3 ( 6x + 15 ) - 3?
a) -2x + 12
b) -2x + 2
c) -2x - 2
d) -2x - 8
Answers
The correct answer is (D) -2x - 8.
To simplify the expression -1/3 ( 6x + 15 ) - 3, we can first apply the distributive property to the term in parentheses:
-1/3 ( 6x + 15 ) - 3 = -1/3 * 6x - 1/3 * 15 - 3
Then we can simplify using the properties of multiplication and division:
-1/3 * 6x - 1/3 * 15 - 3 = -2x - 5 - 3
Finally, we can combine like terms:
-2x - 5 - 3 = -2x - 8
The correct answer is therefore (D) -2x - 8.✅
i dont understand how to do 9, 10, 11, and 12.
instead of solving it, can you give me an example of how to solve each?
Answers
Okay, let’s replace the numbers.
(3m/1n)^-3
Distribute the exponent.
(3m)^-3 / (1n)^-3
To get rid of the fact that th exponents are negative, we can flip the fraction!
(1n)^3 / (3m)^3
Now we distribute the exponent to the numbers and variables
1n^3 / 27m^3
That is your example answer for #9.
10. -(2a)^-2 b°
Anything to the power of 0 is 1.
-(2a)^-2
Since we have a negative exponent, flip the fraction
-(1/(2a)^2)
-1/4a^2
That is your example answer for 10.
11) 2m^-1/3(ab)^-4c^-7
Flip the exponents with negative powers to make it positive
2(ab)^4 c^7 / 3m
distribute the 4 exponent
2a^4b^4c^7/3m
That is your example answer for 11.
12) 4 x y^-1 z^0 / v^-3
Anything to the power of 0 is 1.
4 x y^-1 / v^-3
Flip the variables that have a negative exponent.
4xv^3/y
That is your example answer for 12
Answer:
9)Okay, let’s replace the numbers. (3m/1n)^-3Distribute the exponent. (3m)^-3 / (1n)^-3To get rid of the fact that th exponents are negative, we can flip the fraction!(1n)^3 / (3m)^3Now we distribute the exponent to the numbers and variables1n^3 / 27m^3That is your example answer for #9. 10. -(2a)^-2 b°Anything to the power of 0 is 1. -(2a)^-2Since we have a negative exponent, flip the fraction-(1/(2a)^2)-1/4a^2That is your example answer for 10. 11) 2m^-1/3(ab)^-4c^-7Flip the exponents with negative powers to make it positive2(ab)^4 c^7 / 3mdistribute the 4 exponent 2a^4b^4c^7/3mThat is your example answer for 11. 12) 4 x y^-1 z^0 / v^-3Anything to the power of 0 is 1. 4 x y^-1 / v^-3Flip the variables that have a negative exponent. 4xv^3/yThat is your example answer for 12
Step-by-step explanation:
Tristan is comparing two number patterns based on the information below.
Both patterns start with the number 1.
Pattern A follows the rule “add 3”.
Pattern B follows the rule “add 4”.
How do each of the first 5 terms in Pattern A compare to the first 5 terms in Pattern B? As part of your answer, list the first 5 terms of each pattern.
Answers
Answer:
Pattern B gets larger fast since 4 is greater than 3.
explanation:
Pattern A is ; 1, 4, 7, 10, 13
Pattern B: 1, 5, 9, 13, 17
as u can see pattern b goes up faster
Each week Sara's science teacher gives a 15
-point quiz.
Her current scores are shown in the table.
What is Sara's mean quiz score?
Answers
Answer:31
Step-by-step explanation:
Which would be the best name for a function that takes the size of an engine and returns the maximum speed of a car?
Answer Choices: Size(speed), Engine(speed), Speed(size), Time(speed)
Answers
Answer:
Size
Step-by-step explanation:
Just got the answer out
Write an equation for the following graph.
Answers
Answer:
y=-1/2x+6
Step-by-step explanation:
y=-2/4x +6
An ant is at the top of a tree 11 meters tall, directly overhead of its home, which is 0.1 meter under the ground. What is the distance between the ant's current location and her home?
Answers
Answer: Should be 11.1 distance
Step-by-step explanation:
11+0.1 =11.1
11 tall tree .1 blow ground = 11.1 above home
I need help please!!!!
Answers
Answer:
A
Step-by-step explanation:
:)
The reading on a car’s speedometer may have an error up to 6.25%. The speed limit on a road is 65 miles per hour.
The speedometer shows 67 miles per hour.
Is the car definitely going over the speed limit?
Yes
No
Explain your thinking.
Answers
The speed limit is 65. Accounting for a 6.25% error, then there is a range of speeds that could be considered 65.
The range:
65(0.9375) = 60.9375
65(1.0625) = 69.0625
So, any speed within that range is within the error zone. Therefore, a reading of 67 is not necessarily speeding.
Estimate the total surface area of the Triangular prism represented by the net below
Answers
Answer:
Step-by-step explanation:
it would be c. 116
This is because each rectangle has an area of 36 and there are 3 which equals 108
Also each triangle has an area of 3.9 and there are two so it is 7.8 for both of the triangles
108+15.6 is 115.8
That is approximately 116
That is why its 116
HEEEELLLLLLLPPPPPPPP
The hexagon PQRSTU is plotted on a coordinate plane with vertices P(–1, 0), Q(–1, 3), R(1, 4), S(2, 5), T(4, 4), and U(4, 0). What is the hexagon's perimeter?
15.8 units
14.4 units
17.8 units
12.0 units
Answers
pls help i really need to get this done
Answers
PLEASE HELP!!
What is the perimeter of a rectangle with a length of 15 meters and a width of 8 meters?
16 meters
23 meters
30 meters
46 meters
Answers
Answer:
46
Step-by-step explanation:
2*15+2*8 = 30+16=46
Answer:
46
Step-by-step explanation:
add all of the sides together.
15+15+8+8=46
Keira said that if 6 tickets are sold, there should be 2 tickets left. Is Keira correct?
Answers
According to Keira, if 6 tickets are sold, there should be 2 tickets left. However, we don't have any information about the initial number of tickets available.
If the total number of tickets initially was 8, and 6 tickets were sold, then there would indeed be 2 tickets left, supporting Keira's statement.
However, if the total number of tickets initially was less than 8, or if the statement doesn't specify the initial number of tickets, we cannot determine if Keira's statement is correct.
Therefore, without additional information, we cannot determine the accuracy of Keira's statement.
Jay has 195 baseball cards, Jen has 46 more than Jay, how many more cards does Jen have than Jay? (I will give brainliest)
Answers
Answer:
the total card of Jen will be 241 and 46 more cards Jen have than jay