Explain how this graph demonstrates how the equation y = mx can be derived from the two points (1, m) and (x, y).
Answers
The equation y = mx of the graph is a linear equation
The linear equation that demonstrates the relationship on the graph is y = mx
How to determine the equation from the graphThe points on the graph are given as:
(1, m) and (x, y)
Start by calculating the slope (M)
[tex]M = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]M = \frac{y - m}{x - 1}[/tex]
The linear equation is then calculated as:
[tex]y = M(x - x_1) + y_1[/tex]
This gives
[tex]y = \frac{y - m}{x- 1}(x - 0) + 0[/tex]
[tex]y = \frac{y - m}{x- 1}(x)[/tex]
Cross multiply
[tex]yx-y = yx - mx[/tex]
Evaluate the common terms
[tex]-y =- mx[/tex]
Divide both sides by -1
y = mx
Hence, the equation of the graph is y = mx
Read more about linear equations at:
https://brainly.com/question/14323743
Related Questions
According to a Los Angeles Times study of more than 1 million medical dispatches from to , the response time for medical aid varies dramatically across Los Angeles (LA Times website, November 2012). Under national standards adopted by the Los Angeles Fire Department, rescuers are supposed to arrive within six minutes to almost all medical emergencies. But the Times analysis found that in affluent hillside communities stretching from Griffith Park to Pacific Palisades, firefighters failed to hit that mark nearly of the time. The following data show the response times, in minutes, for emergency calls in the Griffith Park neighborhood.
11.8 10.3 10.7 10.6 11.5 8.3 10.5 10.9 10.7 11.2
Based on this sample of ten response times, compute the following descriptive statistics:
a. Mean, median, and mode
b. Range and standard deviation
c. Should the response time of 8.3 minutes be considered an outlier in comparison to the other response times?
Answers
Answer:
A)Mean :10.65
Median =10.7
Mode : 10.7
B)Range = 3.5
Standard deviation :0.89916
C)The response time of 8.3 minutes should be considered an outlier in comparison to the other response times
Step-by-step explanation:
A)
Data : 11.8 ,10.3, 10.7, 10.6, 11.5, 8.3, 10.5, 10.9, 10.7, 11.2
[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{11.8 +10.3+ 10.7+ 10.6+ 11.5+ 8.3+ 10.5+ 10.9+ 10.7+ 11.2}{10}[/tex]
Mean = 10.65
Median: The mid value of the data
Data in ascending order
8.3
10.3
10.5
10.6
10.7
10.7
10.9
11.2
11.5
11.8
n=10(even)
[tex]Median = \frac{(\frac{n}{2})\text{th term}+(\frac{n}{2}+1)\text{th term}}{2}\\Median = \frac{(\frac{10}{2})\text{th term}+(\frac{10}{2}+1)\text{th term}}{2}\\Median = \frac{10.7+10.7}{2}\\Median = 10.7[/tex]
Mode : the most occurring frequency
10.7 is occurring twice while others are occurring once
So, Mode is 10.7
B) Range = Maximum - Minimum=11.8-8.3=3.5
Standard deviation : [tex]\sqrt{\frac{\sum(x-\bar{x})^2}{n}}[/tex]
Standard deviation :[tex]\sqrt{\frac{(11.8-10.65)^2+(10.3-10.65)^2+......+(10.9-10.65)^2+(10.7-10.65)^2+(11.2-10.65)^2}{10}}[/tex]
Standard deviation :0.89916
C)
8.3
,10.3
,10.5
,10.6
,10.7
,10.7
,10.9
,11.2
,11.5
,11.8
For Q1 ( Median of lower quartile )
8.3
,10.3
,10.5
,10.6
,10.7
[tex]Median = \frac{n+1}{2}\text{th term} =\frac{5+1}{2}=3 \text{rd term}=10.5[/tex]
For Q3( Median of Upper quartile )
10.7
,10.9
,11.2
,11.5
,11.8
[tex]Median = \frac{n+1}{2}\text{th term} =\frac{5+1}{2}=3 \text{rd term}=11.2[/tex]
IQR = Q3-Q1=11.2-10.5=0.7
Range :(Q1-1.5IQR, Q3-1.5IQR)
Range :[tex](10.5-1.5 \times 0.7, 11.2-1.5 \times 0.7)[/tex]
Range :(9.45, 10.15)
8.3 does not lie in this interval
So, the response time of 8.3 minutes should be considered an outlier in comparison to the other response times
Which inequality is represented by the graph?
A. y −3/2x−2
D. y≤−3/2x−2
Answers
Answer:
D.)
Step-by-step explanation:
The discount on a floor lamp is 20% off it is on sale for $17 what is the original price of the floor lamp
Answers
Answer:
$21.25
Step-by-step explanation:
x - x(0.20) = 17
0.8x = 17
x = 21.25
Find a formula for the quadratic function whose graph has vertex (2,4) and y-intercept -3.
Answers
Answer:
[tex]y=-\frac{7}{4}x^2+7x-3\\[/tex]
Step-by-step explanation:
y - 4 = C(x - 2)²
y-intercept = -3, so x = 0, y = -3
-3 - 4 = C(2)²
so C = -7/4
[tex]y = -\frac{7}{4}(x-2)^2+4=-\frac{7}{4}(x^2-4x+4)+4=-\frac{7}{4}x^2+7x-7+4\\y=-\frac{7}{4}x^2+7x-3\\[/tex]
what is the slope of a line parallel 18x+15y=90
Answers
Answer:
-6/5
Step-by-step explanation:
Get y by itself to get the slope. So 18x+15y=90. Move 18x to the other side of the equation. Now you have 15y=-18x+90. Divide both sides by 15 to get y by itself. Now it's y= -18/15x + 6. Reduce -18/15 to the simplest fraction. You have y= -6/5x+6. Any number can replace the 6 in the equation to give you a parallel line...it's the slope that makes it parallel, not the y intercept. So y= -6/5x+10 or y=- -6/5x-1 would satisfy your parallel slope equation.
Answer:
[tex]\displaystyle -1\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]\displaystyle 18x + 15y = 90 \hookrightarrow \frac{15y}{15} = \frac{-18x + 90}{15} \\ \\ \boxed{y = -1\frac{1}{5}x + 6}[/tex]
Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so −1⅕ remains as is.
I am joyous to assist you at any time.
Aanya bought 2 1/2 yards of ribbon. She cuts the ribbon into pieces 3/8 of a yard in length. How many pieces does she have?
Answers
My father’s monthly salary is twice what my mother makes in a month. Their combined salary is P27,000
Please help !
Answers
Step-by-step explanation:
mother salary: x
father salary:2x
total salary =27000
therefore 3x=27000
so x=900 (divided by 3)
therefore mother salary = 900
father salary=2multiplied by 900=1800
Answer:
Father's monthly salary is P18,000
Mother's monthly salary is P9,000
Step-by-step explanation:
The problem above can be solved by using "algebraic expressions."
Let x be the father's monthly salary
Let y be mother's monthly salary
Formula: x + y = P27,000
If father's monthly salary is twice than what mother makes, then: x = 2y, which means,
2y (father's salary) + y (mother's salary) = P27,000
First step: 2y + y = P27,000
Second step: 3y = P27,000
Third step: y = [tex]\frac{P27,000}{3}[/tex]
Fourth step: y = P9,000
So, mother's salary is P9,000. This means we can get father's salary:
2y = 2 × P9,000 = P18,000 (this is the value of x)
So, father's salary is P18,000.
If we combine both of their salaries, the product is P27,000.
x + y = P27,000
P18,000 + P9,000 = P27,000
So, this explains the answer.
(30 pts.) I have the answer I just need someone to show me the steps, please!
Which bowl holds more water if it is filled to a depth of four units?
The hyperboloid z= √(1+x^2+y^2) for 1≤ z ≤ 5
The answer is: The hyperboloid holds more water with a volume of [112π/3]
I just need an explanation!!
5 stars and marked the brainiest if the explanation is done well!!
Answers
paraboloid: v = ∫[0,4]πz dz = 8π cone:
v = ∫[0,4]πz^2 dz = 64/3 π
hyperboloid: v = ∫[1,5]π(z^2-1) dz = 112/3 π
when you see that the cone's radius at the top of the water is √8, while the paraboloid's is only 2.
hope it helps.
look at the picture pleaseeeee
Answers
Step-by-step explanation:
the answer is in the picture
I need help with pre algebra 8th grade
Answers
Answer:
ok whats the problem
Step-by-step explanation:
Step-by-step explanation:
um were is the question
68-95-99.7 Rule
So
LEARNING OBJECTIVE: Identify the percent of data that is between two values
using a given standard deviation, mean, and the 68-95-99.7 rule.
68
At a nearby frozen yogurt shop, the mean cost of a pint of frozen yogurt is $1.50
with a standard deviation of $0.10.
Assuming the data is normally distributed, approximately what percent of
customers are willing to pay between $1.30 and $1.70 for a pint of frozen
yogurt?
T
Answers
9514 1404 393
Answer:
95%
Step-by-step explanation:
The given limits differ from the mean by ...
1.30 -1.50 = -0.20
1.70 -1.50 = 0.20
These values are 2 × the standard deviation of 0.10. The 68-95-99.7 rule tells you that 95% of the population lies within 2 standard deviations of the mean.
For this question, that means 95% of customers are willing to pay between $1.30 and $1.70.
What Is -5 1/2 x -1 1/8
Answers
✨Answer:✨
-6 3/16
✨Step-by-step explanation:✨
-5 1/2 x -1 1/8 = ?
Convert mixed numbers into improper fractions
-11/2 x -9/8 = -99/16 = -6 3/16
PLEASE HELP...
Write an iterated integral of a continuous function f over the region. Use the order dy dx.
R is the triangular region with vertices (0,0), (0,15), and (5,0).
(I just need the double iterated integral no solving necessary)
THANK YOU!!
Answers
Answer:
[tex]\displaystyle \int_{0}^{5}\int_{0}^{-3x+15}f(x,y) \ dy dx[/tex]
========================================================
Explanation:
We're tasked to find the values of a,b,c,d in the following
[tex]\displaystyle \int_{a}^{b}\int_{c}^{d}f(x,y) \ dy dx[/tex]
The equation of the line through the points (0,15) and (5,0) is y = -3x+15
When picking a particular fixed x value, the y values span from y = 0 to y = -3x+15 which determines the bounds of integration for the inner integral.
So this means c = 0 and d = -3x+15
The values of a,b are much easier and they are a = 0 and b = 5 to represent the x coordinates of the left-most and right-most points.
-----------------
Since,
a = 0b = 5c = 0d = -3x+15we go from this
[tex]\displaystyle \int_{a}^{b}\int_{c}^{d}f(x,y) \ dy dx[/tex]
to this
[tex]\displaystyle \int_{0}^{5}\int_{0}^{-3x+15}f(x,y) \ dy dx[/tex]
Without knowing what f(x,y) is, we cannot compute the integral. Luckily it seems like your teacher is only interested in setting up the integral rather than computing its numeric value.
PLEASE HELP I WILL GIVE BRAINLIEST
Answers
[tex]x + 105 + 113 + 75 = 360[/tex]
[tex]x + 293 = 360[/tex]
[tex]x = 360 - 293[/tex]
[tex]x = 67[/tex]
As we know that, for any shape with sides n, the sum of all it's interior angles is (n - 2) × 180°, so as the Shape ABCD is a quadrilateral with 4 sides, so sum of it's all interior angles is just going to be (4 - 2) × 180° = 2 × 180° = 360°, so if we assume the missing angle be [tex]\bf \angle A[/tex], by using the sum property we will be having ;
[tex]{:\implies \quad \sf \angle A+105{\degree}+113{\degree}+75{\degree}=360{\degree}}[/tex]
[tex]{:\implies \quad \sf \angle A+293{\degree}=360{\degree}}[/tex]
[tex]{:\implies \quad \sf \angle A=360{\degree}-293{\degree}}[/tex]
[tex]{:\implies \quad \boxed{\bf{\angle A=67{\degree}}}}[/tex]
Determine if 0.0590222222222222... is rational or irrational and
give a reason for your answer.
Answers
Answer:
Rational
Step-by-step explanation:
It can be represented as a fraction.
332/5625
0.0590222222222222... is a rational number.
We have,
0.0590222222222222.......
We need to determine whether this number is rational or irrational.
What are rational numbers and irrational numbers?A rational number is a number that can be written in p/q form where q≠0.
Some rational numbers are terminating.
Example: 45/2 = 22.5
Some rational numbers are recurring numbers.
Example: 556/3 = 185.33333333333...
The irrational number are those numbers that are non-terminating and non-recurring.
Example: 22/7 = 3.14285714285.....
We have,
0.0590222222222222......
Where 2 is recurring.
So it is a rational number.
Thus 0.0590222222222222... is a rational number.
Learn more about rational and irrational numbers here:https://brainly.com/question/17450097
#SPJ2
Find cos(A) and tan(A)
Answers
Hope this helps.
Find the value of x
A. 25°
B. 85°
C. 75°
D. 105°
Answers
Answer:
75⁰ Please refer to the picture above for the answer
A rare book was offered for sale in 2018 for $800. Because it was so rare, in increased in value by 10% in 2019. It increased in value again in 2020 this time by 20%. If you know how percentages work, you know that it increased by MORE than 30% in this time period. By what percent did it increase over the 2 year period?
Answers
Answer:
32%
Step-by-step explanation:
too lazy to type it out.
Answer:
32%.
Step-by-step explanation:
Value in 2019 = 800 + 10% of 800
= 800 + 0.1*800
= $880.
In 2020 , value
= 880 + 0.2*880
= $1056.
Increase in value over 2 years = 1056 - 800 = $256.
% increase = 100 * 256/800
= 32%.
Factor the expression,
x^2 + 7xy - 44y^2
Answers
Answer:
(x + 11y)(x - 4y)
Step-by-step explanation:
-44 = 11*(-4)
11 + (-4) = 7
so x² + 7xy - 44y² = (x + 11y)(x - 4y)
What is the value of x?
3
4
5
6
Answers
Answer:
x=3
Step-by-step explanation:
2×0.05=0.1
0.09x ÷ 0.09 = 1
2+x = 2+1 = 3
HENCE 3 IS THE ANSWER
Help meeeee pleaseeeeee
Answers
C=(3.14)*(12)
C= 37.68cm
Answer:
37.68 centimeters
Step-by-step explanation:
The circumference of a circle can be found by using the formula πd, where d = diameter. We're given the diameter as 12 centimeters, and we're going to use 3.14 for pi.
3.14 × 12
37.68
Therefore, the answer is 37.68 cm.
Have a lovely rest of your day/night, and good luck w/ your assignments! (‾◡◝)
ANYONE I NEED HELP ASAP!!!!!
Answers
Twice the difference of a number and 2 equals 5
Answers
When something says twice a number it’s always going to be multiplied by 2 and “a number will always be a variable
9514 1404 393
Answer:
2(x -2) = 5
Step-by-step explanation:
If x represents the number, then the difference of the number and 2 is ...
x -2
Twice the difference is ...
2(x -2)
"equals 5" means that product is equal to 5. The appropriate equation is ...
2(x -2) = 5
_____
In case you want a solution ...
Dividing by 2, we get ...
x -2 = 5/2
Adding 2 gives the value of the number:
x = 2 +5/2 = 9/2
x = 4 1/2
The number is 4 1/2.
Please help asap! I will gave brainlest!
Answers
Answer:
[tex]\frac{2\pi}{3}, \: \: \frac{5\pi}{3}[/tex]
Step-by-step explanation:
[tex] \tan \theta = - \sqrt{3} \\ \\ \implies \tan \theta = - \tan \frac{\pi}{3} \\ \\ \implies \: \tan \theta = \tan \bigg(\pi - \frac{\pi}{3} \bigg) \\ \\\implies \: \tan \theta = \tan \bigg(\frac{3\pi - \pi}{3} \bigg)\\ \\\implies \: \tan \theta = \tan \bigg(\frac{2\pi}{3} \bigg)\\ \\\implies \huge \red{\theta = \frac{2\pi}{3}} \\ \\ \\ \tan \theta = - \sqrt{3} \\ \\ \implies \tan \theta = - \tan \frac{\pi}{3} \\ \\ \implies \: \tan \theta = \tan \bigg(2\pi - \frac{\pi}{3} \bigg) \\ \\\implies \: \tan \theta = \tan \bigg(\frac{6\pi - \pi}{3} \bigg)\\ \\\implies \: \tan \theta = \tan \bigg(\frac{5\pi}{3} \bigg)\\ \\\implies \huge \orange{\theta = \frac{5\pi}{3}} \\ \\ \huge \: \purple { \boxed { \bold\theta = \frac{2\pi}{3}, \: \: \frac{5\pi}{3} }}[/tex]
A vehicle hire firm charges $20 as a flat fee for renting a vehicle plus $2 per mile. If the total cost of hiring a vehicle on one occasion is 170, how many miles were driven
Answers
Answer:
85
Step-by-step explanation:
Because 170 divided by 2.
The number of miles is 75 miles if the vehicle hire firm charges $20 as a flat fee for renting a vehicle plus $2 per mile.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A vehicle hire firm charges $20 as a flat fee for renting a vehicle plus $2 per mile.
Let x be the total number of miles:
From the question:
y be the total cost of hiring
y = 20 + 2x
y = 170
170 = 20 + 2x
150 = 2x
x = 150/2
x = 75 miles
Thus, the number of miles is 75 miles if the vehicle hire firm charges $20 as a flat fee for renting a vehicle plus $2 per mile.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ5
Hello can someone please answer this question i will mark you the Brainliest
Answers
Answer:
2(L ×W) +2(L×H)+2(W×H)
Step-by-step explanation:
find the answer of that
Answer:
180 cm 2
Step-by-step explaination:
2 ( lxw) + 2(lxh) + 2(wxh)
40 + 40 + 100
180
A quiz consists of 20 multiple-choice questions, each with 4 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 70 %.
Answers
The lunch lady pushes a 100 kg zombie with 300 N of force. How much is the zombie accelerated? How do you solve is is division or multiplication
Answers
Step-by-step explanation:
Use Newton's second law. Force equals mass times acceleration.
F = ma
300 N = (100 kg) a
a = 3 m/s²
Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (-7,9) and parallel to the line whose equation is 7x - 4y - 9 = 0
The equation of the line in point-slone form is
Answers
Answer:
(y - 9) = 7/4(x + 7)
Step-by-step explanation:
If two lines are parallel to each other, they have the same slope slopes.
The first line is 7x - 4y - 9 = 0.
First let's convert this to y = mx + b form.
7x - 4y - 9 = 0Add 4y to both sides.
7x - 9 = 4yDivide each term by 4.
y = 7/4x - 9/4The slope is 7/4. A line parallel to this one will also have a slope of 7/4.
The standard point-slope form is:
(y - y₁) = m(x - x₁)For the point-slope form, you need two things: a point and a slope.
point: (-7, 9)slope: 7/4.Plug in our given information.
(y - 9) = 7/4(x - (-7))Simplify.
(y - 9) = 7/4(x + 7)Learn with another example.
https://brainly.com/question/26681302
Hope this helps!
Let's consider the information given:
line passes through (-7,9)line is parallel to 7x - 4y - 9 = 0What do we want to solve: put the equation of the line in point-slope form
⇒ point-slope form ⇒ [tex]y-y_{0}=m(x-x_{0} )[/tex]
[tex](x_{0} ,y_{0} )[/tex] : any point on the linem: slope Find the slope of 7x - 4y = 9⇒ first put it into slope-intercept form [tex]y = mx +b[/tex]
-where m is the slope and b is the y-intercept
[tex]7x-4y-9=0\\7x-4y=9\\-4y=-7x+9\\y=\frac{7}{4}x-\frac{9}{4}[/tex]
⇒ Slope is 7/4
2. When two lines are parallel, their two slopes are equal, and since
the line passes through (-7,9), use point-slope form
[tex]y-9=\frac{7}{4}(x+7)[/tex] <== point-slope form
What do we also want: find the general form ⇒ Ax + By = C
A: coefficient of xB: coefficient of yC: constant To find the general form, move all the variables to one side and the constant to the other, using the point-slope form[tex]y-9=\frac{7}{4}(x+7)\\ y-9=\frac{7}{4}x+\frac{49}{4} \\-\frac{7}{4}x+y=9+\frac{49}{4} =\frac{36}{4} +\frac{49}{4} =\frac{85}{4} \\-\frac{7}{4}x+y=\frac{85}{4}[/tex]<== general form
Hope that helps!
What is the value of the expression shown? 10 - 16 + 2
Answers
Answer:
-4
Step-by-step explanation:
First we combat the 10 - 16 so we get - 6
Then we fight the -6 and the 2 to get -4
The value of this fight was -4 :)
Have an amazing day!!
PLEASE RATE AND MARK BRAINLIEST!!!