y = 4x/5 - 22/5
Given slope of line is 4/5 and point is (3,-2)
Slope, Numerical measure of a line's inclination relative to the horizontal. In differential calculus, the slope of a line tangent to the graph of a function is given by that function’s derivative and represents the instantaneous rate of change of the function with respect to change in the independent variable.
The equation of a straight line in the form:
y − y1 = m(x − x1)
where m is the slope of the line = 4/5 (According to question)
and (x1, y1) are the coordinates of a given point on the line.
compare slope-intercept form.
substituting values
(y+2) = (4/5) (x-3)
⇒ y = 4x/5 - 22/5
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Answer:
30 gallons of tea
Step-by-step explanation:
We are looking at the average of cups of tea per minute but we are given the time frame of lunch in hours, so first, we have to convert the hours to minutes:
There are 60 minutes in 1 hour and lunch is 2 hours long. So, multiply 60 by 2 to get 120 minutes total.
Next, we have to find out the number of cups of tea poured during the lunch. We have been told already that an average of 4 cups of tea are poured a minute.
Therefore, multiply 4 by the total number of minutes for lunch. You will multiply 4 by 20 to get 480 cups of tea poured in total during the catered lunch.
Finally, we have to see how many gallons of tea the caterer should bring. We should know that there are 16 cups in one gallon.
That means we have to divide the total number of cups poured by 16. Divide 480 by 16 to get 30 gallons of tea that the caterer should bring.
Given the basis β={(1,−1,3),(−3,4,9),(2,−2,4)}β={(1,−1,3),(−3,4,9),(2,−2,4)} and x=(8,−9,6)x=(8,−9,6), I am to find the corresponding coordinate vector [x]β[x]β. I claim that the coordinate vectors entries x1,x2,x3x1,x2,x3 meet the following criterion:
x1(1,−1,3)+x2(−3,4,9)+x3(2,−2,4)=(8,−9,6)x1(1,−1,3)+x2(−3,4,9)+x3(2,−2,4)=(8,−9,6)This is equivalent to solving the augmented matrix
⎡⎣⎢1−13−3492−248−96⎤⎦⎥[1−328−14−2−93946]which is row equivalent to
⎡⎣⎢100−31020−18−10⎤⎦⎥
Answer:
-29v+145
Step-by-step explanation:
-4(5v – 30 – 6) – 9v
-20v+120+25-9v
-29v+145