What is the y-intercept of the function f(x)=4 - 5x? (Hint: use the commutative property)
1 answer:
Answer:
Therefore the y-intercept of the function is 4.
Step-by-step explanation:
Intercepts:
The line which intersect on x-axis and y-axis are called intercepts.
y-intercept: The line or function which intersect at y-axis. So when the line intersect at y-axis, X coordinate is zero.
So in the given Function Put x = 0 we will get the y-intercept
Put x =0
Therefore the y-intercept of the function is 4.
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The linear equation to model the company's monthly expenses is y = 2.5x + 3650
<em><u>Solution:</u></em>
Let "x" be the units produced in a month
It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers.
Cost per unit = $ 2.50
The company has monthly operating expenses of $350 for utilities and $3300 for salaries
We have to write the linear equation
The linear equation to model the company's monthly expenses in the form of:
y = mx + b
Cost per unit = $ 2.50
Monthly Expenses = $ 350 for utilities and $ 3300 for salaries
Let "y" be the total monthly expenses per month
Then,
Total expenses = Cost per unit(number of units) + Monthly Expenses
Thus the linear equation to model the company's monthly expenses is y = 2.5x + 3650
Answer:
-95.78
Step-by-step explanation:
As the researcher decided to make the number of parties attended per week the explanatory variable, this would be variable x in the regression line, and of course, the variable y would be the number of text messages sent per day.
After constructing the linear regression equation, the researcher found that an approximate value for the actual value of y could be represented by the line
Since this is an approximate value, it is not expected that it coincides with the actual value of y. We define then the residual for each value of x as the difference between the actual value of y and the approximation for the given x.
For the value x = 2 (the student attended 2 parties that week) the actual value of y is 20 (the student sent 20 text messages per day that week).
The approximate value of y would be according to the regression line
Hence, the residual value for x=2 would be
Answer:
The line containing the midpoints of two sides of a triangle is parallel to the third side ⇒ proved down
Step-by-step explanation:
* Lets revise the rules of the midpoint and the slope to prove the
problem
- The slope of a line whose endpoints are (x1 , y1) and (x2 , y2) is
- The mid-point of a line whose endpoints are (x1 , y1) and (x2 , y2) is
* Lets solve the problem
- PQR is a triangle of vertices P (0 , 0) , Q (2a , 0) , R (2b , 2c)
- Lets find the mid-poits of PQ called A
∵ Point P is (x1 , y1) and point Q is (x2 , y2)
∴ x1 = 0 , x2 = 2a and y1 = 0 , y2 = 0
∵ A is the mid-point of PQ
∴
- Lets find the mid-poits of PR which called B
∵ Point P is (x1 , y1) and point R is (x2 , y2)
∴ x1 = 0 , x2 = 2b and y1 = 0 , y2 = 2c
∵ B is the mid-point of PR
∴
- The parallel line have equal slopes, so lets find the slopes of AB and
QR to prove that they have same slopes then they are parallel
# Slope of AB
∵ Point A is (x1 , y1) and point B is (x2 , y2)
∵ Point A = (a , 0) and point B = (b , c)
∴ x1 = a , x2 = b and y1 = 0 and y2 = c
∴ The slope of AB is
# Slope of QR
∵ Point Q is (x1 , y1) and point R is (x2 , y2)
∵ Point Q = (2a , 0) and point R = (2b , 2c)
∴ x1 = 2a , x2 = 2b and y1 = 0 and y2 = 2c
∴ The slope of AB is
∵ The slopes of AB and QR are equal
∴ AB // QR
∵ AB is the line containing the midpoints of PQ and PR of Δ PQR
∵ QR is the third side of the triangle
∴ The line containing the midpoints of two sides of a triangle is parallel
to the third side