Let's look at the first equation.
3y = 5x - 1
y = 5/3 y - 1/3
This line has slope 5/3. A line perpendicular to it has slope -3/5.
The second line is y = -3/5 x + 9.
Its slope is indeed -3/5, so the second line is perpendicular to the first one.
There is an infinite number of lines perpendicular to any given line. You concluded correctly that the two lines in this problem are perpendicular based on the fact that their slopes are negative reciprocals. The second line, y = -3/5 x + 9, is only one line that is perpendicular to the first line. There is an infinite number of lines perpendicular to the first line. All the perpendicular lines have the slope -3/5 and different y-intercepts. The +9 here is just the y-intercept of this specific perpendicular line. Since there is an infinite number of y-intercepts, there is an infinite number of perpendiculars.
20 cm^3 : 1280 cm^3 =
ratio of larger figure to smaller figure is : 64 cm^3 : 1 cm^3....or 64:1
I got it! the Brass would cost $6 each and the Steel Parts would cost $3 each so if you were gonna buy 10 Brass and 13 Parts it would cost $60 for the brass and $39 for the Parts. So $60+$39= $99 And the answer is C
Answer:
about $709 per month
Step-by-step explanation:
Okay, so in order to solve this question, we should follow this formula:
3,000 + 24x 20,000
where 24 is the amount of time we have and x is the variable we are using as to show the unknown amount of money earned per month.
3,000 + 24x 20,000
-3,000 -3,000
24x 17,000
/24 /24
x approximately 709 dollars
so, we substitute x for 709
3,000 + 24(709) 20,000
3,000 + 17,016 20,000
20,016 20,000
which is true
Hope this helps :)
Answer:
b.For each additional dollar paid to a tutor, we expect exam score to increase by 1.5 points, holding number of hours of sleep per week and number of study hours fixed.
Step-by-step explanation:
Hello!
For any multiple regression model, you can define the estimated slope as "the change or modification of the estimated average of Y when one of the explanatory variables increases one unit while the others remain constant.
In this example the dependant variable is:
Y: Exam score
And you have three explanatory variables:
X₁: salary of the teacher ($).
X₂: hours of sleep per week of a student.
X₃: number of study hours of a student.
The estimated model is ŷ= 65 + 1.5X₁ + 0.2X₂ + 0.5X₃
You need to interpret the estimated slope of the amount paid to the teacher b₁= 1.5
The units of the slope are units of Y by units of X, in this case, Y has no units so it is 1/$.
Then we can say that for every additional dollar paid to the teacher, the estimated mean score of the exam will increase by 1.5 1/$ while the weekly sleep hours and study hours remain constant.
I hope it helps!