Let x and y be the numbers of questions worth 5 and 2, respectively. There are a total of 29 questions which means that x + y should be 29. The equations that best describe the conditions are,
x + y = 29
5x + 2y = 100
Solving for x and y gives x = 14 and y = 15. Thus, there are 14 and 15 questions worth 5 and 2, respectively.
Answer:
y = 6x +1
Step-by-step explanation:
To write the slope-intercept form equation for a line, you need to know the slope and the y-intercept. These can be found from their respective formulas.
__
<h3>slope</h3>
The slope of a line between points (x1, y1) and (x2, y2) is given by the formula ...
m = (y2 -y1)/(x2 -x1)
For points (-1, -5) and (0, 1), the slope is ...
m = (1 -(-5))/(0 -(-1)) = 6/1
m = 6
<h3>y-intercept</h3>
The y-intercept is the value of y where the line crosses the y-axis. That axis is where x = 0. There is a formula that can be used to find the y-intercept from the slope and a point on the line:
b = y -mx . . . . . y-intercept of line with slope m through point (x, y)
However, one of the given points is already the y-intercept: (0, 1). It tells you b=1.
<h3>equation</h3>
The slope-intercept equation is ...
y = mx +b
y = 6x +1
Answer:
165 degrees
Step-by-step explanation:
According to the protractor, the angle stretches from 10 degrees to 175 degrees. Subtract 10 from 175 to get the total measurement, and you will get 165. The angle is 165 degrees.
Recall that
. So we can add twice the first equation to the second one to get
Since
, we have
so
If
, then
If
, then
So the solution set is
