Answer:
<ABC = 30°
Step-by-step explanation:
Vertical angles are equal
So
4x+2 = 7x - 19
-7x + 4x = -19 - 2
-3x = -21
x = 7
<ABC = 4(7) + 2 = 28 + 2 = 30
<ABC = 30°
<h2>
Answer:</h2>
The number of pages he will read in one minute is:
<h2>
Step-by-step explanation:</h2>
It is given that:
Charlie reads in every .
We know that:
This means that:
Charlie reads in every .
This means that:
Hence,
Hence,
Answer:
Step-by-step explanation:
The terms of this sum make the arithmetic sequence.
The fomula of a sum of <em>n</em> terms of an arithmetic sequence:
We have
Substitute:
Answer:
3x + 2y = 31
Step-by-step explanation:
Solve the given equation for y to determine the slope of this line:
-3y = -2x = -18, so that y = (2/3)x + 6.
Therefore, a line perpendicular to the given line has the slope -3/2, which is the negative reciprocal of this 2/3.
Using the slope-intercept formula y = mx + b and inserting the knowns (slope = m = -3/2, y = 5 and x = -7), we obtain:
5 = (3/2)(-7) + b, or (after multiplying all terms by 2):
10 = -21 + 2b, or 2b = 31, or b = 31/2.
Then the equation is y = (-3/2)x + 31/2.
Let's put this into standard form. Multiply all terms by 2, obtaining:
2y = -3x + 31, or
3x + 2y = 31 This is the equation of the perpendicular line in question.