Hello there! So, y = mx + b is in slope-intercept form, where m represents the slope, b represents the y-intercept, and y and x remain unfilled. First off, let's solve for the slope. The formula for slope is y2 - y1 / x2 - x1, where you subtract the first x and y coordinates from the second x and y coordinates. So it would be formed like this:
9 - 4 / 6 - (-4)
Let's subtract. 9 - 4 is 5. 6 - (-4) is 10. 5/10 is 1/2 in simplest form. The slope for this equation is 1/2. Now, let's find the y-intercept. We will find that by plugging one of the points into the equation and solving for b. The x and y coordinates will be filled in by that coordinate. Let's use (-4, 4) for this problem. We will also plug in the slope. In this case, the problem will look like this:
4 = (1/2)(-4) + b
Now, let's multiply 1/2 and -4 to get -2. Now, to get b by itself, subtract 2 to both sides to isolate the b. -2 + 2 cancels out. 4 + 2 is 6. b = 6. There. The equation of the line in slope-intercept form is y = 1/2x + 6.
Answer:
Student B is correct
Student A failed to distribute -4 and -6 when opening the brackets in the first step
Step-by-step explanation:
The solution Student A gave was:
2x - 4(3x + 6) = -6(2x + 1) - 4
2x - 12x + 6 = -12x + 1 - 4
-10x + 6 = -12x - 3
2x = -9
x = -4 _1 2 ( -4 1/2)
The solution Student B gave was:
2x - 4(3x + 6) = -6(2x + 1) - 4
2x - 12x - 24 = -12x - 6 - 4
-10x - 24 = -12x - 10
2x = 14
x = 7
Student B is correct.
Explanation of the error:
Student A failed to distribute -4 and -6 when opening the brackets in the first step.
That is,
2x - 4(3x + 6) = -6(2x + 1) - 4
To open this bracket, we will distribute, -4 and -6 so that we get
2x (-4 × 3x) + (-4 × +6) = (-6×2x) + (-6 × +1) - 4
Then we will get
2x -12x -24 = -12x -6 -4
Adding the like terms
-10x - 24 = -12x - 10
Collecting like terms
-10x + 12x = -10 + 24
∴ 2x = 14
x = 14 / 2
Hence,
x = 7
Answer:
Step-by-step explanation:
step 1
Find the equation of the solid line
From the graph take the points (0,3) and (4,11)
Find the slope
The equation of the solid line in slope intercept form is equal to
we have
----> the y-intercept is the point (0,3)
substitute
therefore
The inequality is
step 2
Find the equation of the dashed line
The slope is given
From the graph take the y-intercept (0,-5)
The equation of the solid line in slope intercept form is equal to
we have
substitute
therefore
The inequality is
because the shaded region is below the dashed line
therefore
The system of inequalities is
Answer:the diameter is 7
Step-by-step explanation: 21.98 divide by pi is 7 so diameter is 7
<h3>
Total approximately 16 boxes of flooring will be needed in Stanley's living room. </h3>
Step-by-step explanation:
Here the given question is <u>incomplete</u>.
Stanley is having wood flooring installed in his living room. The installer has used 10 1/2 boxes of flooring on 2/3 of the room. How many total boxes of flooring will be needed for Stanley's living room?
The number of boxes used in the two third of room = 
boxes
So, 
room = 10. 5 boxes
So, 1 room = 
So, total approximately 16 boxes of flooring will be needed in Stanley's living room.
