Answer:
First Image:
1. 3/10
2. 9/10
3. 10
4. -5/3
5. 2/5
6. -5/2
Second Image:
10. y=x-2
Third Image:
1. y=-4/3x-3
2. y=4x-4
3. y=-3/4x+4
4. y=1/3x+3
Step-by-step explanation:
When graphing linear lines, there are just a few, simple things to look out for. The first thing is to look at how far the line goes until it goes through a second point. The second thing is to look at where the line crosses on the y-axis (the vertical barrier). When writing an equation for a linear line, the standard form is y=mx+b, where m is a placeholder for the slope of the line and b is the placeholder for the y-intercept (where the line crosses the y-axis). If the line goes from the upper left to the lower right, the slope is negative. On the other hand, if the line goes from the lower left to the upper right, the slope is positive. When deciding what the slope is, remember that it is written as Rise/Run. So, for example, the second problem in the first image shows a line that goes from the lower left to the upper right, meaning that the slope will be positive. Now, if you look at the red dot at the bottom of the line, just count each box upwards, until you are level with the other red dot at the top right of the graph. Once you have gotten your number (it should be nine), just count the boxes going to the right of where you ended, all the way until you reach the red dot at the top right (you should have counted 10). Now that you have those two numbers, you are able to plug them into Rise/Run. Since you went up nine blocks and right ten blocks, you would write the slope as 9/10. The slope is positive, therefore there is no sign in front of the slope. However, if the slope was negative, then you'd write it as -9/10. Now that you have the slope, you can plug it into the equation. The equation should now look like this: y=9/10x+b. Lastly, you must find the y-intercept. In order to do this, just simply look at the y-axis (the bolded, center line) to see where the line crosses. You should see that it crosses at the halfway point between one and zero, meaning the y-intercept is 1/2, or 0.5. With this, once again plug the value into the equation, which should now look like this: y=9/10x+1/2. With that, the problem has been solved! I hope this helps you out. Good luck!
Answer:
35d-10
Step-by-step explanation:
distribute the -5
1) a
2)b
3)d
4)c
5)a
I hope this helped you!!
Answer:
the area of a trapezoid is equal to half the product of the height and the sum of the two bases. Area = ½ x (Sum of parallel sides) x (perpendicular distance between the parallel sides).
Answer:
The answer is below
Step-by-step explanation:
Let x be the diameter of the semicircle. radius = x/2
The window is a combination of a rectangle and semicircle.
Width of window = diameter = x, let length of the window = y.
Perimeter of semicircle = πr = πx/2
Perimeter of window = x + y + y + πx/2
20 = x + 2y + πx/2
2y + x + πx/2 = 20
2y = 20 - x(1 - π/2)
y = 10 - x(1 - π/2)/2
Area of semicircle = (1/2)πr² = (1/2)π(x/2)²
Area of window = xy + (1/2)π(x/2)²
A = x(10 - x(1 - π/2)/2) + πx²/8
A = 10x - x² - πx²/4 + πx²/8
A = 10x - x² - πx²/8
The maximum area is at dA / dx = 0
dA / dx = 10 - 2x - 2πx/8
0 = 10 - 2x - πx / 4
2x + πx / 4 = 10
2.785x = 10
x = 3.59 feet
Maximum area = 10x - x² - πx²/8 = 10(3.59) - 3.59² - π(3.59²) / 8
Maximum area = 17.95 feet²
