20 PTSS !!! PLEASE HELPP !!
1 answer:
Because it is extremely hard to find the area of this figure all together, it would be in our best interest to split this figure up into three different pieces: the two horizontal rectangles, and the verticle rectangle. We can find the area of all three and add them up. Be aware that there are two different ways that you can break this figure up, As shown in the attachments. I will be using the first image (the one with the tall horizontal rectangles, NOT the almost-squares).
So, we see that we have enough information to solve for the area of the left-most rectangle. Area = lw. 10 x 4 = 40, so the area is 40. Next, we have to notice, that the horizontal rectangles are also the same, so both of the areas of the two horizontal rectangles are 40.
Now, we can find the middle rectangle. We know that the length of the entire thing is 18, but it is taken up by 8 (4+4) of the horizontal triangles, so 18-8=10, so the length Is 10. We also know that the height of the horizontal rectangles is 10, so 10-3=7. Our dimensions for the rectangle are 10x7 or 70 square units. If we add them all together, 40+40+70=150.
The area is 150 square units
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Answer:
Yes, the lines intersect at (3,7). The solution is (3,7).
Explanation:
Step 1. The first line passes through the points:
(-7,2) and (1,6)
and the second line passes through the points:
(-3,-5) and (2,5)
Required: State if the lines intersect, and if so, find the solution.
Step 2. We need to find the slope of the lines.
Let m1 be the slope of the first line and m2 be the slope of the second line.
The formula to find a slope when given two points (x1,y1) and (x2,y2) is:
Using our two points for each line, their slopes are:
The results are:
The slopes are not equal, this means that the lines are NOT parallel, and they will intersect at some point.
Step 3. To find the intersection point (the solution), we need to find the equation for the two lines.
Using the slope-point equation:
Where m is the slope, and (x1,y1) is a point on the line.
For the first line m=1/2, and (x1,y1) is (-7,2). The equation is:
Solving the operations:
Step 4. We do the same for the second line. The slope is 2. and the point (x1,y1) is (-3, -5). The equation is:
Step 5. The two equations are:
Now we need to solve for x and y.
Step 6. Equal the two equations to each other:
And solve for x:
Step 7. Use the second equation:
and substitute the value of x to find the value of y:
The solution is x=3 and y=7, in the form (x,y) the solution is (3,7).
Answer:
Yes, the lines intersect at (3,7). The solution is (3,7).