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denis-greek [22]
3 years ago
12

Create a sequence in which 1 1/4 is added to each number

Mathematics
1 answer:
RSB [31]3 years ago
5 0
1/4 1/2 3/4 1 1 1/4 1 1/2 1 3/4 2...
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Use cross products to find the area of the triangle in the xy-plane defined by (1, 2), (3, 4), and (−7, 7).
Free_Kalibri [48]

I love these. It's often called the Shoelace Formula. It actually works for the area of any 2D polygon.


We can derive it by first imagining our triangle in the first quadrant, one vertex at the origin, one at (a,b), one at (c,d), with (0,0),(a,b),(c,d) in counterclockwise order.


Our triangle is inscribed in the a \times d rectangle. There are three right triangles in that rectangle that aren't part of our triangle. When we subtract the area of the right triangles from the area of the rectangle we're left with the area S of our triangle.


S = ad - \frac 1 2 ab -  \frac 1 2 cd - \frac 1 2 (a-c)(d-b) = \frac 1 2(2 ad - ab -cd - ad +ab +cd -bc) = \frac 1 2(ad -bc)


That's the cross product in the purest form. When we're away from the origin, a arbitrary triangle with vertices A(x_1, y_1), B(x_2, y_2), C(x_3, y_3) will have the same area as one whose vertex C is translated to the origin.


We set a=x_1 - x_3, b= y_1  - y_3, c=x_2 - x_3, d=y_2- y_3


S= ad-bc=(x_1 - x_3)(y_2 - y_3) -(x_2-x_3)(y_1 - y_3)


That's a perfectly useful formula right there. But it's usually multiplied out:


S= x_1y_2 - x_1 y_3  - x_3y_2 + x_3 y_3 - x_2 y_1 + x_2y_3 + x_3 y_1 - x_3 y_3


S= x_1 y_2 - x_2 y_1  + x_2y_3 - x_3y_2   + x_3 y_1 - x_1 y_3


That's the usual form, the sum of cross products. Let's line up our numbers to make it easier.


(1, 2), (3, 4), (−7, 7)

(−7, 7),(1, 2), (3, 4),


[tex]A = \frac 1 2 ( 1(7)-2(-7) + 3(2)-4(1) + -7(4) - (7)(3)

8 0
3 years ago
1 1/4 x 1 1/3 plsss help
vodka [1.7K]

Answer:

exact form: 5/3

decimal form: 1.6 (6 is repeating)

mixed number form: 1  2/3

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Which of the following are the zeroes of the function y = 3 ( x − a )( x + b )y = 3 ( x - a )( x + b ) in terms of a a and bb ?
Murljashka [212]
I believe the answer is <span> bb</span>
8 0
3 years ago
Read 2 more answers
Solve for b.<br><br> 3 (b−4 )+ 5b = 44<br><br><br> b =
Sergeu [11.5K]
B=7
3(b-4)+5b=44
3b-12+5b=44
8b=44+12
8b=56
b=7
7 0
3 years ago
A random sample of 20 purchases showed the sample mean of $48.77 and the sample standard deviation s is $17.58. How large is the
laila [671]

Answer:

<h2>$5.03</h2>

Step-by-step explanation:

Given data          

Sample Mean (M):  $48.77  

Sample Size (n): 20

Standard Deviation (σ) :  $17.58

Confidence Level: 80%

 we know that z*-Values for 80% Confidence  Levels is 1.28

the expression for margin of error is given bellow\

MOE= z*σ/√n

We can now substitute into the expression and solve for the MOE as

MOE= 1.28*17.58/√20

MOE= 22.502/4.47

MOE= 22.502/4.47

MOE= 5.03

The margin of error for a 80 % confidence interval is $5.03

3 0
3 years ago
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