Add 0.5 to each side so you have fabric for the seams and your new numbers are 3 ft and 4 ft
find the area by multiplying 3*4 and get 12 ft
1 yard = 3 feet
12/3= 4 yards
You would need 4 square yards of fabric
Answer:
![715x^4y^9](https://tex.z-dn.net/?f=715x%5E4y%5E9)
Step-by-step explanation:
Given
![(x + y)^{13](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13)
Required
Determine the 10th term
Using binomial expansion, we have:
![(a + b)^n = ^nC_0a^nb^0 + ^nC_1a^{n-1}b^1 + ^nC_2a^{n-2}b^2 +.....+^nC_na^{0}b^n](https://tex.z-dn.net/?f=%28a%20%2B%20b%29%5En%20%3D%20%5EnC_0a%5Enb%5E0%20%2B%20%5EnC_1a%5E%7Bn-1%7Db%5E1%20%2B%20%5EnC_2a%5E%7Bn-2%7Db%5E2%20%2B.....%2B%5EnC_na%5E%7B0%7Db%5En)
For, the 10th term. n = 9
So, we have:
![(a + b)^n = ^nC_{9}a^{n-9}b^{9](https://tex.z-dn.net/?f=%28a%20%2B%20b%29%5En%20%3D%20%5EnC_%7B9%7Da%5E%7Bn-9%7Db%5E%7B9)
![(x + y)^{13} = ^{13}C_{9}x^{13-9}y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5E%7B13%7DC_%7B9%7Dx%5E%7B13-9%7Dy%5E9)
![(x + y)^{13} = ^{13}C_{9}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5E%7B13%7DC_%7B9%7Dx%5E4y%5E9)
Apply combination formula
![(x + y)^{13} = \frac{13!}{(13-9)!9!}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B13%21%7D%7B%2813-9%29%219%21%7Dx%5E4y%5E9)
![(x + y)^{13} = \frac{13!}{4!9!}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B13%21%7D%7B4%219%21%7Dx%5E4y%5E9)
![(x + y)^{13} = \frac{13*12*11*10*9!}{4!9!}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B13%2A12%2A11%2A10%2A9%21%7D%7B4%219%21%7Dx%5E4y%5E9)
![(x + y)^{13} = \frac{13*12*11*10}{4!}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B13%2A12%2A11%2A10%7D%7B4%21%7Dx%5E4y%5E9)
![(x + y)^{13} = \frac{13*12*11*10}{4*3*2*1}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B13%2A12%2A11%2A10%7D%7B4%2A3%2A2%2A1%7Dx%5E4y%5E9)
![(x + y)^{13} = \frac{17160}{24}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B17160%7D%7B24%7Dx%5E4y%5E9)
![(x + y)^{13} = 715x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20715x%5E4y%5E9)
Hence, the 10th term is ![715x^4y^9](https://tex.z-dn.net/?f=715x%5E4y%5E9)
Answer:
1. H = 29 cm
2. θ = 44°
Step-by-step explanation:
1. We can find the height of the triangle by considering the isosceles triangle as two right triangles. The height can be found by using Pitagoras:
![L^{2} = H^{2} + B^{2}](https://tex.z-dn.net/?f=%20L%5E%7B2%7D%20%3D%20H%5E%7B2%7D%20%2B%20B%5E%7B2%7D%20)
Where:
L: is the sides of the isosceles triangle = 42 cm
B: is the base = 30 cm
H: is the height =?
Then, the height is:
![H = \sqrt{L^{2} - B^{2}} = \sqrt{(42 cm)^{2} - (30 cm)^{2}} = 29.4 cm = 29 cm](https://tex.z-dn.net/?f=%20H%20%3D%20%5Csqrt%7BL%5E%7B2%7D%20-%20B%5E%7B2%7D%7D%20%3D%20%5Csqrt%7B%2842%20cm%29%5E%7B2%7D%20-%20%2830%20cm%29%5E%7B2%7D%7D%20%3D%2029.4%20cm%20%3D%2029%20cm%20)
2. The two equal angles (θ) can be found using the following trigonometric identity:
![cos(\theta) = \frac{B}{L}](https://tex.z-dn.net/?f=%20cos%28%5Ctheta%29%20%3D%20%5Cfrac%7BB%7D%7BL%7D%20)
![\theta = cos^{-1}(\frac{30 cm}{42 cm}) = 44.4^{\circ} = 44^{\circ}](https://tex.z-dn.net/?f=%20%5Ctheta%20%3D%20cos%5E%7B-1%7D%28%5Cfrac%7B30%20cm%7D%7B42%20cm%7D%29%20%3D%2044.4%5E%7B%5Ccirc%7D%20%3D%2044%5E%7B%5Ccirc%7D%20)
Hence, the two equal angles are 44°.
I hope it helps you!
Answer:
6
Step-by-step explanation:
x, or the amount of days is the independent variable.