Answer:
The Product of 7⋅(−4)⋅(−6) −168 −3 is<em> </em><u>-3</u>
Plot the points on a graph and join them to form a closed figure. two sides that are parallel shows it is a trapezoid
Answer:
The area of the resulting figure is
times smaller than the area of the original figure
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
I assume that the figure is a rectangle or a triangle
Let
z------> the scale factor
x-----> the area of the resulting figure
y----> the area of the original figure
so
![z^{2}=\frac{x}{y}](https://tex.z-dn.net/?f=z%5E%7B2%7D%3D%5Cfrac%7Bx%7D%7By%7D)
we have
![z=\frac{1}{2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B1%7D%7B2%7D)
substitute
![(\frac{1}{2})^{2}=\frac{x}{y}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B2%7D%3D%5Cfrac%7Bx%7D%7By%7D)
![(\frac{1}{4})=\frac{x}{y}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%29%3D%5Cfrac%7Bx%7D%7By%7D)
![x=y/4](https://tex.z-dn.net/?f=x%3Dy%2F4)
therefore
The area of the resulting figure is
times smaller than the area of the original figure
Answer:
480
Step-by-step explanation:
Answer:
63 yd²
Step-by-step explanation:
Use the formula:
![\text{area of triangle} = \frac{1}{2} \times \text{side}_1 \times \text{side}_2 \times \sin{(\text{includ\e ed angle})}](https://tex.z-dn.net/?f=%5Ctext%7Barea%20of%20triangle%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Ctext%7Bside%7D_1%20%5Ctimes%20%5Ctext%7Bside%7D_2%20%5Ctimes%20%5Csin%7B%28%5Ctext%7Binclud%5Ce%20ed%20angle%7D%29%7D)
<u>Given:</u>
side₁ = 14.5 yd
side₂ = 9 yd
included angle = 106°
Insert values in formula.
![\text{area of triangle} = \frac{1}{2} \times \text{side}_1 \times \text{side}_2 \times \sin{(\text{includ\e ed angle})}](https://tex.z-dn.net/?f=%5Ctext%7Barea%20of%20triangle%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Ctext%7Bside%7D_1%20%5Ctimes%20%5Ctext%7Bside%7D_2%20%5Ctimes%20%5Csin%7B%28%5Ctext%7Binclud%5Ce%20ed%20angle%7D%29%7D)
![\text{area of triangle} = \frac{1}{2} \times 14.5 \text{ yd} \times 9 \text{ yd} \times \sin{(106^\circ)}](https://tex.z-dn.net/?f=%5Ctext%7Barea%20of%20triangle%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%2014.5%20%5Ctext%7B%20yd%7D%20%5Ctimes%209%20%5Ctext%7B%20yd%7D%20%20%5Ctimes%20%5Csin%7B%28106%5E%5Ccirc%29%7D)
![\text{area of triangle} = 65.25 \times \sin{(106^\circ)} \text{ yd}^2](https://tex.z-dn.net/?f=%5Ctext%7Barea%20of%20triangle%7D%20%3D%2065.25%20%20%5Ctimes%20%5Csin%7B%28106%5E%5Ccirc%29%7D%20%20%5Ctext%7B%20yd%7D%5E2)
![\text{area of triangle} \approx 62.7222 \text{ yd}^2](https://tex.z-dn.net/?f=%5Ctext%7Barea%20of%20triangle%7D%20%5Capprox%2062.7222%20%20%5Ctext%7B%20yd%7D%5E2)
Rounded to the nearest whole square yard:
![\text{area of triangle} = 63 \text{ yd}^2](https://tex.z-dn.net/?f=%5Ctext%7Barea%20of%20triangle%7D%20%3D%2063%20%20%5Ctext%7B%20yd%7D%5E2)