Answer:
The unknown angle is 80
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
Let the unknown angle be x
20+80+x = 180
Add like terms
100+x = 180
Subtract 100 from each side
100-100+x=180-100
x = 80
15 pounds each and 16 watermelons= 240 pounds. (15x16=240)
Answer:
20.04 units
Step-by-step explanation:
The diagram shows right triangle ABC. Use the definition of the cosine:
![\cos \angle C=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}\\ \\\cos \angle C=\dfrac{BC}{AC}\\ \\\cos 51^{\circ}=\dfrac{BC}{27}\\ \\BC=27\cdot \cos 51^{\circ}\\ \\BC\approx 20.04\ units](https://tex.z-dn.net/?f=%5Ccos%20%5Cangle%20C%3D%5Cdfrac%7B%5Ctext%7BAdjacent%20leg%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%5C%5C%20%5C%5C%5Ccos%20%5Cangle%20C%3D%5Cdfrac%7BBC%7D%7BAC%7D%5C%5C%20%5C%5C%5Ccos%2051%5E%7B%5Ccirc%7D%3D%5Cdfrac%7BBC%7D%7B27%7D%5C%5C%20%5C%5CBC%3D27%5Ccdot%20%5Ccos%2051%5E%7B%5Ccirc%7D%5C%5C%20%5C%5CBC%5Capprox%2020.04%5C%20units)
If the polygons are similar then the sides are in proportion.
![\dfrac{32}{24}=\dfrac{32:8}{24:8}=\dfrac{4}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B32%7D%7B24%7D%3D%5Cdfrac%7B32%3A8%7D%7B24%3A8%7D%3D%5Cdfrac%7B4%7D%7B3%7D)
Therefore we have the equations:
![\dfrac{x-1}{6}=\dfrac{4}{3}\qquad\text{cross multiply}\\\\3(x-1)=(4)(6)\\\\3x-3=24\qquad\text{add 3 to both sides}\\\\3x=27\qquad\text{divide both sides by 3}\\\\\boxed{x=9}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-1%7D%7B6%7D%3D%5Cdfrac%7B4%7D%7B3%7D%5Cqquad%5Ctext%7Bcross%20multiply%7D%5C%5C%5C%5C3%28x-1%29%3D%284%29%286%29%5C%5C%5C%5C3x-3%3D24%5Cqquad%5Ctext%7Badd%203%20to%20both%20sides%7D%5C%5C%5C%5C3x%3D27%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5C%5Cboxed%7Bx%3D9%7D)
![\dfrac{y+1}{21}=\dfrac{4}{3}\qquad\text{cross multiply}\\\\3(y+1)=(21)(4)\\\\3y+3=84\qquad\text{subtract 3 from both sides}\\\\3y=81\qquad\text{divide both sides by 3}\\\\\boxed{y=27}](https://tex.z-dn.net/?f=%5Cdfrac%7By%2B1%7D%7B21%7D%3D%5Cdfrac%7B4%7D%7B3%7D%5Cqquad%5Ctext%7Bcross%20multiply%7D%5C%5C%5C%5C3%28y%2B1%29%3D%2821%29%284%29%5C%5C%5C%5C3y%2B3%3D84%5Cqquad%5Ctext%7Bsubtract%203%20from%20both%20sides%7D%5C%5C%5C%5C3y%3D81%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5C%5Cboxed%7By%3D27%7D)
Answer:
See attachment for rectangle
Step-by-step explanation:
Given
![A = (-6,0)](https://tex.z-dn.net/?f=A%20%3D%20%28-6%2C0%29)
![B = (-4,0)](https://tex.z-dn.net/?f=B%20%3D%20%28-4%2C0%29)
![Area = 12](https://tex.z-dn.net/?f=Area%20%3D%2012)
Required
Draw the rectangle
First, we calculate the distance between A and B using distance formula;
![AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D)
So, we have:
![AB = \sqrt{(-6 - -4)^2 + (0- 0)^2}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%28-6%20-%20-4%29%5E2%20%2B%20%280-%200%29%5E2%7D)
![AB = \sqrt{(-2)^2 + (0)^2}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%28-2%29%5E2%20%2B%20%280%29%5E2%7D)
![AB = \sqrt{4 + 0}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B4%20%2B%200%7D)
![AB = \sqrt{4}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B4%7D)
![AB = 2](https://tex.z-dn.net/?f=AB%20%3D%202)
The above represents the length of the triangle.
Next, calculate the width using:
![Length * Width = Area](https://tex.z-dn.net/?f=Length%20%2A%20Width%20%3D%20Area)
![2* Width = 12](https://tex.z-dn.net/?f=2%2A%20Width%20%3D%2012)
Divide both sides by 2
![Width = 6](https://tex.z-dn.net/?f=Width%20%3D%206)
This implies that, the width of the rectangle is 6 units.
We have:
![A = (-6,0)](https://tex.z-dn.net/?f=A%20%3D%20%28-6%2C0%29)
![B = (-4,0)](https://tex.z-dn.net/?f=B%20%3D%20%28-4%2C0%29)
Since A and B are at the upper left and right, then the ther two points are below.
6 units below each of the above point are:
=> ![C = (-6,-6)](https://tex.z-dn.net/?f=C%20%3D%20%28-6%2C-6%29)
=> ![D = (-4,-6)](https://tex.z-dn.net/?f=D%20%3D%20%28-4%2C-6%29)
Hence, the points of the rectangle are:
![A = (-6,0)](https://tex.z-dn.net/?f=A%20%3D%20%28-6%2C0%29)
![B = (-4,0)](https://tex.z-dn.net/?f=B%20%3D%20%28-4%2C0%29)
![C = (-6,-6)](https://tex.z-dn.net/?f=C%20%3D%20%28-6%2C-6%29)
![D = (-4,-6)](https://tex.z-dn.net/?f=D%20%3D%20%28-4%2C-6%29)
<em>See attachment for rectangle</em>