Answer:
1857 miles.
Step-by-step explanation:
We have been given that the scale on a map is 1 cm:30 mi. The distance on the map between San Francisco, CA, and Chicago, IL, is 61.9 cm. We are asked to find the actual distance between San Francisco and Chicago.
We will use proportions to solve our given problem.
![\frac{\text{Actual distance}}{\text{Map distance}}=\frac{30\text{ miles}}{1\text{ cm}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BActual%20distance%7D%7D%7B%5Ctext%7BMap%20distance%7D%7D%3D%5Cfrac%7B30%5Ctext%7B%20miles%7D%7D%7B1%5Ctext%7B%20cm%7D%7D)
Upon substituting map distance between San Francisco and Chicago, we will get:
![\frac{\text{Actual distance}}{61.9\text{ cm}}=\frac{30\text{ miles}}{1\text{ cm}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BActual%20distance%7D%7D%7B61.9%5Ctext%7B%20cm%7D%7D%3D%5Cfrac%7B30%5Ctext%7B%20miles%7D%7D%7B1%5Ctext%7B%20cm%7D%7D)
![\frac{\text{Actual distance}}{61.9\text{ cm}}\cdot 61.9\text{ cm}=\frac{30\text{ miles}}{1\text{ cm}}\cdot 61.9\text{ cm}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BActual%20distance%7D%7D%7B61.9%5Ctext%7B%20cm%7D%7D%5Ccdot%2061.9%5Ctext%7B%20cm%7D%3D%5Cfrac%7B30%5Ctext%7B%20miles%7D%7D%7B1%5Ctext%7B%20cm%7D%7D%5Ccdot%2061.9%5Ctext%7B%20cm%7D)
![\text{Actual distance}=30\text{ miles}\cdot 61.9](https://tex.z-dn.net/?f=%5Ctext%7BActual%20distance%7D%3D30%5Ctext%7B%20miles%7D%5Ccdot%2061.9)
![\text{Actual distance}=1857\text{ miles}](https://tex.z-dn.net/?f=%5Ctext%7BActual%20distance%7D%3D1857%5Ctext%7B%20miles%7D)
Therefore, the actual distance between San Francisco and Chicago is 1857 miles.
This involvea factoring the polynomial into binomials and solving.
So make it (3x+1)(x-7)
X equals 7 and -1/3
Answer:
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ANSWER
36√3 square units.
EXPLANATION
The area of a parallelogram is obtained by multiplying the base by the height.
We use the sine ratio to obtain the height.
![\sin(60 \degree) = \frac{h}{6}](https://tex.z-dn.net/?f=%20%5Csin%2860%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7Bh%7D%7B6%7D%20)
![h = 6 \sin(60 \degree)](https://tex.z-dn.net/?f=h%20%3D%206%20%5Csin%2860%20%5Cdegree%29%20)
![h = 3 \sqrt{3}](https://tex.z-dn.net/?f=h%20%3D%203%20%5Csqrt%7B3%7D%20)
The area becomes:
![12 \times 3 \sqrt{3} = 36 \sqrt{3} {units}^{2}](https://tex.z-dn.net/?f=12%20%5Ctimes%203%20%5Csqrt%7B3%7D%20%20%3D%2036%20%5Csqrt%7B3%7D%20%7Bunits%7D%5E%7B2%7D%20%20)