Now, notice the "tickmarks" on the angles, that means those two angles are equal, now if ∡ABC is 110, then the remaining is 70, 180 - 110, and if you subtract the 70 from 110, what's left is ∡DBC.
<span>No, because the –1 in the numerator and denominator is not a common factor and cannot be canceled.</span>
Answer:
![\large \boxed{\sf \text{The rate of the boat is } 53 \ km/h \text{, the rate of the current is }8\ km/h \ \ }](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5Csf%20%5Ctext%7BThe%20rate%20of%20the%20boat%20is%20%7D%2053%20%5C%20km%2Fh%20%5Ctext%7B%2C%20the%20rate%20of%20the%20current%20is%20%7D8%5C%20km%2Fh%20%5C%20%5C%20%7D)
Step-by-step explanation:
Hello, let's note v the rate of the boat and r the rate of the current. We can write the following
![\dfrac{135}{v-r}=3=\dfrac{183}{v+r}](https://tex.z-dn.net/?f=%5Cdfrac%7B135%7D%7Bv-r%7D%3D3%3D%5Cdfrac%7B183%7D%7Bv%2Br%7D)
It means that
![135(v+r)=183(v-r)\\\\135 v + 135r=183v-183r\\\\\text{ *** We regroup the terms in v on the right and the ones in r to the left***}\\\\(135+183)r=(183-135)v\\\\318r=48v\\\\\text{ *** We divide by 48 both sides ***}\\\\\boxed{v = \dfrac{318}{48} \cdot r= \dfrac{159}{24} \cdot r}](https://tex.z-dn.net/?f=135%28v%2Br%29%3D183%28v-r%29%5C%5C%5C%5C135%20v%20%2B%20135r%3D183v-183r%5C%5C%5C%5C%5Ctext%7B%20%2A%2A%2A%20We%20regroup%20the%20terms%20in%20v%20on%20the%20right%20and%20the%20ones%20in%20r%20to%20the%20left%2A%2A%2A%7D%5C%5C%5C%5C%28135%2B183%29r%3D%28183-135%29v%5C%5C%5C%5C318r%3D48v%5C%5C%5C%5C%5Ctext%7B%20%2A%2A%2A%20We%20divide%20by%2048%20both%20sides%20%2A%2A%2A%7D%5C%5C%5C%5C%5Cboxed%7Bv%20%3D%20%5Cdfrac%7B318%7D%7B48%7D%20%5Ccdot%20r%3D%20%5Cdfrac%7B159%7D%7B24%7D%20%5Ccdot%20r%7D)
But we can as well use the second equation:
![3(v+r)=183\\\\v+r=\dfrac{183}{3}=61\\\\\dfrac{159}{24}r+r=61\\\\\dfrac{159+24}{24}r=61\\\\\boxed{r = \dfrac{61*24}{183}=8}](https://tex.z-dn.net/?f=3%28v%2Br%29%3D183%5C%5C%5C%5Cv%2Br%3D%5Cdfrac%7B183%7D%7B3%7D%3D61%5C%5C%5C%5C%5Cdfrac%7B159%7D%7B24%7Dr%2Br%3D61%5C%5C%5C%5C%5Cdfrac%7B159%2B24%7D%7B24%7Dr%3D61%5C%5C%5C%5C%5Cboxed%7Br%20%3D%20%5Cdfrac%7B61%2A24%7D%7B183%7D%3D8%7D)
and then
![\boxed{v=\dfrac{159*8}{24}=53}](https://tex.z-dn.net/?f=%5Cboxed%7Bv%3D%5Cdfrac%7B159%2A8%7D%7B24%7D%3D53%7D)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
1. 15
2. -2
Step-by-step explanation:
First, since -4 is in parentheses, we want to take it out of parentheses. This might make sense but now it becomes 12 + 7 - 4. If it doesn't make sense, I'm sorry because I don't know how to explain it. Now we add 12 to 7 and we come out with 19. Then we subtract 4 and get 15. We want to do the same for number 2. We take -6.25 out of the parentheses and we have -1.75 - 6.25 + 6. When you subtract a negative something from a negative, we get more negative. So now we have -8 + 6. Which then equals -2. I hope this helps!