a=6, b=2
Step-by-step explanation:
Use simplification into substitution
![\frac{a}{3} =1+\frac{2}{b}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B3%7D%20%3D1%2B%5Cfrac%7B2%7D%7Bb%7D)
![a=3(1+\frac{2}{b})](https://tex.z-dn.net/?f=a%3D3%281%2B%5Cfrac%7B2%7D%7Bb%7D%29)
![a=3+\frac{6}{b}](https://tex.z-dn.net/?f=a%3D3%2B%5Cfrac%7B6%7D%7Bb%7D)
We can now plug this value of <em>a</em> into the second equation.
![\frac{3+\frac{6}{b} }{4} +\frac{3}{b} =3](https://tex.z-dn.net/?f=%5Cfrac%7B3%2B%5Cfrac%7B6%7D%7Bb%7D%20%7D%7B4%7D%20%2B%5Cfrac%7B3%7D%7Bb%7D%20%3D3)
Get rid of fractions in the numerators and/or denominators
![\frac{3b+6}{4b} +\frac{3}{b} =3](https://tex.z-dn.net/?f=%5Cfrac%7B3b%2B6%7D%7B4b%7D%20%2B%5Cfrac%7B3%7D%7Bb%7D%20%3D3)
Then we can match the denominators
![\frac{3b+6}{4b} +\frac{12}{4b} =3](https://tex.z-dn.net/?f=%5Cfrac%7B3b%2B6%7D%7B4b%7D%20%2B%5Cfrac%7B12%7D%7B4b%7D%20%3D3)
Combine
![\frac{3b+18}{4b} =3](https://tex.z-dn.net/?f=%5Cfrac%7B3b%2B18%7D%7B4b%7D%20%3D3)
Divide both sides by three
![\frac{b+6}{4b} =1](https://tex.z-dn.net/?f=%5Cfrac%7Bb%2B6%7D%7B4b%7D%20%3D1)
Get rid of fractions
![b+6=4b](https://tex.z-dn.net/?f=b%2B6%3D4b)
Single out <em>b</em>
![6=3b](https://tex.z-dn.net/?f=6%3D3b)
![b=2](https://tex.z-dn.net/?f=b%3D2)
Now we can plug it into the equation
![\frac{a}{3} -\frac{2}{2} =1](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B3%7D%20-%5Cfrac%7B2%7D%7B2%7D%20%3D1)
![\frac{a}{3} =2](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B3%7D%20%3D2)
![a=6](https://tex.z-dn.net/?f=a%3D6)
Now we can check it;
![\frac{6}{3} -\frac{2}{2} =1](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B3%7D%20-%5Cfrac%7B2%7D%7B2%7D%20%3D1)
↑CORRECT
![\frac{6}{4} +\frac{3}{2} =3](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B4%7D%20%2B%5Cfrac%7B3%7D%7B2%7D%20%3D3)
↑CORRECT
If the pond were a rectangle, then:
length=15 m
width=6 m
We would have to calculate the perimeter of this rectangle.
Perimeter of a rectangle=2(length)+2(width)
Perimeter of this rectangle=2(15 m)+2(6 m)=30 m+12 m=42 m
We need 42 m and I only have 40 m, therefore, it would not be enough for fencing the pond.
1. simplify 1/3 ( c + 1 ) to c + 1/3 ( c + 1 over 3 = 1/6 (3c - 5)
2. simplify 1/6 (3c - 5) to 3c - 5 over 6 ( c + 1 over 3 = 3c - 5 over 6 )
3. multiply both sides by 6 [The LCM of 3, 6] 2(c + 1) = 3c - 5
4. expand (2c + 2 = 3c - 5)
5. subtract 2c from both sides (2 = 3c - 5 - 2c)
6. simplify 3c - 5 - 2c to c - 5 (2 = c - 5)
7. add 5 to both sides (2 + 5 = c)
8. simplify 2 + 5 to 7 (7 = c)
9. switch sides (c = 7 )
so in conclusion the answer is 7.
Answer:
1, 4 complementary
2, 3 supplementary
5, 6 neither
Step-by-step explanation:
complementary angles are angles in which the sum of both is equal to 90 degrees. supplementary angles are angles in which their sum is equal to 180 degrees.
hope that helps
Answer: See Explanation
Step-by-step Explanation: Heather rolls a far umber cube 60times and finds the probabilityof a 4 Landingface ups 1 Heather wants to roll the fair number cube 12 more times, and on the frst nI rolls, a 3 lands face up each time. Which statement best describes the probability of Heather roling a 4 on the 12th roll? The probability of rolling a 4 on the 12th roll is less than The probablity of rolling a 4 on the 12th roll is more than The probablity of rolling a 4 on the 12th roll is equal to The probability of rolling a 4 on the 12th roll is equal to 10.