00000000000 that would be ur answer
Answer:
a : b = 19 : 7
Step-by-step explanation:
Given
4a - 5b : 5a + 4b = 1 : 3
Expressing in fractional form, that is
=
( cross- multiply )
3(4a - 5b) = 5a + 4b ← distribute left side
12a - 15b = 5a + 4b ( subtract 5a from both sides )
7a - 15b = 4b ( add 15b to both sides )
7a = 19b ( divide both sides by 7 )
a =
b ( divide both sides by b )
= ![\frac{19}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B19%7D%7B7%7D)
That is a : b = 19 : 7
Answer:
4,5,6 are the three consecutive numbers. 16, 25 and 36 are their squares.
Step-by-step explanation:
Let the three consecutive numbers be x, (x+1), (x+2)
Now, the squares of these three numbers are ![x^{2} ,(x+1)^{2} ,(x+2)^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2C%28x%2B1%29%5E%7B2%7D%20%2C%28x%2B2%29%5E%7B2%7D)
Sum = 77
∴by the problem ,
![x^{2} +(x+1)^{2}+(x+2)^{2} = 77\\x^{2} +(x^{2} +2x+1)+(x^{2}+4x +4) = 77\\x^{2} +x^{2} +2x+1+x^{2} +4x +4 = 77\\3x^{2} +6x+5 = 77\\3x^{2} +6x = 77-5\\3x^{2} + 6x = 72\\3x^{2} +6x-72= 0\\](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%28x%2B1%29%5E%7B2%7D%2B%28x%2B2%29%5E%7B2%7D%20%20%3D%2077%5C%5Cx%5E%7B2%7D%20%2B%28x%5E%7B2%7D%20%2B2x%2B1%29%2B%28x%5E%7B2%7D%2B4x%20%2B4%29%20%3D%2077%5C%5Cx%5E%7B2%7D%20%2Bx%5E%7B2%7D%20%2B2x%2B1%2Bx%5E%7B2%7D%20%2B4x%20%2B4%20%3D%2077%5C%5C3x%5E%7B2%7D%20%2B6x%2B5%20%3D%2077%5C%5C3x%5E%7B2%7D%20%2B6x%20%3D%2077-5%5C%5C3x%5E%7B2%7D%20%2B%206x%20%3D%2072%5C%5C3x%5E%7B2%7D%20%2B6x-72%3D%200%5C%5C)
{Taking 3 common }
![x^{2} +2x- 24 = 0\\](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B2x-%2024%20%3D%200%5C%5C)
{By factorization}
![x^{2} +2x- 24 =0\\ x^{2} +6x-4x-24=0\\x(x+6)-4(x+6)=0\\(x+6)(x-4)=0\\](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B2x-%2024%20%3D0%5C%5C%20x%5E%7B2%7D%20%2B6x-4x-24%3D0%5C%5Cx%28x%2B6%29-4%28x%2B6%29%3D0%5C%5C%28x%2B6%29%28x-4%29%3D0%5C%5C)
Therfore,
![x= -6,4\\](https://tex.z-dn.net/?f=x%3D%20-6%2C4%5C%5C)
<em>X can't be negetive </em>
∴ ![x =4\\x+1=5\\x+2=6](https://tex.z-dn.net/?f=x%20%3D4%5C%5Cx%2B1%3D5%5C%5Cx%2B2%3D6)
The squares of the three consecutive numbers are 16, 25, 36
The three consecutive numbers whose sum is 77 are 4, 5, 6
Answer:
(a)
or ![-2 < 1](https://tex.z-dn.net/?f=-2%20%3C%201)
(b)
or
Step-by-step explanation:
Given
--- North Dakota
--- Cheyenne, Wyoming
Solving (a): Inequality to compare both temperatures
From the given temperatures, we can conclude that:
or ![N < C](https://tex.z-dn.net/?f=N%20%3C%20C)
Because
i.e. 1 is greater than -2
or
i.e. -2 is less than 1
Solving (b): Inequality to compare the absolute values of the temperatures
We have:
![N = -2F](https://tex.z-dn.net/?f=N%20%3D%20-2F)
![C = 1F](https://tex.z-dn.net/?f=C%20%3D%201F)
The absolute values are:
![|N| = |-2|](https://tex.z-dn.net/?f=%7CN%7C%20%3D%20%7C-2%7C)
![|N| =2](https://tex.z-dn.net/?f=%7CN%7C%20%3D2)
![|C| = |1|](https://tex.z-dn.net/?f=%7CC%7C%20%3D%20%7C1%7C)
![|C| = 1](https://tex.z-dn.net/?f=%7CC%7C%20%3D%201)
By comparison:
or ![|C| < |N|](https://tex.z-dn.net/?f=%7CC%7C%20%3C%20%7CN%7C)
Because
i.e. 2 is greater than 1
or
i.e. 1 is less than 2