If she needs to use 225g of flour for each cake and wants to make 18 cakes she will need 4050g (225x18=4050) of flour but she only has 360g which is obviously not enough flour. For one cake she needs 75g of sugar and since she needs to make 18 cakes she needs 1350g (75x18=1350) of sugar. She only has 135g so it’s not enough.
In slope intercept form it is y=2/3x-4
In point slope form it is 2/3x-y-4 :)
Answer:
![y=9x](https://tex.z-dn.net/?f=y%3D9x)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form
or ![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
In this problem we have
y=18 when x=2
Find the value of the constant of proportionality k
----> ![k=\frac{18}{2}=9](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B18%7D%7B2%7D%3D9)
therefore
The equation is equal to
![y=9x](https://tex.z-dn.net/?f=y%3D9x)
Answer:
A = 32°, a = 19, b = 14, B=22.98°, C = 125.02°, c = 29.36
Step-by-step explanation:
We have two sides of the triangle and we have an angle.
A = 32 °, a = 19, b = 14
We use the sine theorem to find the angle B.
We know that according to the sine theorem it is true that:
![\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28A%29%7D%7Ba%7D%3D%5Cfrac%7Bsin%28B%29%7D%7Bb%7D%3D%5Cfrac%7Bsin%28C%29%7D%7Bc%7D)
![\frac{sin(32\°)}{19}=\frac{sin(B)}{14}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%2832%5C%C2%B0%29%7D%7B19%7D%3D%5Cfrac%7Bsin%28B%29%7D%7B14%7D)
![sin(B)=14*\frac{sin(32\°)}{19}\\\\B=Arcsin(14*\frac{sin(32\°)}{19})\\\\B=22.98\°](https://tex.z-dn.net/?f=sin%28B%29%3D14%2A%5Cfrac%7Bsin%2832%5C%C2%B0%29%7D%7B19%7D%5C%5C%5C%5CB%3DArcsin%2814%2A%5Cfrac%7Bsin%2832%5C%C2%B0%29%7D%7B19%7D%29%5C%5C%5C%5CB%3D22.98%5C%C2%B0)
We know that the sum of the internal angles of a triangle is always equal to 180.
So:
![C=180-32-22.98\\\\C=125.02\°](https://tex.z-dn.net/?f=C%3D180-32-22.98%5C%5C%5C%5CC%3D125.02%5C%C2%B0)
Finally we find the c side
![\frac{sin(A)}{a}=\frac{sin(C)}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28A%29%7D%7Ba%7D%3D%5Cfrac%7Bsin%28C%29%7D%7Bc%7D)
![\frac{sin(32\°)}{19}=\frac{sin(125.02)}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%2832%5C%C2%B0%29%7D%7B19%7D%3D%5Cfrac%7Bsin%28125.02%29%7D%7Bc%7D)
![0.02789=\frac{sin(125.02)}{c}](https://tex.z-dn.net/?f=0.02789%3D%5Cfrac%7Bsin%28125.02%29%7D%7Bc%7D)
![c=\frac{sin(125.02)}{0.02789}\\\\c=29.36](https://tex.z-dn.net/?f=c%3D%5Cfrac%7Bsin%28125.02%29%7D%7B0.02789%7D%5C%5C%5C%5Cc%3D29.36)
Given:
The equation is:
![2-\dfrac{5}{6}x=\dfrac{7}{8}](https://tex.z-dn.net/?f=2-%5Cdfrac%7B5%7D%7B6%7Dx%3D%5Cdfrac%7B7%7D%7B8%7D)
To find:
The simplified for of the given equation so that it does have fractions.
Solution:
We have,
![2-\dfrac{5}{6}x=\dfrac{7}{8}](https://tex.z-dn.net/?f=2-%5Cdfrac%7B5%7D%7B6%7Dx%3D%5Cdfrac%7B7%7D%7B8%7D)
Denominators values are 6 and 8. LCM of 6 and 8 is 24 so multiply both sides by 24.
![24\left(2-\dfrac{5}{6}x\right)=24\times \dfrac{7}{8}](https://tex.z-dn.net/?f=24%5Cleft%282-%5Cdfrac%7B5%7D%7B6%7Dx%5Cright%29%3D24%5Ctimes%20%5Cdfrac%7B7%7D%7B8%7D)
![24(2)-24\left(\dfrac{5}{6}x\right)=24\times \dfrac{7}{8}](https://tex.z-dn.net/?f=24%282%29-24%5Cleft%28%5Cdfrac%7B5%7D%7B6%7Dx%5Cright%29%3D24%5Ctimes%20%5Cdfrac%7B7%7D%7B8%7D)
![48-4\times 5x=3\times 7](https://tex.z-dn.net/?f=48-4%5Ctimes%205x%3D3%5Ctimes%207)
![48-20x=21](https://tex.z-dn.net/?f=48-20x%3D21)
Therefore, the required equation is
.