Let x represent the amount of sugar needed to make one batch of cookies.
We have been given that Pia used
of her sugar to make
of a batch of cookies. We are asked to find the amount of sugar needed to make whole batch.
We can represent our given information in an equation as:
![\frac{3}{4}x=\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7Dx%3D%5Cfrac%7B2%7D%7B3%7D)
Let us solve for x.
![\frac{4}{3}\cdot \frac{3}{4}x=\frac{4}{3}\cdot \frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Ccdot%20%5Cfrac%7B3%7D%7B4%7Dx%3D%5Cfrac%7B4%7D%7B3%7D%5Ccdot%20%5Cfrac%7B2%7D%7B3%7D)
![x=\frac{4\cdot 2}{3\cdot 3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Ccdot%202%7D%7B3%5Ccdot%203%7D)
![x=\frac{8}{9}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B8%7D%7B9%7D)
Therefore, Pia needs
of her sugar to make 1 whole batch of cookies.
The sign of the product of -21 and 451 is going to be negative. That is because of the rule when you are multiplying a positive number times a negative number. A positive number times a negative number will always be negative. Here are some helpful rules to know:
positive * positive = positive
negative * positive = negative
negative * negative = positive (the negatives cancel each other out)
Since this question has numbers that fit the second case, the answer will be negative.
Answer:
a) RTP
b) MN
c) x=7
Step-by-step explanation:
hope this helps
Answer:
y = 2x - 3
Step-by-step explanation:
Start by writing out the given equation.
-2x + y = -3
The goal is to isolate the variable y.
For this equation, all you need to do is add 2x to each side.
-2x + y + 2x = -3 + 2x
Therefore, the answer is y = 2x -3.
I don't know if you are are familiar with the equation y = mx + b, but here's a little refresher. m is the slope, or in this case 2. b is the y-intercept, or in this case -3.
The equation y = mx + b is slope intercept form, so if you know this, you should be able to write any equation in slope intercept form.
Hope this helps!
If
varies directly as
, then there is some constant
for which
![x=ay^2](https://tex.z-dn.net/?f=x%3Day%5E2)
Similarly, there is some constant
such that
![y=bz^3](https://tex.z-dn.net/?f=y%3Dbz%5E3)
Given that
when
, we have
![\begin{cases}-16=ay^2\\y=8b\end{cases}\implies-16=a(8b)^2\implies ab^2=-\dfrac14](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D-16%3Day%5E2%5C%5Cy%3D8b%5Cend%7Bcases%7D%5Cimplies-16%3Da%288b%29%5E2%5Cimplies%20ab%5E2%3D-%5Cdfrac14)
Now when
, we get
![\begin{cases}x=ay^2\\y=\frac b8\end{cases}\implies x=a\left(\dfrac b8\right)^2=\dfrac{ab^2}{64}=\dfrac{-\frac14}{64}=\boxed{-\dfrac1{256}}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%3Day%5E2%5C%5Cy%3D%5Cfrac%20b8%5Cend%7Bcases%7D%5Cimplies%20x%3Da%5Cleft%28%5Cdfrac%20b8%5Cright%29%5E2%3D%5Cdfrac%7Bab%5E2%7D%7B64%7D%3D%5Cdfrac%7B-%5Cfrac14%7D%7B64%7D%3D%5Cboxed%7B-%5Cdfrac1%7B256%7D%7D)