Answer:
2800
Step-by-step explanation:
The dress's price increased by a factor of 9/7 so to undo this you flip the numbers around to get 7/9 and multiply the new price by this to get the original price.
Answer:
x = - 2 , y = 2
( - 2, 2)
Step-by-step explanation:
![y = - \frac{1}{2} x + 1 \\ y = 2x + 6](https://tex.z-dn.net/?f=y%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%2B%201%20%5C%5C%20y%20%3D%202x%20%2B%206)
first equation add 1/2 to both sides
second equation subtract 2x from both sides
![y + \frac{1}{2} x = 1 \\ y - 2x = 6](https://tex.z-dn.net/?f=y%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%3D%201%20%5C%5C%20y%20-%202x%20%3D%206)
Solve the first equation
![y + \frac{1}{2} x = 1](https://tex.z-dn.net/?f=y%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%3D%201)
subtract x/2 from both sides
![y = - \frac{1}{2} x + 1](https://tex.z-dn.net/?f=y%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%2B%201)
substitute
for y in the other equation
![- \frac{1}{2} x + 1 - 2x = 6](https://tex.z-dn.net/?f=-%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%2B%201%20-%202x%20%3D%206)
add
to 2x
![- \frac{5}{2} x + 1 = 6](https://tex.z-dn.net/?f=-%20%20%5Cfrac%7B5%7D%7B2%7D%20x%20%2B%201%20%3D%206)
subtract 1 from both sides
![- \frac{5}{2} x = 5](https://tex.z-dn.net/?f=-%20%20%5Cfrac%7B5%7D%7B2%7D%20x%20%3D%205)
divide both sides by ![- \frac{5}{2}](https://tex.z-dn.net/?f=-%20%20%5Cfrac%7B5%7D%7B2%7D)
x = - 2
substitute the value of x into an equation
![y = - \frac{1}{2} ( - 2) + 1](https://tex.z-dn.net/?f=y%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B2%7D%20%28%20-%202%29%20%2B%201)
distribute
y = 1 + 1
y = 2
x = -2, y = 2
( - 2, 2)
Answer:
x = 2
Step-by-step explanation:
Step 1: Convert to math
5x + 1 = 3x + 5
Step 2: Solve for <em>x</em>
- Subtract 4x on both sides: 2x + 1 = 5
- Subtract 1 on both sides: 2x = 4
- Divide both sides by 2: x = 2
Step 3: Check
<em>Plug in x to verify it's a solution.</em>
5(2) + 1 = 3(2) + 5
10 + 1 = 6 + 5
11 = 11
From the point-slope formula, we have:
![y-y_0=m(x-x_0)](https://tex.z-dn.net/?f=y-y_0%3Dm%28x-x_0%29)
where m is the slope, (x_0,y_0) are known points.
In this case, we have the slope and two points, we can substitute in the formula to get:
![\begin{gathered} \text{if:} \\ (x,y)=(-6,-4) \\ \text{and} \\ (x_0,y_0)=(a,2) \\ \Rightarrow-4-2=\frac{2}{3}(-6-a) \\ \Rightarrow-6=-\frac{2\cdot6}{3}-\frac{2}{3}a \\ \Rightarrow-6=-4-\frac{2}{3}a \\ \Rightarrow-6+4=-\frac{2}{3}a \\ \Rightarrow-2=-\frac{2}{3}a\Rightarrow a=-\frac{2}{-\frac{2}{3}}=\frac{3\cdot2}{2}=\frac{6}{2}=3 \\ a=3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bif%3A%7D%20%5C%5C%20%28x%2Cy%29%3D%28-6%2C-4%29%20%5C%5C%20%5Ctext%7Band%7D%20%5C%5C%20%28x_0%2Cy_0%29%3D%28a%2C2%29%20%5C%5C%20%5CRightarrow-4-2%3D%5Cfrac%7B2%7D%7B3%7D%28-6-a%29%20%5C%5C%20%5CRightarrow-6%3D-%5Cfrac%7B2%5Ccdot6%7D%7B3%7D-%5Cfrac%7B2%7D%7B3%7Da%20%5C%5C%20%5CRightarrow-6%3D-4-%5Cfrac%7B2%7D%7B3%7Da%20%5C%5C%20%5CRightarrow-6%2B4%3D-%5Cfrac%7B2%7D%7B3%7Da%20%5C%5C%20%5CRightarrow-2%3D-%5Cfrac%7B2%7D%7B3%7Da%5CRightarrow%20a%3D-%5Cfrac%7B2%7D%7B-%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Cfrac%7B3%5Ccdot2%7D%7B2%7D%3D%5Cfrac%7B6%7D%7B2%7D%3D3%20%5C%5C%20a%3D3%20%5Cend%7Bgathered%7D)
therefore, a=3
Note: you can also find a if you use the slope formula.