Answer:
C) (-1, -4) and (4, 6)
Step-by-step explanation:
![\textsf{Equation 1}:y=2x-2](https://tex.z-dn.net/?f=%5Ctextsf%7BEquation%201%7D%3Ay%3D2x-2)
![\textsf{Equation 2}:y=x^2-x-6](https://tex.z-dn.net/?f=%5Ctextsf%7BEquation%202%7D%3Ay%3Dx%5E2-x-6)
Substitute Equation 1 into Equation 2 and solve for x:
![\implies 2x-2=x^2-x-6](https://tex.z-dn.net/?f=%5Cimplies%202x-2%3Dx%5E2-x-6)
![\implies x^2-3x-4=0](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2-3x-4%3D0)
Find two numbers that multiply to -4 and sum to -3: -4 and 1
Rewrite the middle term as the sum of these two numbers:
![\implies x^2-4x+x-4=0](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2-4x%2Bx-4%3D0)
Factorize the first two terms and the last two terms separately:
![\implies x(x-4)+1(x-4)=0](https://tex.z-dn.net/?f=%5Cimplies%20x%28x-4%29%2B1%28x-4%29%3D0)
Factor out the common term
:
![\implies (x+1)(x-4)=0](https://tex.z-dn.net/?f=%5Cimplies%20%28x%2B1%29%28x-4%29%3D0)
![\implies (x+1)=0 \implies x=-1](https://tex.z-dn.net/?f=%5Cimplies%20%28x%2B1%29%3D0%20%5Cimplies%20x%3D-1)
![\implies (x-4)=0 \implies x=4](https://tex.z-dn.net/?f=%5Cimplies%20%28x-4%29%3D0%20%5Cimplies%20x%3D4)
Substitute the found values of x into Equation 1 and solve for y:
![x=-1 \implies y=2(-1)-2=-4](https://tex.z-dn.net/?f=x%3D-1%20%5Cimplies%20y%3D2%28-1%29-2%3D-4)
![x=4 \implies y=2(4)-2=6](https://tex.z-dn.net/?f=x%3D4%20%5Cimplies%20y%3D2%284%29-2%3D6)
Therefore, the solution to the system of equations is:
(-1, -4) and (4, 6)
Answer:
![\displaystyle 2x - 3y = 6\:OR\:y = \frac{2}{3}x - 2 \\ \\ 3x - 2y = 40\:OR\:y = \frac{3}{2}x - 20](https://tex.z-dn.net/?f=%5Cdisplaystyle%202x%20-%203y%20%3D%206%5C%3AOR%5C%3Ay%20%3D%20%5Cfrac%7B2%7D%7B3%7Dx%20-%202%20%5C%5C%20%5C%5C%203x%20-%202y%20%3D%2040%5C%3AOR%5C%3Ay%20%3D%20%5Cfrac%7B3%7D%7B2%7Dx%20-%2020)
Step-by-step explanation:
2 = ⅔[6] + b
4
![\displaystyle -2 = b \\ \\ y = \frac{2}{3}x - 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20-2%20%3D%20b%20%5C%5C%20%5C%5C%20y%20%3D%20%5Cfrac%7B2%7D%7B3%7Dx%20-%202)
If you want it in <em>Standard Form</em>:
y = ⅔x - 2
- ⅔x - ⅔x
_________
−⅔x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid it.]
−3[−⅔x + y = −2]
![\displaystyle 2x - 3y = 6](https://tex.z-dn.net/?f=%5Cdisplaystyle%202x%20-%203y%20%3D%206)
_______________________________________________
−5 = 3⁄2[10] + b
15
![\displaystyle -20 = b \\ \\ y = \frac{3}{2}x - 20](https://tex.z-dn.net/?f=%5Cdisplaystyle%20-20%20%3D%20b%20%5C%5C%20%5C%5C%20y%20%3D%20%5Cfrac%7B3%7D%7B2%7Dx%20-%2020)
If you want it in <em>Standard</em><em> </em><em>Form</em>:
y = 3⁄2x - 20
- 3⁄2x - 3⁄2x
__________
−3⁄2x + y = −20 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]
−2[−3⁄2x + y = −20]
![\displaystyle 3x - 2y = 40](https://tex.z-dn.net/?f=%5Cdisplaystyle%203x%20-%202y%20%3D%2040)
* Parallel Lines have SIMILAR <em>RATE OF CHANGES</em> [<em>SLOPES</em>], so ⅔ and 3⁄2 remain the way they are.
I am joyous to assist you anytime.
Can you please say how many snow globes there are so, we can give you an answer?
Answer:
d
Step-by-step explanation:
since since the scale factor is 3 angle ab abyou multiply 6 * 3 to get 18
Answer:
Answer b: Sales of trench coats increased 8.3 percentage points faster than total coat sales.
Step-by-step explanation:
First add all the sales for 2006, and do the same for the 2007 sales, so we can compare both total sales numbers:
For 2006 we have:
103+297+210+213+137 = 960 total sales
For 2007 we have:
127+223+210+285+259 = 1104 total sales
The percent increase is calculated as the difference between the final value minus the original value, divided by the original value and multiplied by 100:
For the total number of coats we have that the percent increase is:
%
For the trench coats (which went from 103 sales tp 127 sales) we have the following percent increase:
%
Therefore, the percent increase in trench coats was larger than the percent increase in total sales by:
23.3 % - 15% = 8.3%