A scale factor is a number which scales or multiplies a quantity, e.g a scale factor of two would mean to multiply whatever the value is by two. Since there are no specific values for LMN and OPQ, the scale factor of the two would be 1/1 because they are one quantity with respect to the other.
The remainder is less than the divisor because if the remainder was greater than the the divisor, you have to wrong quotint.
<em> OR you can also write</em>
<em></em>
In other words, you should incress your quotinet until your remnider is less than your divisor.
<u>Hope this helped!</u>
Answer:
Choice A
Step-by-step explanation:
In each case, each equation has an equation of a line in y = mx + b form equaling another equation of a line in y = mx + b form. If the two sides are equal, it is the same equation, there are infinitely many solutions. If the sides are different, then if the slopes are different, the lines intersect at one point, and there is exactly 1 solution. If the slopes are equal, the lines are parallel, and there is no solution.
(Choice A) -10x-10=-10x-10
In Choice A, both sides of the equation are equal, so there are infinitely many solutions.
(Choice B) 10x-10=-10x+10
(Choice C) 10x-10=-10x-10
(Choice D) -10x-10=-10x+10
In choices B through D, the two sides are not equal, so there is either 1 solution (B and C since they have different slopes) or no solution (D since the slopes are equal).
Answer: 292
Step-by-step explanation:
Given
There are 240 members in a labor union
The number increases by 5% each year
After 1 year it is
![\Rightarrow 240+5\%\times 240\\\Rightarrow 240(1+0.05)](https://tex.z-dn.net/?f=%5CRightarrow%20240%2B5%5C%25%5Ctimes%20240%5C%5C%5CRightarrow%20240%281%2B0.05%29)
After 2 years
Similarly, after 4 years
![\Rightarrow 240(1+0.05)^4\\\Rightarrow 291.72\approx 292](https://tex.z-dn.net/?f=%5CRightarrow%20240%281%2B0.05%29%5E4%5C%5C%5CRightarrow%20291.72%5Capprox%20292)
Answer:
![f(x)=(x-1)^{2}+6](https://tex.z-dn.net/?f=f%28x%29%3D%28x-1%29%5E%7B2%7D%2B6)
Step-by-step explanation:
First, subtract 7 from each side.
![-7=x^{2} -2x](https://tex.z-dn.net/?f=-7%3Dx%5E%7B2%7D%20-2x)
Now, add in a blank on each side so you can write in your new term that will complete the square. We'll call that term 's' for now.
![-7+s=x^{2} -2x+ s](https://tex.z-dn.net/?f=-7%2Bs%3Dx%5E%7B2%7D%20-2x%2B%20s)
The next step is to take half of the b term, and then square that. In this case, half of '
' is
. If we square that we get
. So that is the term we will put in for
.
![-7+1=x^{2} -2x+1](https://tex.z-dn.net/?f=-7%2B1%3Dx%5E%7B2%7D%20-2x%2B1)
Simplify:
![-6=x^{2} -2x+1](https://tex.z-dn.net/?f=-6%3Dx%5E%7B2%7D%20-2x%2B1)
If you look at the right side of the equation, we can factor. That's because we <u>completed the square</u>. We can use the 'guess and check' method to factor. Remember, this is where we use 2 sets of parentheses and fill in the blanks.
![-6=(x-1)(x-1)](https://tex.z-dn.net/?f=-6%3D%28x-1%29%28x-1%29)
If we were to FOIL the right side we would end up with
.
Since we have 2 '(x-1)' terms next to each other, we can simplify to:
![-6=(x-1)^{2}](https://tex.z-dn.net/?f=-6%3D%28x-1%29%5E%7B2%7D)
Now, all we need to do is add 6 to both sides and we have the vertex form.
![f(x)=(x-1)^{2}+6](https://tex.z-dn.net/?f=f%28x%29%3D%28x-1%29%5E%7B2%7D%2B6)
I hope this helps!