The answer to 21 is a translation
The coordinates to 22 is A'(2,5), B'(2,3), C'(5,3)
Answer:
12
Step-by-step explanation:
Since its a square, all the sides are the same.
(2x+8)4=20x+8
8x+32=20x+8
32-8=20x-8x
24=12x
x=2
2x+8= 2(2)+8= 12
Answer:
C, E, and F
Explanation:
There are two ways to answer this question. First, you could simply input each answer into both equations to see which one works but that would take quite a long time.
A better way is to simply solve each equation for x.
You could rewrite
2x + 7 < -3
as
2x + 7 = -3
and solve:
Subtract 7 from both sides
![(2x + 7) -7 = (-3) - 7\\2x = -10](https://tex.z-dn.net/?f=%282x%20%2B%207%29%20-7%20%3D%20%28-3%29%20-%207%5C%5C2x%20%3D%20-10)
Now divide both sides by 2
![\frac{2x}{2} = \frac{-10}{2}\\x = -5](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%20%20%3D%20%5Cfrac%7B-10%7D%7B2%7D%5C%5Cx%20%3D%20-5)
Now we can simply replace the equals sign with the inequality
x < -5
Where you can run into trouble is if you have to multiply or divide by a negative number across the equation, you must flip the inequality sign. It's best to leave it there to remind you, but I switched it out just to show that it's no different than a typical algebraic equation.
Now, we know that x can be any value less than -5. Let's find out the same thing for the second equation:
![x - 8 + 3x < -4\\(x + 3x) -8 < -4\\4x - 8 < -4\\(4x - 8) + 8 < (-4) + 8\\4x < 4\\\frac{4x}{4} < \frac{4}{4}\\x < 1](https://tex.z-dn.net/?f=x%20-%208%20%2B%203x%20%3C%20-4%5C%5C%28x%20%2B%203x%29%20-8%20%3C%20-4%5C%5C4x%20-%208%20%3C%20-4%5C%5C%284x%20-%208%29%20%2B%208%20%3C%20%28-4%29%20%2B%208%5C%5C4x%20%3C%204%5C%5C%5Cfrac%7B4x%7D%7B4%7D%20%3C%20%5Cfrac%7B4%7D%7B4%7D%5C%5Cx%20%3C%201)
Now we know that x must be less than 1 for the second equation. So, now we can choose the answers that are both less than -5 and less than 1.
These answers are:
C. -10
E. -8.24
and
F. -15/2 which is -7.5
NOTE: -5 is equal to but not less than -5 so G is not included.
Sample size, n = 75
Point estimate, p = 52/75 = 0.693
Z at 99.7% confidence interval ≈ 2.96
Population mean interval = p+/- Z*Sqrt [p(1-p)/n]
Substituting;
Population mean interval = 0.693 +/- 2.96*Sqrt [0.693(1-0.693)/75] = 0.693+/-0.158 = (0.535,0.851) or (53.5%,85.1%)
x' = 24/5
The rule for variable to variable' is multiply by 6/5, shown as y to y'