Answer:
(-infinity, 2) U [-3]
Step-by-step explanation:
Step 1: we want to solve both equations for x. To do so, get the x variable by itself in both equations.
1.) 3x+4 = 5x+10
-6 = 2x (subtract 10 from both sides and 3x from both sides)
-3 = x (divide 2 from both sides)
2.) -5x + 7 > -3
-5x > -10 (subtract 7 from both sides)
x < 2
(divide both sides by -5, notice that dividing by a negative by a negative number flips the direction on > to < .)
Step 2: apply interval notation to these answers. Since x DOES equal -3 in equation one, it'll be in a bracket. On the contrary, since x has to be LESS THAN 2, it will have a parentheses.
So, our answer is: (-infinity, 2) U [-3]
*note the parentheses around infinity because something cannot equal infinity, it's not just one number*
Answer:
f(k) = 2*k + 1
Step-by-step explanation:
The 'f' function takes the variable, doubles it, and then adds 1.
So f(k) = 2*k + 1
f(g) = 2*g + 1
f(m) = 2*m + 1, and so on
It doesn't really matter which variable you use, the function still does the same thing to it.
Answer:
The correct answer is C) 4.6
Step-by-step explanation:
To find this, use the trigonometry functions. In this case, since we have the hypotenuse and are looking for the opposite, we use Sin.
Sin(α) = OPP/HYP
Sin(50) = x/6
6Sin(50) = x
4.6 = x
Answer: Tiffany can be certain the trapezoids are congruent.
Step-by-step explanation: Two figures are <u>congruent</u> when their corresponding angles are equal and they have the same shape and size.
A figure can go thorugh 3 types of transformations:
- <em>Rotation</em>: the figure is turned around a fixed point;
- <em>Reflection</em>: is created by fliping over the figure over a line;
- <em>Translation</em>: move the figure to another location, without changing its size;
As long the figure doesn't change its size or shape, it doesn't matter if it's rotated, reflected or translated, they will be congruent.
When the trapezoid was rotated creating another one, the two shapes didn't change its size or shape, so Tiffany can be certain they are congruent.
Step-by-step explanation:
The probability that either Jack or Jill will be selected on the first draw is 2/30.
The probability that the other person will be selected on the second draw is 1/29.
The probability of both events is (2/30) (1/29), which simplifies to 1/435.