5x + 2(x + 1) ≤ 23
Distribute the 2.
5x + 2x + 2 ≤ 23
Combine like terms.
7x + 2 ≤ 23
Subtract 2 from both sides.
7x ≤ 21
Divide both sides by 7
x ≤ 3
Answer:
Rounded to a whole number, the player has 12 bonus stars.
Step-by-step explanation:
Since the video game establishes that for every 1,333 points of attack power 3 levels are gained, and that the player has a total of 0.21 million attack points, to determine the number of levels that player has it is necessary to perform the following calculation :
0.21 million = 210,000
210,000 / 1,333 x 3 = Levels
472.6 = Levels
Now, every 38 levels, the game awards a bonus star. To determine the amount of bonus stars that the player has, the following division must be made:
472.6 / 38 = X
12.43 = X
Thus, rounded to a whole number, the player has 12 bonus stars.
Answer:
B and D
Step-by-step explanation:
Take a look at all the options x=4, 3, 1, 2 > 0
So, we just care about the domain where x>0, which is 
.
Then plug in x we will have the right answer.
The ladder, leaning against the building, forms a right triangle with height "a" being the distance from the ground to the window, and hypotenuse "c" being the length of the ladder.
Because it's a right triangle, we can use trigonometric ratios to find the angles we're missing.
For part A), to solve for the angle between the base of the ladder and the ground, you'll want to use sine, because we know the lengths of the opposite side and the hypotenuse.
Sin(x) = a/c , solve for angle x in degrees or radians.
For part B), finding the angle between the top of the ladder and the building, remember that the sum of the angles in a triangle is 180 degrees, or pi radians, depending on which unit your teacher prefers.
Assuming degrees, we can say that angle y = 180-90-x. You are simply subtracting the two known angles to find the third.
For part C) use the Pythagorean theorem. You're looking for the length of the base, "b". Recall:
a^2 + b^2 = c^2
Plug in the known values, and solve for b.
