Answer:
f(x) = { x, -5 ≤ x < 0 and 3x - 3, 1 ≤ x < 5
Step-by-step explanation:
The equation of one line is y = x
The equation of the other line is y = 3x - 3
Altogether,
f(x) = { x, -5 ≤ x < 0 and 3x - 3, 1 ≤ x < 5
Answer: See below
Step-by-step explanation:
In scientific notation, you can tell that it is greater or less than 1 by looking at the exponent. The scientific notation looks like _.__×10⁻. Note: The little lines are blanks for you to fill in. The dot at the bottom is a decimal.
If the exponent on top of 10 is positive, you are moving the decimal to the right side, making the number greater.
If the exponent on top of 10 is negative, you are moving the decimal to the left side, making it smaller and smaller.
By those statements, you can tell if a number is greater or less than 1 by looking at the exponent.
This question has this set of answer choices:
a) when the plane cuts three faces of the cube, separating one corner from the others
b) when the plane passes through a pair of vertices that do not share a common face
c) when the plane is perpendicular to the base and intersects two adjacent vertical faces
d) when the plane makes an acute angle to the base and intersects three vertical faces
e) not enough information to answer the question
The right answer is the first choice: a) when the plane cuts three faces of the cube, separating one corner from the others
You can see a picture of this case in the figure attached: as you can see the cross section (in pink) is a triangle.
Answer:
1st angle: 128°
2nd angle: 32°
3rd angle: 20°
Step-by-step explanation:
You can start by setting up an equation. 180=x+4x+x-12. It sould all add up to 180 because angles of a triangle always add up to 180, and x represents the second triangle (you use the second angle as x because the other two angles elaborate off of this second angle). Then you solve. Add 12 to 180 and get 192. Then you can add like terms and make it 192=6x (you add the x's together). Lastly divide 192 by 6 and get 32. So the measurement of angle 2 is 32°. Then you multiply 32 by 4 to get the 1st angle measure, being 128. Lastly subtract 12 from 32 and get 20 for angle three. To check you work add the three angle measures you got and see if they =180, if so then you are correct.