To answer question 12, you first need to know the definition of a <em>prism</em> and a<em> pyramid.
</em>A <em>pyramid </em> is a 3-D structure with one base, whose outer faces are made of triangles, and meet at a single point at the top.
A <em>prism</em> is any 3-D shape with a base of any number of sides, another base with the same amount of sides, and faces joining the two together on every side of the bases.
12.
Shape A is a <em>pyramid</em>, because it has one base, and all the faces join together in at one point.
Shape B is a <em>prism</em>, because it has two bases, and faces joining every side of the bases.
Shape C is a <em>prism.</em>
Shape D is a <em>pyramid.
</em>For #13, you have to know the definition of a cube to figure out the math of how many cubes there are.
A cube is a 3-D shape with six sides, all made up of squares of the same size.
The box has a volume of 120 cubic inches, and each cube is 1 inch. Since every side of a cube is equal, a 1-inch cube is one cubic inch.
This means that a box with a volume of 120 cubic inches will fit 120 of the 1 inch cubes.
1 layer of the cubes, in the diagram, is 8 cubes by 3 cubes, or 24 cubes total.
To find the number of layers needed to fill the box, you divide 120 by 24.
120 ÷ 24 = 5
The answer to #13 is 5 layers.
Answer:
y = -4x + 5
Step-by-step explanation:
Here, we want to get the equation of the line that passes through the given points
The general form is;
y = mx + b
where m is the slope and b is the y intercept
To find the slope, we use the slope formula
this is ;
m = (y2-y1)/(x2-x1)
(x1,y1) = (0,5)
(x2,y2) = (2,-3)
m = (-3-5)/(2-0) = -8/2 = -4
To get the y-intercept we simply substitute one of the points
But we know that the y-intercept is the y-value when x = 0
From the point we can see (0,5) which means that the y-intercept is 5
so the equation of the line is;
y = -4x + 5
Because it was reflected across the x axis, the distance between the two points is twice the distance of the old point from the x axis, and the distance from the old point from the x axis equals the distance from the new point to the x axis. The distance from the x axis is the absolute value of the x=y value. 7.5 is the y value, meaning the point is 7.5 units away from y=0, the x axis. The new point is twice this from the old point. 7.5 x 2 = 15. The new point is 15 units away from the old point.
Answer:
2 vertical asymptotes occurring at x = 5 and x = -1
Step-by-step explanation:
given
recall that asymptotic occur at the locations that will make the equation undefined. In this case, the asymptote will occur at x-locations which will cause the denominator to become zero (and hence undefined)
Equating the denominator to zero,
(x-5)(x+1) = 0
(x-5) =0
x = 5 (first asymptote)
or (x+1) = 0
x = -1 (2nd asymptote)
