Answer:
a) SAS
b) Volume of DEF is 4 times the Volume of ABC
Step-by-step explanation:
a) since they have one same/congruent angle (angle B and angle E) and other two sides are in the same ratio, they are similar by SAS similarity theorem.
40/20 = 30/15 = 2
Therefore Δ ABC is similar to Δ DEF
b) Volume of a prism
= base area × height
Let height be 'h cm'
With Base ABC:
Volume = ½×20×15×h = 150h cm³
With Base DEF:
Volume = ½×40×30×h = 600h cm³
600h/150h = 4
Prism with base DEF has a greater volume; it's 4 times of the volume of the prism with base ABC
Answer:
y=2.5x
Step-by-step explanation:
To get the equation in y = mx + b format, we need to find m and b, the slope and y-intercept.
To find the slope, we need two points on a graph, which we have.
First, the slope
The formula for slope is

Our points, (6, 15) and (2, 5)
Plugging into our equation:
, which is 10 divided by 4, which is 2.5
Our equation now:

To find our b, we need to plug in one x value.
(6, 15) are our pair of points.
6 = x
15 = y
=>
=>

If b is 0, then we don't need to include b.
Our equation is 
You need 12 square roots of 1764 ?
<span>Why not find the square root of 1764 first (it's 42) and then take 12 of those ?
Hope this helps!</span>
Average speed for car a = 1280 / 16 = 80 mph
Car b travels at 80 - 0.5 = 79.5 mph.
Distance car b will travel in same time = 16*79.5 = 1272 miles.
This is a geometric sequence, with the first term: 1/64
The common ratio is found through the ratio of the first two terms and the second and third term.


Since there is a common difference of 2, we can generalise this sequence to find the nth term:

a is the first term, r is the common ratio, and n is the nth term in the sequence.

Substituting n = 7, we get:



Thus, the next term in the sequence is 1.