Answer and Step-by-step explanation:
Decreased by 20%
Answer:
a = 
b = 12
c = 
Step-by-step explanation:
Since the triangles are right triangles with 60 and 45 degree angles, their side lengths follow special triangles.
A 45-45-90 right triangle has side lengths 
.
A 30-60-90 right triangle has side lengths 
.
Starting with the top triangle which has a 60 degree angle, its side length 6 corresponds to a side length of 1 in the special triangle. It is 6 times bigger so its remaining sides will be 6 times bigger too.
Side a corresponds to side length 
. Therefore, 
.
Side b corresponds to side length 2, b = 2*6 = 12.
The bottom triangle has a 45 degree angle, its side length b= 12 corresponds to 
. This means was multiplied by 
. This means that side c is 
.
Answer:
Step-by-step explanation:
Answer:
y=2x
Step-by-step explanation:
Every y value is double the x value on top.
y=6:
6 = 3 × ?
? = 2
y=10:
10 = 5 × ?
? = 2
And so on....
So the equation that represents this data is :
y=2x
Answer:
a) False
b) False
c) True
d) False
e) False
Step-by-step explanation:
a. A single vector by itself is linearly dependent. False
If v = 0 then the only scalar c such that cv = 0 is c = 0. Hence, 1vl is linearly independent. A set consisting of a single vector v is linearly dependent if and only if v = 0. Therefore, only a single zero vector is linearly dependent, while any set consisting of a single nonzero vector is linearly independent.
b. If H= Span{b1,....bp}, then {b1,...bp} is a basis for H. False
A sets forms a basis for vector space, only if it is linearly independent and spans the space. The fact that it is a spanning set alone is not sufficient enough to form a basis.
c. The columns of an invertible n × n matrix form a basis for Rⁿ. True
If a matrix is invertible, then its columns are linearly independent and every row has a pivot element. The columns, can therefore, form a basis for Rⁿ.
d. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix. False
Row operations can not affect linear dependence among the columns of a matrix.
e. A basis is a spanning set that is as large as possible. False
A basis is not a large spanning set. A basis is the smallest spanning set.
