Answer:
B x = sqrt(41)
Step-by-step explanation:
Since the large triangle is isosceles, the smaller triangles on the right side and left side are congruent right triangles.
The base of each smaller right triangle is 4 units long (8/2 = 4).
The vertical leg is 5.
Use the Pythagorean theorem to find x.
a^2 + b^2 = c^2
4^2 + 5^2 = x^2
16 + 25 = x^2
x^2 = 41
x = sqrt(41)
Answer: B x = sqrt(41)
Answer:
4 months
Step-by-step explanation:
Franco's provider = 60 + 42.95x
Marshal's provider = 57.95x
Where,
x = number of months
Equate both charges
Franco's provider = Marshal's provider
60 + 42.95x = 57.95x
Subtract 42.95x From both sides
60 + 42.95x - 42.95x = 57.95x - 42.95x
60 = 15x
Divide both sides by 15
60 / 15 = 15x / 15
4 = x
x = 4 Months
Franco and Marshal would have paid the same amount for high-speed Internet service after 4 months
First of all not to be rude, but it is order of operations not properties of operations. Second, you can solve equations by going in the order of PEMDAS or Parentheses, Exponents, Multiplication, division, addition, and subtraction. Multiplication and division are switchable, addition and subtraction. If you do not follow this order you get the equation or inequality wrong.
2(4x - 7) -1 = 11
8x - 14 -1 = 11
8x - 15 = 11
+ 15 + 15
8x = 26
/8 /8
x = 3. 25 ------> Rounded: 3.30
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.
