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tigry1 [53]
3 years ago
7

What is the measure of angle c?

Mathematics
1 answer:
lana [24]3 years ago
3 0

Answer:

65

Step-by-step explanation:

Angle A=70

Angle B=180-135=45.

70+45=115. A triangle has 180 degrees.

Angle C=180-115=65

Hope I helped!

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Determine whether the set of vectors is a basis for ℛ3. Given the set of vectors , decide which of the following statements is t
schepotkina [342]

Answer:

(A) Set A is linearly independent and spans R^3. Set is a basis for R^3.

Step-by-Step Explanation

<u>Definition (Linear Independence)</u>

A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.

<u>Definition (Span of a Set of Vectors)</u>

The Span of a set of vectors is the set of all linear combinations of the vectors.

<u>Definition (A Basis of a Subspace).</u>

A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.

Given the set of vectors  A= \left(\begin{array}{[c][c][c][c]}1 & 0 & 0 & 0\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 1\end{array} \right) , we are to decide which of the given statements is true:

In Matrix A= \left(\begin{array}{[c][c][c][c]}(1) & 0 & 0 & 0\\ 0 & (1) & 0 & 1\\ 0 & 0 & (1) & 1\end{array} \right) , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column. R^3 has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans R^3.

Therefore Set A is linearly independent and spans R^3. Thus it is basis for R^3.

8 0
3 years ago
A collection of quarters and nickels is worth $3.70. There are 22 coins in all. How many of each coin are there?
ladessa [460]
9 numbers of nickels

13 numbers of quarters
3 0
2 years ago
3. Are these ratios equivalent? 35:28 and 10:8 *
attashe74 [19]

Reduce each ratio to its minimum expression to find if they are equal.

35:28

\begin{gathered} \frac{35}{28}=\frac{7\cdot5}{7\cdot4} \\ =\frac{5}{4} \end{gathered}

10:8

\begin{gathered} \frac{10}{8}=\frac{2\cdot5}{2\cdot4} \\ =\frac{5}{4} \end{gathered}

Since both ratios reduce to 5:4, they are equivalent.

Another way to check a:b is equivalent to c:d, is that a*d = b*c

In this case, this will be true if 35 times 8 is equal to 10 times 28:

\begin{gathered} 35\cdot8=280 \\ 10\cdot28=280 \end{gathered}

Since both products are equal, then the ratios are equivalent.

4 0
11 months ago
Solve 7 3/4- 5 5/4=
Kaylis [27]

Hey!

----------------------------------------------

Solution:

(5/4 = 1 1/4) and (1 1/4 + 6 = 6 1/4)

= 7 3/4 - 6 1/4 (5/4 = 1 1/4)

= 1 2/4 or 1 1/2

----------------------------------------------

Answer:

1 2/4 or 1 1/2

----------------------------------------------

Hope This Helped! Good Luck!

8 0
3 years ago
Worth 20 points, please help!
serg [7]

Answer: 3


Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. Find the prime factorization of 27:

27=3*3*3 or 27=3^{3}

2.  The index of the radical is 3, therefore, you have rewrite it as following:

\sqrt[3]{27}=\sqrt[3]{3^{3}}=3^{\frac{3}{3}}=3^{1}=3

3. Therefore, as you can see, the answer is 3.


5 0
3 years ago
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