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3 years ago

Diane has $1.85 in dimes and nickels. She has a total of 24 coins. How many of each kind does she have?

1 answer:

3 0

<span>Let the nickels be x and the dimes be y
x + y = 24
5x + 10y = 185
5x + 5y = 120
5y = 65
y=13
x=11
Answer: 11 nickels and 5 dimes</span>

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For the following exercises, determine whether the relation is a function.

elixir [45]

Answer:

The given relation $\{(a, b),(c, d),(e, d)\}$ is a function.

Step-by-step explanation:

A relation $\{(a, b),(c, d),(e, d)\}$ is given.

It is required to determine whether the given relation is a function.

To determine whether the given function is a relation, identify the domain and range and then check whether the given relation is a function.

Step 1 of 1

The given relation is {(a, b),(c, d),(e, d)}.

The set of the first components of each ordered pair is called the domain.

From the relation, the domain is {a, c, e}.

The set of the second components of each ordered the range.

From the relation, the range is {b, d, d}.

The given relation is a function. But it is not a one-to-one function.

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2 years ago

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3 years ago

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Compute the greatest root of x^4-x^3-19x^2+4x+60=0. Express your answer in simplified radical form.

erik [133]

Answer:

your answer can be either

Step-by-step explanation:

x = 5

x = 3

x= 0.0000 - 2.0000 i

x= 0.0000 + 2.0000 i

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((((x4)-(8•(x3)))+19x2)-32x)+60 = 0

Step 2 :

Equation at the end of step 2 :

((((x4) - 23x3) + 19x2) - 32x) + 60 = 0

Step 3 :

Polynomial Roots Calculator :

3.1 Find roots (zeroes) of : F(x) = x4-8x3+19x2-32x+60

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 1 and the Trailing Constant is 60.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,3 ,4 ,5 ,6 ,10 ,12 ,15 ,20 , etc

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3 years ago

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Irina-Kira [14]

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4 years ago

13. Determine whether B = {(-1, 1,-1), (1, 0, 2), (1, 1, 0)} is a basis of R3.

Sholpan [36]

Answer: Yes, the given set of vectors is a basis of R³.

Step-by-step explanation: We are given to determine whether the following set of three vectors in R³ is a basis of R³ or not :

B = {(-1, 1,-1), (1, 0, 2), (1, 1, 0)} .

For a set to be a basis of R³, the following two conditions must be fulfilled :

(i) The set should contain three vectors, equal to the dimension of R³

and

(ii) the three vectors must be linearly independent.

The first condition is already fulfilled since we have three vectors in set B.

Now, to check the independence, we will find the determinant formed by theses three vectors as rows.

If the value of the determinant is non zero, then the vectors are linearly independent.

The value of the determinant can be found as follows :

$D\\\\\\=\begin{vmatrix} -1& 1 & -1\\ 1 & 0 & 2\\ 1 & 1 & 0\end{vmatrix}\\\\\\=-1(0\times0-2\times1)+1(2\times1-1\times0)-1(1\times1-0\times1)\\\\=(-1)\times(-2)+1\times2-1\times1\\\\=2+2-1\\\\=3\neq 0.$

Therefore, the determinant is not equal to 0 and so the given set of vectors is linearly independent.

Thus, the given set is a basis of R³.

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3 years ago