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4 years ago

Answer to the best of your ability and explain why you chose the answer you chose

Mathematics

1 answer:

Anastasy [175]4 years ago

5 0

Answer: y = 5x + 2 (first answer)
.....................

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Select all the correct graphs. Choose the graphs that indicate equations with no solution.

Natali [406]

Answer:

The first and last graph.

General Formulas and Concepts:

Algebra I

Solving systems of equations graphically

Step-by-step explanation:

In order for a systems of equations to have a solution set, the 2 graphs must intersect at at least 1 point. Here, we see that graphs 1 and 5 do not intersect each other at all.

Therefore, the rest of the graphs have solutions and #1 and #5 do no have any solutions.

3 0

3 years ago

4.5 , 3.25 , 2 , 0.75 next three terms

LiRa [457]

-.5 , -1.75, 3 hope that's what you wanted

6 0

4 years ago

Determine if the columns of the matrix form a linearly independent set. Justify your answer. [Start 3 By 4 Matrix 1st Row 1st Co

Volgvan

Answer:

Linearly Dependent for not all scalars are null.

Step-by-step explanation:

Hi there!

1)When we have vectors like $v_{1},v_{2},v_{3}, ...$ we call them linearly dependent if we have scalars $a_{1},a_{2},a_{3},...$ as scalar coefficients of those vectors, and not all are null and their sum is equal to zero.

$a_{1}\vec{v_{1}}+a_{2}\vec{v_{2}}+a_{3}\vec{v_{3}}+...a_{m}\vec{v_{m}}=0$

When all scalar coefficients are equal to zero, we can call them linearly independent

2) Now let's examine the Matrix given:

$\begin{bmatrix}1 &-2 &2 &3 \\ -2 & 4 & -4 &3 \\ 0&1 &-1 & 4\end{bmatrix}$

So each column of this Matrix is a vector. So we can write them as:

$\vec{v_{1}}=\left \langle 1,-2,1 \right \rangle,\vec{v_{2}}=\left \langle -2,4,-1 \right \rangle,\vec{v_{3}}=\left \langle 2,-4,4 \right \rangle\vec{v_{4}}=\left \langle 3,3,4 \right \rangle$ Or

Now let's rewrite it as a system of equations:

$a_{1}\begin{bmatrix}1\\ -2\\ 0\end{bmatrix}+a_{2}\begin{bmatrix}-2\\ 4\\ 1\end{bmatrix}+a_{3}\begin{bmatrix}2\\ -4\\ -1\end{bmatrix}+a_{4}\begin{bmatrix}3\\ 3\\ 4\end{bmatrix}=\begin{bmatrix}0\\ 0\\ 0\end{bmatrix}$

2.1) Since we want to try whether they are linearly independent, or dependent we'll rewrite as a Linear system so that we can find their scalar coefficients, whether all or not all are null.

Using the Gaussian Elimination Method, augmenting the matrix, then proceeding the calculations, we can see that not all scalars are equal to zero. Then it is Linearly Dependent.

$\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ -2 &4 &-4 &3 \\ 0 & 1 &-1 &4 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )R_{1}\times2 +R_{2}\rightarrow R_{2}\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ 0 &0 &9 &0\\ 0 & 1 &-1 &4 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )\ R_{2}\Leftrightarrow R_{3}\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ 0 &1 &-1 &4 \\ 0 &0 &9 &0 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )$ $\left\{\begin{matrix}1a_{1} &-2a_{2} &+2a_{3} &+3a_{4} &=0 \\ &1a_{2} &-1a_{3} &+4a_{4} &=0 \\ & & &9a_{4} &=0 \end{matrix}\right.\Rightarrow a_{1}=0, a_{2}=a_{3},a_{4}=0$

$S=\begin{bmatrix}0\\ a_{3}\\ a_{3}\\ 0\end{bmatrix}$

3 0

3 years ago

What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?

11111nata11111 [884]

Answer:

(D). 28

Step-by-step explanation:

We have been given that the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number.

We know that smallest prime is 2. The product of 2 and 7 is 14.

Let us divide our given numbers by 14.

(A) 7.

$\frac{7}{14}=\frac{1}{2}$

The quotient is not a integer or prime number.

(B). 14

$\frac{14}{14}=1$

We know that 1 is not a prime number.

(C) 24.

$\frac{24}{14}=\frac{12}{7}$

The quotient is not a integer or prime number.

(D). 28

$\frac{28}{14}=2$

Since 2 is a prime number, therefore, 28 is the smallest integer that can be divided by the product of a prime number and 7 and yield a prime number.

4 0

3 years ago

The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative

olga2289 [7]

Answer:

A≈1075.21

d Diameter

Using the formulas

Solving forA

≈

1075.21009

Step-by-step explanation:

4 0

3 years ago