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3 years ago

Reina and Sam are multiplying (8^4)^5 (7^3)^9 Is either of them correct?

Mathematics

1 answer:

PilotLPTM [1.2K]3 years ago

6 0

Answer:

Sam is correct.

Step-by-step explanation:

Exponent rules state that when an number with an exponent is raised to a power, the two exponents multiply. For example, a^2^2=a^4.

You might be interested in

What is the area of the object above? A. 248 sq in B. 228 sq in C. 320 sq in D. 328 sq in

chubhunter [2.5K]

Answer:

which object tho

Step-by-step explanation:

5 0

2 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

Jennifer stands on a sidewalk with her bicycle and notices the air is motionless. She then rides her bicycle north at a constant

SVETLANKA909090 [29]

B because if jennifer stands on a sidewalk with her bicycle u have to divide that by 7 multiply by 8

8 0

3 years ago

After twenty movies, the value of her card is now 100 how much money did she start with

ch4aika [34]

Answer:

2000

Step-by-step explanation:

20*100=2000

6 0

3 years ago

I WILL MARK BRAINLIEST!

algol [13]

Initially the number of rose bushes are 18 and number of holly bushes are 6.

<h3>What is linear equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose initially the number of rose bushes is x and number of holly bushes is y

x = 3y …(1)

Then I moved seven of my rose bushes to my grandfather’s garden:

= (x - 7)

Planted 11 new holly bushes in my garden:

= (y + 11)

x - 7 = y + 11 - 6

x - y = 12 ...(2)

After solving equation (1) and (2):

x = 18

y = 6

Thus, initially the number of rose bushes are 18 and number of holly bushes are 6.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

3 0

2 years ago