What's the other number if the average of 63 and one other number is 33.

vagnhestagn
2022-09-27
Answered

What's the other number if the average of 63 and one other number is 33.

You can still ask an expert for help

Tristin Durham

Answered 2022-09-28
Author has **6** answers

The average of two numbers is the sum of the two numbers, divided by 2. Like this:

$\frac{{x}_{1}+{x}_{2}}{2}=avg$

We are given $x}_{1$,avg and are asked to find $x}_{2$:

$\frac{63+{x}_{2}}{2}=33$

$(63+{x}_{2})=66$

${x}_{2}=3$

$\frac{{x}_{1}+{x}_{2}}{2}=avg$

We are given $x}_{1$,avg and are asked to find $x}_{2$:

$\frac{63+{x}_{2}}{2}=33$

$(63+{x}_{2})=66$

${x}_{2}=3$

asked 2021-06-01

Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2022-11-09

Find the slope of any line perpendicular to the line passing through (3,8) and (20,−5)

asked 2022-06-22

Consider a system of linear equations $Ax=b$ where $A$ is an $n\times n$ matrix. Suppose that b is a non-zero vector such that ${A}^{t}b=0$. Which is true about any such system?

I am given 5 choices for what this means: The system has infinitely many solutions, is inconsistent, is consistent, is over determined, or is in row echelon form.

Unfortunately, I have yet to completely rule out a single one. I don't think it can be over determined, because then wouldn't the equations be undefined based on the fact that if there were more equations than unknowns then $Ax$ would not be possible. I don't recall any theorems discussing whether the system is consistent or inconsistent using the transposition and b, which stems to the infinitely many solutions.

I am given 5 choices for what this means: The system has infinitely many solutions, is inconsistent, is consistent, is over determined, or is in row echelon form.

Unfortunately, I have yet to completely rule out a single one. I don't think it can be over determined, because then wouldn't the equations be undefined based on the fact that if there were more equations than unknowns then $Ax$ would not be possible. I don't recall any theorems discussing whether the system is consistent or inconsistent using the transposition and b, which stems to the infinitely many solutions.

asked 2022-06-24

I'm reading a textbook at the moment that provides the following linear equation,

$\alpha \mathbf{v}+\mathbf{v}\times \mathbf{a}=\mathbf{b},$

and asks to solve for $\mathbf{v}$. The form of $\mathbf{v}$ is given as

$\mathbf{v}=\frac{{\alpha}^{2}\mathbf{b}-\alpha (\mathbf{b}\times \mathbf{a})+(\mathbf{a}\cdot \mathbf{b})\mathbf{a}}{\alpha ({\alpha}^{2}+|\mathbf{a}{|}^{2})}.$

It's easy enough to verify that this is the correct solution. However, I can't figure out how I'd solve for $\mathbf{v}$ if given just the original equation.

Are there any general approaches to solving this kind of equation systematically?

Edit: $\mathbf{a}$,$\mathbf{b}$ and $\mathbf{v}$ are all vectors, whereas $\alpha $ is a scalar such that $\alpha \ne 0$.

$\alpha \mathbf{v}+\mathbf{v}\times \mathbf{a}=\mathbf{b},$

and asks to solve for $\mathbf{v}$. The form of $\mathbf{v}$ is given as

$\mathbf{v}=\frac{{\alpha}^{2}\mathbf{b}-\alpha (\mathbf{b}\times \mathbf{a})+(\mathbf{a}\cdot \mathbf{b})\mathbf{a}}{\alpha ({\alpha}^{2}+|\mathbf{a}{|}^{2})}.$

It's easy enough to verify that this is the correct solution. However, I can't figure out how I'd solve for $\mathbf{v}$ if given just the original equation.

Are there any general approaches to solving this kind of equation systematically?

Edit: $\mathbf{a}$,$\mathbf{b}$ and $\mathbf{v}$ are all vectors, whereas $\alpha $ is a scalar such that $\alpha \ne 0$.

asked 2022-09-17

For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?

asked 2022-09-28

Find the slope of the line perpendicular to $y=\frac{9}{4}x-7$

asked 2022-11-07

Find the slope of the line perpendicular to $y=\frac{2}{3}x-6$