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JulsSmile [24]
3 years ago
12

What is the solution to this system of linear equations? x + y = 4 x − y = 6 A: (4, 6) B: (6, 4) C: (5, −1) D: (−1, 5)

Mathematics
1 answer:
zhuklara [117]3 years ago
4 0

Answer:

C

Step-by-step explanation:

Given the 2 equations

x + y = 4 → (1)

x - y = 6 → (2)

Add the 2 equations term by term to eliminate y, that is

2x = 10 ( divide both sides by 2 )

x = 5

Substitute x = 5 into either of the 2 equations and evaluate for y

Substituting into (1)

5 + y = 4 ( subtract 5 from both sides )

y = - 1

solution is (5, - 1 ) → C

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compute the projection of → a onto → b and the vector component of → a orthogonal to → b . give exact answers.
Nina [5.8K]

\text { Saclar projection } \frac{1}{\sqrt{3}} \text { and Vector projection } \frac{1}{3}(\hat{i}+\hat{j}+\hat{k})

We have been given two vectors $\vec{a}$ and $\vec{b}$, we are to find out the scalar and vector projection of $\vec{b}$ onto $\vec{a}$

we have $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$

The scalar projection of$\vec{b}$onto $\vec{a}$means the magnitude of the resolved component of $\vec{b}$ the direction of $\vec{a}$ and is given by

The scalar projection of $\vec{b}$onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|}$

$$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\sqrt{1^2+1^1+1^2}} \\&=\frac{1^2-1^2+1^2}{\sqrt{3}}=\frac{1}{\sqrt{3}}\end{aligned}$$

The Vector projection of $\vec{b}$ onto $\vec{a}$ means the resolved component of $\vec{b}$ in the direction of $\vec{a}$ and is given by

The vector projection of $\vec{b}$ onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|^2} \cdot(\hat{i}+\hat{j}+\hat{k})$

$$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\left(\sqrt{1^2+1^1+1^2}\right)^2} \cdot(\hat{i}+\hat{j}+\hat{k}) \\&=\frac{1^2-1^2+1^2}{3} \cdot(\hat{i}+\hat{j}+\hat{k})=\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})\end{aligned}$$

To learn more about scalar and vector projection visit:brainly.com/question/21925479

#SPJ4

3 0
1 year ago
I need all help possible.
Leviafan [203]
So there are 52 horses
12 of them are white
how many are black?
52 - 12 = 40
there are 40 black horses
12 white horses to 40 black horses
12:40 
12/40

Hope this helps :)
5 0
3 years ago
Find a number that is 5 times as much as 4 divided by 2
barxatty [35]
10....

4 x 5 ÷ 2 is 10
4 0
3 years ago
Read 2 more answers
If 5\9 of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank?
Blizzard [7]

Answer:

It would take 3.6 mins.

Step-by-step explanation:

In order to find this, we simply divide the amount of time by the amount of the tank that is filled.

2 ÷ 5/9 = 3.6

7 0
3 years ago
The double number line shows that Toni can type 180180180 words in 222 minutes. Based on the ratio shown in the double number li
vfiekz [6]

Answer:

<h3>Toni can type words in 3 minutes is 270 words</h3>

Step-by-step explanation:

Given that the double number line shows that Toni can type 180 words in 2 minutes.

<h3>To find how many words can Toni type in 3 minutes:</h3>

From the given Toni can type 180 words in 2 minutes,

⇒ Toni can type \frac{180}{2}

= 90

<h3>∴ 90 words per minute </h3>

For Toni would be able to type words in 3 minutes is

90\times 3

= 270

<h3>∴ 270 words per minute.</h3><h3>∴ Toni can type words in 3 minutes is 270 words.</h3>
6 0
3 years ago
Read 2 more answers
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