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Nesterboy [21]
3 years ago
14

(x+y,x-y)=(8,0) find the value of x and y​

Mathematics
1 answer:
solmaris [256]3 years ago
3 0
X=8 y=0 there’s your answer
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Jacob traveled 171 miles in 3.8 hours. He wants to know how many miles he traveled in one hour, so he set up this problem:
Makovka662 [10]

The answer is 45


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8 0
2 years ago
Read 2 more answers
Find two vectors in R2 with Euclidian Norm 1<br> whoseEuclidian inner product with (3,1) is zero.
alina1380 [7]

Answer:

v_1=(\frac{1}{10},-\frac{3}{10})

v_2=(-\frac{1}{10},\frac{3}{10})

Step-by-step explanation:

First we define two generic vectors in our \mathbb{R}^2 space:

  1. v_1 = (x_1,y_1)
  2. v_2 = (x_2,y_2)

By definition we know that Euclidean norm on an 2-dimensional Euclidean space \mathbb{R}^2 is:

\left \| v \right \|= \sqrt{x^2+y^2}

Also we know that the inner product in \mathbb{R}^2 space is defined as:

v_1 \bullet v_2 = (x_1,y_1) \bullet(x_2,y_2)= x_1x_2+y_1y_2

So as first condition we have that both two vectors have Euclidian Norm 1, that is:

\left \| v_1 \right \|= \sqrt{x^2+y^2}=1

and

\left \| v_2 \right \|= \sqrt{x^2+y^2}=1

As second condition we have that:

v_1 \bullet (3,1) = (x_1,y_1) \bullet(3,1)= 3x_1+y_1=0

v_2 \bullet (3,1) = (x_2,y_2) \bullet(3,1)= 3x_2+y_2=0

Which is the same:

y_1=-3x_1\\y_2=-3x_2

Replacing the second condition on the first condition we have:

\sqrt{x_1^2+y_1^2}=1 \\\left | x_1^2+y_1^2 \right |=1 \\\left | x_1^2+(-3x_1)^2 \right |=1 \\\left | x_1^2+9x_1^2 \right |=1 \\\left | 10x_1^2 \right |=1 \\x_1^2= \frac{1}{10}

Since x_1^2= \frac{1}{10} we have two posible solutions, x_1=\frac{1}{10} or x_1=-\frac{1}{10}. If we choose x_1=\frac{1}{10}, we can choose next the other solution for x_2.

Remembering,

y_1=-3x_1\\y_2=-3x_2

The two vectors we are looking for are:

v_1=(\frac{1}{10},-\frac{3}{10})\\v_2=(-\frac{1}{10},\frac{3}{10})

5 0
3 years ago
Casey has n nickels. Megan has 4 times as many nickels as Casey has. Write and expression for the total number of nickels Casey
AnnyKZ [126]

Step-by-step explanation:

Let n be the number of nickels that Casey has.

We are told that Megan has 4 times as many nickels as Casey has, therefore, the number of nickels that Megan has will be 4*n.

Now we will add the amounts of nickels that Casey and Megan have to find the total amount of nickels.

\text{Total number of nickels Casey and Megan have}=n+4*n

Therefore, the expression n+4*n will represent the total number of nickels that Casey and Megan have .

Upon combining like terms we will get,

\text{Total number of nickels Casey and Megan have}=(1+4)n

\text{Total number of nickels Casey and Megan have}=5n

Therefore, Casey and Megan have 5n nickels.

6 0
3 years ago
sara buys 3 gallons of juice. she want to fill 1 pint bottles with juice. how many 1 pint bottles can sara completely fill with
Mandarinka [93]

Answer:

So Sara can fill 24 pint bottles completly with 3 gallons of juice.

Step-by-step explanation:

This question can be solved using a rule of three.

Each pint has 0.125 gallons. How many pints are 3 gallons?

1 pint - 0.125 gallons

x pints - 3 gallons

0.125x = 3

x = \frac{3}{0.125}

x = 24

So Sara can fill 24 pint bottles completly with 3 gallons of juice.

8 0
3 years ago
Your mom opens an account to save money for a family vacation. The account earns an annual interest rate of 4%. She earns $37 in
Veronika [31]
The formula would be I=(37)(.04)(6) which would give you $8.88
6 0
3 years ago
Read 2 more answers
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