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Hitman42 [59]
2 years ago
7

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. x + y = 6 x

- y = 0
Mathematics
1 answer:
Mnenie [13.5K]2 years ago
8 0

The solution of the system of equations contains one point

<h3>How to determine the number of solutions?</h3>

The system is given as:

x + y = 6

x - y = 0

Add both equations

2x = 6

Divide by 2

x = 3

Substitute x = 3 in x - y = 0

3 - y = 0

Solve for y

y = 3

So, we have x =3 and y = 3

Hence, the solution of the system of equations contains one point

Read more about system of equations at:

brainly.com/question/14323743

#SPJ1

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Which of the following sets of data will have the smallest Standard Deviation?
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The formula for standard deviation is in attachment the mean (or average is subtracted from each data sample then squared, then summed up for all data samples, then divided by the number of samples, then finally the square root is taken.

The first row of data will have a standard deviation of 0.

The second row of numbers will have a low standard deviation because the differences between the sample data values are low ( <10).

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What smaller number can you get other than 0?

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3 years ago
Find the equation of the tangent of x^2- xy + y^2 =7 at (-1, 2)
Citrus2011 [14]

Answer:

<u>It</u><u> </u><u>is</u><u> </u><u>3</u><u>y</u><u> </u><u>=</u><u> </u><u>4</u><u>x</u><u> </u><u>+</u><u> </u><u>1</u><u>0</u>

Step-by-step explanation:

Let's first get the slope of the curve.

[ slope is the derivative of the equation ]

{x}^{2}  - xy +  {y}^{2}  = 7

introduce dy/dx :

\frac{d}{dx} ( {x}^{2}  - xy +  {y}^{2} ) =  \frac{d}{dx} (7) \\  \\ 2x - (y +  \frac{dy}{dx} ) + 2y \frac{dy}{dx}  = 0

make dy/dx the subject:

2x - y -  \frac{dy}{dx}  + 2y \frac{dy}{dx}  = 0 \\  \\ 2y \frac{dy}{dx}  -  \frac{dy}{dx}  = y - 2x \\  \\  \frac{dy}{dx} (2y - 1) = y - 2x \\  \\  \frac{dy}{dx}  =  \frac{y - 2x}{2y - 1}

At point (-1, 2):

\frac{dy}{dx}  =  \frac{2 - 2( - 1)}{2(2) - 1}  \\  \\ slope =  \frac{4}{3}

but a tangent has the same slope as the curve:

y = mx + c

m is the slope

c is the y-intercept

At (-1, 2):

2 = ( - 1 \times  \frac{4}{3} ) + c \\  \\ c = 2 +  \frac{4}{3}  \\  \\ c =  \frac{10}{3}

equation:

y =  \frac{4}{3} x +  \frac{10}{3}  \\  \\ { \boxed{3y = 4x + 10}}

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3 years ago
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3 years ago
Lamar's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lamar $4.40 per pound, and type
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Answer:

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Step-by-step explanation:

Let x = the number of pounds of type A coffee

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This means the sum of type A coffee and type B coffee for the month is 129 and the total cost is $658.80

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x = 129-y = 129-76

= 53 pounds

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