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3 years ago

What is the solution to the system of equations? {x+y=7x=y+3

Mathematics

1 answer:

abruzzese [7]3 years ago

7 0

<h3>Answer:</h3>

x=5, y=2

<h3>Explanation:</h3>

The second equation gives an expression for x that can be substituted into the first equation.

... (y+3) +y = 7 . . . . . .substitute y+3 for x

... 2y + 3 = 7 . . . . . . . colect terms

... 2y = 4 . . . . . . . . . . subtract 3 from both sides

... y = 2 . . . . . . . . . . . . divide both sides by 2

Using the expression for x, we can find its value.

... x = y + 3

... x = 2 + 3 . . . . . . . . . substitute for y

... x = 5

The solution is (x, y) = (5, 2).

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What are the center and the radius of the circle 4x2 + 4y2 - 8x + 16y -4 = 0?

Sedaia [141]

Answer:

Center of circle: (1, -2)

Radius: √6

Step-by-step explanation:

First, we need to isolate the constant:

$4x^2 + 4y^2 - 8x + 16y = 4$

Then, we can divide the whole equation by 4:

$x^2+y^2-2x+4y=1$

Then, we can complete the square(reminder: (a+b)^2 = a^2 + 2ab + b^2)

$(x^2-2x)+(y^2+4y)=1\\(x^2-2x+1)+(y^2+4y)=1+1\\(x^2-2x+1)+(y^2+4y+4)=1+1+4\\(x-1)^2+(y+2)^2=6$

Now that we got the standard equation of the circle, we can find the center and radius by using the equation $(x-h)^2+(y-k)^2=r^2$ , where (h, k) is the coordinate of the center, and r is the radius.

Therefore, the center of the circle is (1, -2), and the radius of the circle is √6.

8 0

3 years ago

What are the factors of m2 – 6m + 6m – 36? (m – 2)(m + 18) (m – 3)(m + 3) (m – 4)(m + 9) (m – 6)(m + 6)

max2010maxim [7]

<span>(m – 6)(m + 6) is the answer.
If you distribute them, you'll get </span><span>m^2 - 36</span>

4 0

3 years ago

Read 2 more answers

OMG FREE BRAINLIEST HURRY UP

solniwko [45]

Me please

thanks so much btw, haha

4 0

2 years ago

Read 2 more answers

A cake shop can make 240 boxes of cakes for 8 days. How many cakes can the shop make in 12 days?

denpristay [2]

Answer:

<h2>360 cakes</h2>

Step-by-step explanation:

<h2>soln:</h2><h2>onecake =240\8=30</h2><h2>then 12 cakes =30×12=360</h2>

6 0

2 years ago

Read 2 more answers

3.3.1. Calculate the new cost per night of the standard and family standard chalets. Round of (4) your answer to the nearest hun

Taya2010 [7]

The information to complete the table is given below:

Equation that shows the relationship between the cost per night C and the number of people staying in the chalet n: C= 4000-100(n-1)

<h3>What is Equation?</h3>

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in math when you do not know the exact number in a calculation.

Given that:

Pules Rs 4000 per night but will decrease the amount by R100 per person occupying the chalet.

Number of People Cost per night

1 4000

2 3900

3 3800

4 3700

5 3600

6 3500

7 3400

8 3300

9 3200

10 3100

let C be cost per night and n be the number of people of staying in chalet.

equation: C= 4000-100(n-1)

for n=1: C= 4000- 0=4000

n=2, C= 4000-100(1)= 3900

The graph is attached below:

Learn more about equation here:

brainly.com/question/10413253

#SPJ1

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2 years ago