MATHEMATICS MIDDLE SCHOOL

How do you solve x+2x=15 ; 5x=2y+3 using the substitution method?
please explain

Answers

Answer 1
Answer:     The subtitution method is where you fill in a number into the place of the variable, the check the problem to see if the number fits by solving it..
x+2x=15
    I don't see why someone would use the substitution method on this one. x+2x can be 3x because of how multiplication works like addition. Then you'd have 3x=15. You can then find the value of x by dividing each side by 3 so that the variable is alone. You'll have x=5
5x=2y+3
    If the equations are part of the same problem, then you'll have 25=2y+3.
You could also solve this normaly, but I'll use the method you want this time.
You could put a number like 6 in for y. Then solve. You'll have that 25=15. Meaning 6 is too small, so then you could use a number such as 12. Solve, and you'll get 25=27. The answer would be too large, but barely. You could move down one, to 11. you'll have 25=25, so eleven is correct. Sorry if I typed too much.
    If you wish to use the subtitution method, simply place a digit, that you think might fit, into the place where the variable is.


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The sun is about 93 x 10 to the 6 power miles from earth. What is the distance written as a whole number?

Answers

93 x 10 to the power 6
93 x 10^6
93000000 miles
93000000 is your asnwer look above for work

You can buy 2 DVDs for the same price you would pay for 3 CDs selling for $13.20 a piece.Explain how you could find the price of 1 DVD.

Answers

So,

3 CD's sell for $13.20 each.
3 * 13.20 = $39.60

$39.60 is also the price for 2 DVD's.

Divide $39.60 by 2.
$19.80

Each DVD is $19.80.

a 13 ft ladder is placed against the side of the building. The bottom of the ladder is 5 ft away from the bottom of the building. how far up the building will the ladder reach?

Answers

The final answer is x=12
So the ladder will reach 12 feet up

A historical marker is in the shape of a parallelogram. The height is 5.7 M. Area of the marker is 22.8 m to the power of 2. What is the length of the base of the marker?

Answers

If the area is 22.8^(2) and the height is 5.7...
you simply divide 22.8 by 5.7
giving you the base of 4metres

to double check try...
5.7 x 4

Help Please!!!!!! The equation of a circle is x² + y² - 4x + 2y - 31 = 0. What is the center and the radius of the circle? Show your work.

Answers

The center of the circle is  (2, - 1) and the radius is 6 units.

What are the types of equations of a circle?

The equation for a circle has the generic form x² + y² + 2gx + 2fy + c = 0.

The standard equation of a circle is x² + y² = r².

The polar form of the equation of the circle is (rcosθ)² + (rsinθ)² = p².

Given, The equation of a circle is x² + y² - 4x + 2y - 31 = 0.

We know, In x² + y² + 2gx + 2fy + c = 0, The center of the circle is,

(- g, - f) and radius is \sqrt{g^2 + f^2 - c.

Therefore, 2gx = - 4x and 2fy = 2y.

2g = - 4 and 2f = 2.

g = - 2 and f = 1.

- g = 2 and - f = - 1.

So, The center is (2, - 1).

And the radius is, \sqrt{2^2 + -1^2 + 31.

= \sqrt{4 + 1 + 31.

= \sqrt{36.

= 6 units.

learn more about circles here :

brainly.com/question/29288238

#SPJ3

Answer:

centre = (2, - 1), radius = 6

Step-by-step explanation:

Rearrange the equation by placing the x and y terms together and adding 31 to both sides

Given

x² + y² - 4x + 2y - 31 = 0, then

x² - 4x + y² + 2y = 31

Use the method of completing the square

add ( half the coefficient of the x/y term )² to both sides

x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1

(x - 2)² + (y + 1)² = 36

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

compare to (x - 2)² + (y + 1)² = 36, then

centre = (2, - 1) and r = √(36) = 6

A home improvement store sold wind chimes for $30 each.A costumer signed up for a free membership card and recieved a 5% discount off the price.Sales tax of 5% was applied after the disscount.What was the final price of the windchime?Show your work.

Answers

5%=.05
$30 x .05 = $1.5
Take $1.5 off of the $30.
After discount, the price was $28.5.
Sales price needs to be added.
$28.5 x .05 = $1.4
$28.5 + $1.4 = $29.9
$29.9 is the final price of the  wind chime.

Answer: 29.9

How to solve this problem

5%=.05

$30 x .05 = $1.5

Take $1.5 off of the $30.

After discount, the price was $28.5. Sales price needs to be added.

$28.5 x .05 = $1.4
$28.5 + $1.4 = $29.9

$29.9 is the final price of the wind chime.
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