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seraphim [82]
3 years ago
10

Which two steps should be used first in solving the system of equations

Mathematics
2 answers:
Inessa05 [86]3 years ago
7 0

Answer:

The value of x , y  using substitution method is 2 , 5

Step-by-step explanation:

Given as :

The two linear equation as

6 y - 4 x = 22            .......1

y + 2 x = 9                

Let y = 9 - 2 x             .......2

Now, using substitution method

Substitute the value of y from eq 2 into eq 1

i.e 6 × (9 - 2 x) - 4 x = 22

Or, 54 - 12 x - 4 x = 22

Or, 12 x + 4 x = 54 - 22

Or, 16 x = 32

∴  x = \dfrac{32}{16}

i.e x = 2

Now, Put the value of x into eq 2

∴ y = 9 - 2 x

So, y = 9 - 2 × 2

Or, y = 9 - 4

i.e y = 5

So, The value of x , y = 2 , 5

Hence, The value of x , y  using substitution method is 2 , 5   Answer

Goryan [66]3 years ago
7 0

Answer:

first step :  option B

second step :  option D

Step-by-step explanation:

  • first,  Solve the second equation for y and then substitute this value into the first  equation.
  • after this, you will get the value of y then substitute this value in of the equations to get x.
  • so, option B will be the first step to solve and option D is the second step.
  • the other two steps are wrong.
  • this is a standard way to solve any 2 given equations with 2 variables.
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alina1380 [7]

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Step-by-step explanation:

To find the perimeter of a figure, you have to add up all the sides. 10 + 2 + 2 + 3 + 1 + 8= 26, therefore the perimeter of the figure is 26 m.

8 0
3 years ago
BRAINLIESTTT ASAP!!! PLEASE ANSWER :)
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Step-by-step explanation:

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3 years ago
Read 2 more answers
A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen?
Len [333]

Answer:

(a) Selection = 6724520

(b) At\ most\ 12 = 6553976

(c) At\ most\ 8 = 6066720

(d) At\ most\ 12\ red\ and\ at\ most\ 8\ blue =  5896638

Step-by-step explanation:

Given

Colors = 8

Balloons = 28 --- at least

Solving (a): 28 combinations

From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

n => 28 + 8-1= 35

r = 28

Selection = ^{35}^C_{28

Selection = \frac{35!}{(35 - 28)!28!}

Selection = \frac{35!}{7!28!}

Selection = \frac{35*34*33*32*31*30*29*28!}{7!28!}

Selection = \frac{35*34*33*32*31*30*29}{7!}

Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}

Selection = \frac{33891580800}{5040}

Selection = 6724520

Solving (b): At most 12 red balloons

First, we calculate the ways of selecting at least 13 balloons

Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)

So:

n => 15 + 8 -1 = 22

r = 15

Selection of at least 13 =

At\ least\ 13 = ^{22}C_{15}

At\ least\ 13 = \frac{22!}{(22-15)!15!}

At\ least\ 13 = \frac{22!}{7!15!}

At\ least\ 13 = 170544

Ways of selecting at most 12  =

At\ most\ 12 = Total - At\ least\ 13 --- Complement rule

At\ most\ 12 = 6724520- 170544

At\ most\ 12 = 6553976

Solving (c): At most 8 blue balloons

First, we calculate the ways of selecting at least 9 balloons

Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)

So:

n => 19+ 8 -1 = 26

r = 19

Selection of at least 9 =

At\ least\ 9 = ^{26}C_{19}

At\ least\ 9 = \frac{26!}{(26-19)!19!}

At\ least\ 9 = \frac{26!}{7!19!}

At\ least\ 9 = 657800

Ways of selecting at most 8  =

At\ most\ 8 = Total - At\ least\ 9 --- Complement rule

At\ most\ 8 = 6724520- 657800

At\ most\ 8 = 6066720

Solving (d): 12 red and 8 blue balloons

First, we calculate the ways for selecting 13 red balloons and 9 blue balloons

Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)

So:

n =6+6-1 = 11

r = 6

Selection =

^{11}C_6 = \frac{11!}{(11-6)!6!}

^{11}C_6 = \frac{11!}{5!6!}

^{11}C_6 = 462

Using inclusion/exclusion rule of two sets:

Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)

Only\ 12\ red\ and\ only\ 8\ blue\ = 170544+ 657800- 462

Only\ 12\ red\ and\ only\ 8\ blue\ = 827882

At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue

At\ most\ 12\ red\ and\ at\ most\ 8\ blue =  6724520 - 827882

At\ most\ 12\ red\ and\ at\ most\ 8\ blue =  5896638

3 0
3 years ago
A trapezoid is 14 centimeters high and has bases that measure 13.5 centimeters and 27.5 centimeters. What is the area of the tra
Alexxandr [17]
Hello!

We can find the area of the trapezoid using the formula for area of a trapezoid:

FORMULA: 

A = [(b + b) * h / 2]

SUBSTITUTE: 

A = [(13.5 + 27.5) * 14 / 2]

SOLVE: 

A = 41 * 14 / 2

A = 574 / 2 

A = 287 cm²

So, the area of the trapezoid is 287 cm².


7 0
4 years ago
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