All categories

3 years ago

3 x + 2 y = 6 4 x + y = 1 Solve the system of equations.

1 answer:

8 0

<h2>3x + 2y = 6</h2><h2>4x + y = 1</h2><h2>Solve the second equation for y:</h2><h2>y = -4x + 1</h2><h2 /><h2>Substitute -4x + 1 for y in the first equation.</h2><h2>3x + 2(-4x + 1) = 6</h2><h2>3x - 8x + 2 = 6</h2><h2>-5x = 4</h2><h2>x = -4/5</h2><h2 /><h2>Now substitute x with -4/5 in the first original equation.</h2><h2>3x + 2y = 6</h2><h2>3 * (-4/5) + 2y = 6</h2><h2>-12/5 + 2y = 6</h2><h2 /><h2>-12 + 10y = 30</h2><h2>10y = 42</h2><h2>y = 42/10</h2><h2>y = 21/5</h2><h2><em>Solution: (-4/5, 21/5)</em></h2>

Hope this helped! ~

You might be interested in

Edwina and georgia had the same number of bottles.Edwina and georgia had a mix of big bottles and small bottles.Edwina had 5 sma

Aleks04 [339]

Answer:

20 big bottles

14000 ml

Step-by-step explanation:

Let :

Small bottles = x ; big bottles = y

Capacity of small bottle = 400ml

Capacity of big bottle = 600 ml

Edwina :

Number of small bottles = 5

Georgi :

Number of big bottles = 16

Since Numbe of bottles are siad to be the same :

5 + y = 16 + x

y - x = 16 - 5

y - x = 11

y = 11 + x - - - (1)

Total capacity of Edwina's bottle is 800 ml more Than Georgi's total :

Edwina :

5(400) + 600y

Georgi :

400x + 16(600)

2000 + 600y = 800 + 400x + 9600

2000 + 600y = 10400 + 400x

600y - 400x = 10400 - 2000

600y - 400x = 8400 - - - (2)

Substitute y = 11+x for y in (2)

600(11+x) - 400x = 8400

6600 + 600x - 400x = 8400

200x = 8400 - 6600

200x = 1800

x = 1800 / 200

x = 9

Number of big bottles Edwina has :

y = 11 + x

y = 11 + 9

y = 20

Total capacity of Edwina's bottles :

5(400) + 600y

2000 + 600(20) = 2000 + 12000 = 14000 ml

7 0

3 years ago

Tentukan hasil dari (tanpa menghitung satu persatu)

liubo4ka [24]

a . 1 + 3 + 5 + 7 + 9 + ... + 99 = 2500

b. 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100 = -50

c. -100 - 99 - 98 - .... -2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50 = -3775

<h3>Further explanation</h3>

Let us learn about Arithmetic Progression.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

$\large {\boxed {T_n = a + (n-1)d } }$

$\large {\boxed {S_n = \frac{1}{2}n ( 2a + (n-1)d ) } }$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>d = common difference between adjacent numbers</em>

Let us now tackle the problem!

<h2>Question a :</h2>

1 + 3 + 5 + 7 + 9 + ... + 99

<em>initial term = a = 1</em>

<em>common difference = d = ( 3 - 1 ) = 2</em>

Firstly , we will find how many numbers ( n ) in this series.

$T_n = a + (n-1)d$

$99 = 1 + (n-1)2$

$99-1 = (n-1)2$

$98 = (n-1)2$

$\frac{98}{2} = (n-1)$

$49 = (n-1)$

$n = 50$

At last , we could find the sum of the numbers in the series using the above formula.

$S_n = \frac{1}{2}n ( 2a + (n-1)d )$

$S_{50} = \frac{1}{2}(50) ( 2 \times 1 + (50-1) \times 2 )$

$S_{50} = 25 ( 2 + 49 \times 2 )$

$S_{50} = 25 ( 2 + 98 )$

$S_{50} = 25 ( 100 )$

$\large { \boxed { S_{50} = 2500 } }$

<h2>Question b :</h2>

In this question let us find the series of even numbers first , such as :

2 + 4 + 6 + 8 + ... + 100

<em>initial term = a = 2</em>

<em>common difference = d = ( 4 - 2 ) = 2</em>

<em />

Firstly , we will find how many numbers ( n ) in this series.

$T_n = a + (n-1)d$

$100 = 2 + (n-1)2$

$100-2 = (n-1)2$

$98 = (n-1)2$

$\frac{98}{2} = (n-1)$

$49 = (n-1)$

$n = 50$

We could find the sum of the numbers in the series using the above formula.

$S_n = \frac{1}{2}n ( 2a + (n-1)d )$

$S_{50} = \frac{1}{2}(50) ( 2 \times 2 + (50-1) \times 2 )$

$S_{50} = 25 ( 4 + 49 \times 2 )$

$S_{50} = 25 ( 4 + 98 )$

$S_{50} = 25 ( 102 )$

$\large { \boxed { S_{50} = 2550 } }$

At last , we could find the result of the series.

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100

= ( 1 + 3 + 5 + 7 + ... + 99 ) - ( 2 + 4 + 6 + 8 + ... + 100 )

= 2500 - 2550

= -50

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100 = -50

<h2>Question c :</h2>

-100 - 99 - 98 - .... -2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50

<em>initial term = a = -100</em>

<em>common difference = d = ( -99 - (-100) ) = 1</em>

<em />

Firstly , we will find how many numbers ( n ) in this series.

$T_n = a + (n-1)d$

$50 = -100 + (n-1)1$

$50+100 = (n-1)$

$150 = (n-1)$

$n = 151$

We could find the sum of the numbers in the series using the above formula.

$S_n = \frac{1}{2}n ( 2a + (n-1)d )$

$S_{151} = \frac{1}{2}(151) ( 2 \times (-100) + (151-1) \times 1 )$

$S_{151} = 75.5 ( -200 + 150 )$

$S_{151} = 75.5 ( -50 )$

$\large { \boxed { S_{151} = -3775 } }$

<h3>Learn more</h3>

Geometric Series : brainly.com/question/4520950
Arithmetic Progression : brainly.com/question/2966265
Geometric Sequence : brainly.com/question/2166405

<h3>Answer details</h3>

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

3 0

3 years ago

Read 2 more answers

Which of the following is the correct graph of the compound inequality 4p + 1 < −11 or 6p + 3 > 39?

mrs_skeptik [129]

The correct graph to the inequality is a number line with open dot at <em>negative 3</em> with shading to the left and an open dot at 6 with shading to the right. The correct option is the second option

<h3>Linear Inequalities </h3>

From the question, we are to determine the graph for the given compound inequality

The given compound inequality is

4p + 1 < −11 or 6p + 3 > 39

Solve the inequalities separately

4p + 1 < −11

4p < -11 - 1

4p < -12

p < -12/4

p < -3

6p + 3 > 39

6p > 39 - 3

6p > 36

p > 36/6

p > 6

Thus,

p < -3 OR p > 6

Hence, the correct graph to the inequality is a number line with open dot at <em>negative 3</em> with shading to the left and an open dot at 6 with shading to the right. The correct option is the second option

Learn more on Linear Inequalities here: brainly.com/question/5994230

#SPJ1

4 0

1 year ago

Type 785 words in 10 minutes and 28 seconds<br> words per minute

sukhopar [10]

Answer:

Seven hundred and eighty-five

6 0

3 years ago

A bakery sells 4 dozen cupcakes every 3 hours. If the bakery is open 8 hours each day, how many days does it take to sell 640 cu

zmey [24]

5 days does it take to sell 640 cupcakes.

Given:

A bakery sells 4 dozen cupcakes every 3 hours.

If the bakery is open 8 hours each day.

4 dozen cupcakes = 4*12 cupcakes

= 48 cupcakes

48 cupcakes = 3 hours

divide by 3 on both sides

3hours/3 = 48/3 cupcakes

1 hour = 16 cupcakes

Number of cupcakes for 8 hours = 8 * 16 = 128 cupcakes.

128 cupcakes sells in one day.

To sell 640 cupcakes = 640/128

= 5 days.

Therefore 5 days does it take to sell 640 cupcakes.

Learn more about the bakery and cupcakes here:

brainly.com/question/14466478

#SPJ1

8 0

1 year ago