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3 years ago

Solving Linear Equat Solve the linear equation: 3.4 + 2(9.7 – 4.8x) = 61.2

Mathematics

2 answers:

JulijaS [17]3 years ago

8 0

Answer:

Step-by-step explanation:

Simplifying

3.4 + 2(9.7 + -4.8x) = 61.2

3.4 + (9.7 * 2 + -4.8x * 2) = 61.2

3.4 + (19.4 + -9.6x) = 61.2

Combine like terms: 3.4 + 19.4 = 22.8

22.8 + -9.6x = 61.2

Solving

22.8 + -9.6x = 61.2

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-22.8' to each side of the equation.

22.8 + -22.8 + -9.6x = 61.2 + -22.8

Combine like terms: 22.8 + -22.8 = 0.0

0.0 + -9.6x = 61.2 + -22.8

-9.6x = 61.2 + -22.8

Combine like terms: 61.2 + -22.8 = 38.4

-9.6x = 38.4

Divide each side by '-9.6'.

x = -4

Simplifying

x = -4

siniylev [52]3 years ago

6 0

Answer:

Step-by-step explanation:

3.4 + 19.4 - 9.6x = 61.2

22.8 - 9.6x = 61.2

-9.6x = 61.2 - 22.8

-9.6x = 38.4

x = -4

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1. Solve each system of linear equations below, then check your work.

Brut [27]

Answer:

$a) \: x = - 3 \: and \: y = 2 \\ b) \: x = 1 \: and \: y = - \frac{5}{4} \\ c) \: \: x = 25 \: and \: y = 0 \\ d ) \: x = 10 \: and \: y = - 12$

Step-by-step explanation:

$question (a) \: \: \: 3x - y = - 11 \\ \: \: \: - x + y = 5 \\ \\ 2x = - 6 \\ \frac{2}{2} x = \frac{ - 6}{2} \\ x = - 3$

$\\ since \: x = - 3 \: then \: y = \\ \\ - x + y = 5 \\ - ( - 3) + y = 5 \\ y = 5 - 3 \\ y = 2$

$\\ (check) \\ recall \: that \: x = - 3 \: and \: y = 2 \\ \\ - x + y = 5 \\ - ( - 3) + 2 = 5 \\ 3 + 2 = 5 \\ 5 = 5$

$question (b) \: \: \: -2y + 3 = 4x + 2 \\ 6x + 4y = 1 \\ \\ ( - 4x - 2y = - 1) \times 2 \\\: \: \: 6x + 4y = 1 \\ \\ - 8x - 4y = - 2 \\ 6x + 4y = 1 \\ \\ - 2x = - 2$

$\frac{ - 2}{ - 2} x = \frac{ - 2}{ - 2} \\ x = 1 \\ \\ since \: x = 1 \: then \: y = \\ \\ 6x + 4y = 1 \\ 6(1) + 4y = 1$

$4y = - 6 + 1 \\ \frac{4}{4} y = - \frac{ 5}{4} \\ y = - \frac{ 5}{4} \\ \\ (check) \\ - 2y + 3 = 4x + 2$

$- 2( - \frac{5}{4} ) + 3 = 4(1) + 2 \\ \frac{5}{2} + 3 = 6\\ 6 = 6$

$question (c) \: \: \: 32y - x = - 25 \\ \: \: \: 5x = 100 + x - 8y \\ \\ 32y - x = - 25 \\ 8y + 5x - x = 100 \\ \\ (32y - x = - 25) \times 4 \\ 8y + 4x = 100$

$128y - 4x = - 100 \\ 8y + 4x = 100 \\ 136y = 0 \\ y = 0 \\ \\ since \: y = 0 \: then \: x = \\ \\ 32y - x = - 25 \\ 32(0) - x = - 25 \\ - x = - 25 - 0 \\ \frac{ - 1}{ - 1} x = \frac{ - 25}{ - 1} \\ x = 25 \\$

$(check) \\ 5x = 100 + x - 8y \\ 5(25) = 100 + (25) - 8(0) \\ 125 = 125 - 0 \\ 125 = 125$

$question (d) \: \: \: 2y + 3x = 6 \\ \: \: \: 4x + 5y + 20 = 0 \\ \\ ( 2y + 3x = 6) \times 4 \\ (5y + 4x = - 20) \times - 3 \\ \\ 8y + 12x = 24 \\ - 15y - 12x = 60$

$- 7y = 84 \\ \frac{ - 7}{ - 7} y = \frac{84}{ - 7} \\ y = - 12 \\ \\ since \: y = - 12 \: then \: x = \\ \\ 2y + 3x = 6 \\ 2( - 12) + 3x = 6 \\ - 24 + 3x = 6 \\ 3x = 6 + 24 \\ x = 10 \\ \\ (check) \\ 4x + 5y + 20 = 0 \\$

$4(10) + 5( - 12) + 20 = 0 \\ 40 - 60 + 20 = 0 \\ - 20 + 20 = 0 \\ 0 = 0$

5 0

1 year ago

Roberto ran 3/8 laps , juliette ran 2/3 laps and cora ran 1 1/4 laps. how many did they run together

ELEN [110]

Answer:

3 19/24

Step-by-step explanation:

$\frac{3}{8} + \frac{2}{3} + \frac{11}{4} = \frac{9 + 16 + 66}{24} = \frac{91}{24} = 3 \frac{19}{24 }$

hope it helps

3 0

1 year ago

Pls help, thank you

Lemur [1.5K]

Answer:

y = -3x² + 7x - 9

Step-by-step explanation:

Given quadratic function:

y = ax² + bx + c

Points on the graph:

(-2,-35), (1,-5), (3,- 15)

Substitute values of x and y and solve the system of equations:

-35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c ⇔ eq 1
-5 = a(1)² + b(1) + c ⇒ -5 = a + b + c ⇔ eq 2
-15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c ⇔ eq 3

Subtract eq 2 from eq 1:

-35 - (-5) = 4a - 2b + c - a - b - c
-30 = 3a - 3b
b = a + 10 ⇔ eq 4

Subtract eq 2 from eq 3:

-15 - (-5) = 9a + 3b + c - a - b - c
-10 = 8a + 2b
b = -4a - 5 ⇔ eq 5

Compare eq 4 and eq 5, solve for a:

a + 10 = -4a - 5
a + 4a = -5 - 10
5a = -15
a = -3

Find the value of b using eq 4:

b = -3 + 10
b = 7

Find the value of c using eq 2:

-5 = -3 + 7 + c
c = -5 - 4
c = -9

We now have a, b and c:, the function is:

y = -3x² + 7x - 9

8 0

2 years ago

Read 2 more answers

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bija089 [108]

Answer:

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4 0

2 years ago

Elimination method 2x -3y=7 3x-2y=13

strojnjashka [21]

Answer:

x = 5 and y = 1 or (5, 1)

Step-by-step explanation:

2x -3y=7

3x-2y=13

Multiply (1st) equation by 3 and (2nd) equation by 2

6x -9y=21

6x-4y=26

----------------subtract

-5y = - 5

y = 1

Substitute y = 1 into 2x -3y=7

2x -3(1)=7

2x - 3 = 7

2x = 10

x = 5

Answer

x = 5 and y = 1 or (5, 1)

7 0

2 years ago