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3 years ago

Standard form of a linear equation -2x+3=4y

Mathematics

1 answer:

zhuklara [117]3 years ago

3 0

Answer:

y=-1/2x+3/4

Step-by-step explanation:

just divide the entire equation by 4, so that y is isolated.

The standard form equation of a line is y=mx+b

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The sum of two numbers is 19 and their products is 78. What is the larger number ?

Sunny_sXe [5.5K]

78 = 2 x 3 x 13
1 x 78
2 x 39 = 78
3 x 26=78
6 x 13 = 78

larger number is 13

5 0

3 years ago

A bag contains white matarles and red marables,126 in total.The number of whit marables is 6 more than 5 than 5 times the number

denis-greek [22]

Answer:106

Step-by-step explanation:

Let number of white marbles be w

Let number of red marbles be r

w+r = 126---------1

w = 6 +5r-----------2

Put eqn 2 in eqn 1

6+ 5r + r = 126

6 + 6r = 126

6r = 120

r = 20

w = 6 +5r =6+100

= 106

3 0

3 years ago

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit

coldgirl [10]

Changing the equation into slope form: $y = mx + c$ , where $m$ is the slope [gradient] and $c$ is the y-intercept.

$2x+3y=1470$
$3y = -2x+1470$
$y= - \frac{2}{3}x+ \frac{1470}{3}$
$y=- \frac{2}{3}x+490$

The gradient is $- \frac{2}{3}$ and y-intercept is at $y=490$

Graphing $y=- \frac{2}{3}x+490$ using slope-intercept method:
a) The slope is a negative slope. The line will go 'down hill'
b) The line must pass the point (0, 490)
c) The line will intercept the x-axis at y = 0
   $0 = - \frac{2}{3}x+490$
   $\frac{2}{3}x = 490$
   $2x = 1470$
   $x = \frac{1470}{2}$
   $x = 735$
So, x-intercept is at (735, 0)

The graph of this function is shown below. The intercepts are labelled at:
y = 490
x = 735

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Next month's profit equation

$2x+3y=1593$

Rewriting this into slope-equation form

$3y = -2x+1593$
$y=- \frac{2}{3}+ \frac{1593}{3}$
$y= - \frac{2}{3}+531$

The gradient, $m$ , equals to $- \frac{2}{3}$
The y-intercept, $c$ , equals to 531

The equation still has the same gradient with last month's profit equation but different y-intercept.

-------------------------------------------------------------------------------------------------------------

A linear graph show points of (0, 300) and (450, 0)

We work out the slope:
$\frac{300-0}{0-450} = \frac{300}{-450}=- \frac{20}{30} =- \frac{2}{3}$

Y-intercept at x = 0, so it's at y = 300

Equation $y = - \frac{2}{3}+300$

6 0

3 years ago

In a certain clothing store,6 shirts and 3 ties cost $79.50 ,and 3 shirts and 2 ties cost $41. determine the cost of each shirt.

Komok [63]

Answer:

Each shirt cost $12

Step-by-step explanation:

First, we have to interpret this question and turn each to an equation, letting shirts represent the letter s and ties represent the letter t.

6 shirts and 3 ties cost $79.50 would be interpreted to 6s+3t=79.5 ,and 3 shirts and 2 ties cost $41 would be interpreted to 3s+2t=41

Hence we have two equations, and we solve them simultaneously.

6s+3t=79.5 (Equation 1)

3s+2t=41 (Equation 2)

We can either use the substitution method or the elimination method but for the sake of this question, we use the Elimination method.

6s+3t=79.5 (Equation 1)

3s+2t=41 (Equation 2)

We multiply equation 1 by 2 and we multiply equation 2 by 3, I'm prefer to eliminate the

2(6s+3t=79.5)

12s+6t=159 Equation 3

3(3s+2t=41)

9s+6t=123 Equation 4

We subtract equation 4 from equation 3.

12s+6t=159

9s+6t=123

12s-9s=3s

6t-6t=0

159-123=36

We therefore have

3s=36

Divide both sides by 3

s=36/3

s=12

One shirt cost $12

3 0

3 years ago

A contractor bought 7.6 ft2 of sheet metal. She has used 3.5 ft2 so far and has $123 worth of sheet metal remaining. The equati

Sergio039 [100]

Answer:

Sheet metal remaining = 4.1x

cost per square foot of sheet metal = $30

Step-by-step explanation:

Total sheet metal bought = 7.6 ft2

Total sheet metal used = 3.5 ft2

Given equation:

7.6x − 3.5x = 123

Where,

x = cost per square foot

7.6x − 3.5x

Sheet metal remaining = 4.1x

7.6x − 3.5x = 123

4.1x = 123

x = 123 / 4.1

x = $30

Cost per square foot = $30

5 0

3 years ago