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3 years ago

TELL ME WHERE THESE GO PLEASE?

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

3 0

Answers

-x + 5y = 4 ⇔ slope 1/5, y-intercept 4/5

5y - x = 15 ⇔ slope: 1/5, y-intercept: 3

2y - 3x = 7 ⇔ slope: 3/2, y-intercept: 7/2

2y = 5x + 7 ⇔ slope: 5/2, y-intercept: 7/2

Explanation

-x + 5y = 4

5y = x + 4

y = (1/5)x + 4/5 slope 1/5, y-intercept 4/5

5y - x = 15

5y = x + 15

y = (1/5)x + 3 slope: 1/5, y-intercept: 3

2y - 3x = 7

2y = 3x + 7

y = (3/2)x + 7/2 slope: 3/2, y-intercept: 7/2

2y = 5x + 7

y = (5/2)x + 7/2 slope: 5/2, y-intercept: 7/2

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3 years ago

4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant

Ivan

Question:

The quantities x and y are in proportion

x y

4 6

30 45

8 b

a 15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

Answer:

$a = 10$ and $b = 12$

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

$(x_1,y_1) = (4,6)$

$(x_2,y_2) = (30,45)$

The slope (m) is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{45 - 6}{30 -4}$

$m = \frac{39}{26}$

$m = 1.5$

The equation is then calculated using:

$y - y_1 = m(x - x_1)$

This gives:

$y - 6 = 1.5(x - 4)$

$y - 6 = 1.5x - 6$

$y = 1.5x$

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in $y = 1.5x$

$b = 1.5 * 8$

$b = 12$

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in $y = 1.5x$

$15 = 1.5 * a$

Solve for a

$a = \frac{15}{1.5}$

$a = 10$

Solving (b): The constant of variation.

This has been solved in (a) above as:

$m = 1.5$

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

This shows direct variation

3 0

3 years ago