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3 years ago

7

The table shows a proportional relationship between the weight on a spring scale and the distance the spring has stretched.

2 answers:

Svetlanka [38]3 years ago

7 0

Answer:

See below

Step-by-step explanation:

<u>As per the first row of proportional relationship, the proportion is:</u>

y = kx
28 = k*20
k = 28/20 = 1.4

<u>The function is therefore:</u>

y = 1.4x

a) Table is filled in below:

<u>distance (cm) | weight (newtons)</u>

20 | 28

55 | 55*1.4 = 77

140/1.4 = 100 | 140

1 | 1*1.4 = 1.4

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

b) The scale should consider the coefficient 1.4, therefore x- axis will have a scale of 100 with intervals of 1 cm and y- axis will have a scale of 140 with intervals of 1.4 newtons

Ira Lisetskai [31]3 years ago

3 0

Answer:

55= 39 2/7

Step-by-step explanation:

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3 years ago

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Wewaii [24]

Answer:

1. $P(x)$ ÷ $Q(x)$ ---> $\frac{-3x + 2}{3(3x - 1)}$

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3. $P(x) - Q(x)$ ---> $\frac{-2(12x - 5)}{(3x - 1)(-3x + 2)}$

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Step-by-step explanation:

Given that:

1. $P(x) = \frac{2}{3x - 1}$

$Q(x) = \frac{6}{-3x + 2}$

Thus,

$P(x)$ ÷ $Q(x)$ = $\frac{2}{3x - 1}$ ÷ $\frac{6}{-3x + 2}$

Flip the 2nd function, Q(x), upside down to change the process to multiplication.

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$\frac{2(-3x + 2)}{6(3x - 1)}$

$= \frac{-3x + 2}{3(3x - 1)}$

2. $P(x) + Q(x)$ = $\frac{2}{3x - 1} + \frac{6}{-3x + 2}$

Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:

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$\frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)}$

$\frac{12x - 2}{(3x - 1)(-3x + 2)}$

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$\frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)}$

$\frac{-24x + 10}{(3x - 1)(-3x + 2)}$

$= \frac{-2(12x - 5}{(3x - 1)(-3x + 2)}$

4. $P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2}$

$P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)}$

$P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)}$

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