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3 years ago

14

How could you use a number line to help assist in adding or subtracting rational numbers?

1 answer:

hichkok12 [17]3 years ago

7 0

One example of number line of rational numbers is shown below

To help with addition, for example, 0.1 + 0.3, you'd start from 0.1 on the number line and then hop on three lines to the right. You should end at 0.4 and that's the answer

To help with subtraction, you would have to 'hop back'.

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Step-by-step explanation:

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3 years ago

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3 years ago

1) 3 (x - y)² - 10 (x-y) + 8

katovenus [111]

Answer:

$(3x-3y-4)(x-y-2)$

Step-by-step explanation:

Given expression:

$3(x-y)^2-10(x-y)+8$

Let u = (x - y):

$\implies 3u^2-10u+8$

To factor a quadratic in the form $ax^2+bx+c$ find two numbers that multiply to $ac$ and sum to $b$ :

$\implies ac=3 \cdot 8=24$

$\implies b=-10$

Therefore, the numbers are: -6 and -4.

Rewrite $b$ as the sum of these two numbers:

$\implies 3u^2-6u-4u+8$

Factor the first two terms and the last two terms separately:

$\implies 3u(u-2)-4(u-2)$

Factor out the common term (u - 2):

$\implies (3u-4)(u-2)$

Substitute back in u = (x - y):

$\implies (3(x-y)-4)((x-y)-2)$

Simplify:

$\implies (3x-3y-4)(x-y-2)$

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2 years ago