Math / Algebra

QuestionSi représente 1 et que la couleur jaune représente des quantités négatives, détermine l'opposé de l'expression représentée par chacun de ces schémas. Exprime tes réponses avec des schémas et des symboles. a) b)

Studdy Solution

STEP 1

What is this asking? We need to find the opposite of the expressions shown in the diagrams, and show our answers both as diagrams and symbols! Watch out! Remember, yellow means negative, and we're looking for opposites!
Don't mix those up.

STEP 2

1. Express diagram (a) symbolically.
2. Find the opposite of (a).
3. Express diagram (b) symbolically.
4. Find the opposite of (b).

STEP 3

Alright, let's break down diagram (a).
We've got a yellow rectangle, which represents $-x$ , and a purple square, which represents $1$ .

STEP 4

So, putting it together, diagram (a) represents $-x + 1$ .

STEP 5

To find the opposite, we multiply the entire expression by $-1$ .
This flips the sign of each term!

STEP 6

$(-1) \cdot (-x + 1) = (-1) \cdot (-x) + (-1) \cdot (1) = x - 1$ So, the opposite of $-x + 1$ is $x - 1$ .

STEP 7

In diagram form, this means a blue rectangle ( $x$ ) and a yellow square ( $-1$ ).

STEP 8

Now, let's tackle diagram (b)!
We have two big blue squares, which represent $2x^2$ (two times $x$ squared), and a small yellow square, which means $-1$ .

STEP 9

So, diagram (b) represents $2x^2 - 1$ .

STEP 10

Just like before, we multiply the whole expression by $-1$ to find its opposite.

STEP 11

$(-1) \cdot (2x^2 - 1) = (-1) \cdot (2x^2) + (-1) \cdot (-1) = -2x^2 + 1$ The opposite of $2x^2 - 1$ is $-2x^2 + 1$ .

STEP 12

As a diagram, this would be two big yellow squares ( $-2x^2$ ) and a small purple square ( $1$ ).

STEP 13

For diagram (a), the opposite is $x - 1$ , represented by a blue rectangle and a yellow square.
For diagram (b), the opposite is $-2x^2 + 1$ , represented by two large yellow squares and a small purple square.

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QuestionSi représente 1 et que la couleur jaune représente des quantités négatives, détermine l'opposé de l'expression représentée par chacun de ces schémas. Exprime tes réponses avec des schémas et des symboles. a) b)

Studdy Solution

STEP 1

What is this asking? We need to find the opposite of the expressions shown in the diagrams, and show our answers both as diagrams and symbols! Watch out! Remember, yellow means negative, and we're looking for opposites!
Don't mix those up.

STEP 2

1. Express diagram (a) symbolically.
2. Find the opposite of (a).
3. Express diagram (b) symbolically.
4. Find the opposite of (b).

STEP 3

Alright, let's break down diagram (a).
We've got a yellow rectangle, which represents $-x$ , and a purple square, which represents $1$ .

STEP 4

So, putting it together, diagram (a) represents $-x + 1$ .

STEP 5

To find the opposite, we multiply the entire expression by $-1$ .
This flips the sign of each term!

STEP 6

$(-1) \cdot (-x + 1) = (-1) \cdot (-x) + (-1) \cdot (1) = x - 1$ So, the opposite of $-x + 1$ is $x - 1$ .

STEP 7

In diagram form, this means a blue rectangle ( $x$ ) and a yellow square ( $-1$ ).

STEP 8

Now, let's tackle diagram (b)!
We have two big blue squares, which represent $2x^2$ (two times $x$ squared), and a small yellow square, which means $-1$ .

STEP 9

So, diagram (b) represents $2x^2 - 1$ .

STEP 10

Just like before, we multiply the whole expression by $-1$ to find its opposite.

STEP 11

$(-1) \cdot (2x^2 - 1) = (-1) \cdot (2x^2) + (-1) \cdot (-1) = -2x^2 + 1$ The opposite of $2x^2 - 1$ is $-2x^2 + 1$ .

STEP 12

As a diagram, this would be two big yellow squares ( $-2x^2$ ) and a small purple square ( $1$ ).

STEP 13

For diagram (a), the opposite is $x - 1$ , represented by a blue rectangle and a yellow square.
For diagram (b), the opposite is $-2x^2 + 1$ , represented by two large yellow squares and a small purple square.

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QuestionSi représente 1 et que la couleur jaune représente des quantités négatives, détermine l'opposé de l'expression représentée par chacun de ces schémas. Exprime tes réponses avec des schémas et des symboles. a) b)

Studdy Solution

STEP 1

What is this asking? We need to find the opposite of the expressions shown in the diagrams, and show our answers both as diagrams *and* symbols! Watch out! Remember, yellow means negative, and we're looking for *opposites*!Don't mix those up.

STEP 2

1. Express diagram (a) symbolically.2. Find the opposite of (a).3. Express diagram (b) symbolically.4. Find the opposite of (b).

STEP 3

Alright, let's break down diagram (a).We've got a yellow rectangle, which represents −x-x−x, and a purple square, which represents 111.

STEP 4

So, putting it together, diagram (a) represents −x+1-x + 1−x+1.

STEP 5

To find the opposite, we multiply the entire expression by −1-1−1.This flips the sign of each term!

STEP 6

(−1)⋅(−x+1)=(−1)⋅(−x)+(−1)⋅(1)=x−1 (-1) \cdot (-x + 1) = (-1) \cdot (-x) + (-1) \cdot (1) = x - 1 (−1)⋅(−x+1)=(−1)⋅(−x)+(−1)⋅(1)=x−1 So, the opposite of −x+1-x + 1−x+1 is x−1x - 1x−1.

STEP 7

In diagram form, this means a blue rectangle (xxx) and a *yellow* square (−1-1−1).

STEP 8

Now, let's tackle diagram (b)!We have two big blue squares, which represent 2x22x^22x2 (two times xxx squared), and a small *yellow* square, which means −1-1−1.

STEP 9

So, diagram (b) represents 2x2−12x^2 - 12x2−1.

STEP 10

Just like before, we multiply the whole expression by −1-1−1 to find its opposite.

STEP 11

(−1)⋅(2x2−1)=(−1)⋅(2x2)+(−1)⋅(−1)=−2x2+1 (-1) \cdot (2x^2 - 1) = (-1) \cdot (2x^2) + (-1) \cdot (-1) = -2x^2 + 1 (−1)⋅(2x2−1)=(−1)⋅(2x2)+(−1)⋅(−1)=−2x2+1 The opposite of 2x2−12x^2 - 12x2−1 is −2x2+1-2x^2 + 1−2x2+1.

STEP 12

As a diagram, this would be two big *yellow* squares (−2x2-2x^2−2x2) and a small purple square (111).

STEP 13

For diagram (a), the opposite is x−1x - 1x−1, represented by a blue rectangle and a yellow square.For diagram (b), the opposite is −2x2+1-2x^2 + 1−2x2+1, represented by two large yellow squares and a small purple square.

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What is this asking? We need to find the opposite of the expressions shown in the diagrams, and show our answers both as diagrams and symbols! Watch out! Remember, yellow means negative, and we're looking for opposites!
Don't mix those up.

1. Express diagram (a) symbolically.
2. Find the opposite of (a).
3. Express diagram (b) symbolically.
4. Find the opposite of (b).

Alright, let's break down diagram (a).
We've got a yellow rectangle, which represents $-x$ , and a purple square, which represents $1$ .

So, putting it together, diagram (a) represents $-x + 1$ .

To find the opposite, we multiply the entire expression by $-1$ .
This flips the sign of each term!

$(-1) \cdot (-x + 1) = (-1) \cdot (-x) + (-1) \cdot (1) = x - 1$ So, the opposite of $-x + 1$ is $x - 1$ .

In diagram form, this means a blue rectangle ( $x$ ) and a yellow square ( $-1$ ).

Now, let's tackle diagram (b)!
We have two big blue squares, which represent $2x^2$ (two times $x$ squared), and a small yellow square, which means $-1$ .

So, diagram (b) represents $2x^2 - 1$ .

Just like before, we multiply the whole expression by $-1$ to find its opposite.

$(-1) \cdot (2x^2 - 1) = (-1) \cdot (2x^2) + (-1) \cdot (-1) = -2x^2 + 1$ The opposite of $2x^2 - 1$ is $-2x^2 + 1$ .

As a diagram, this would be two big yellow squares ( $-2x^2$ ) and a small purple square ( $1$ ).

For diagram (a), the opposite is $x - 1$ , represented by a blue rectangle and a yellow square.
For diagram (b), the opposite is $-2x^2 + 1$ , represented by two large yellow squares and a small purple square.