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Here are the solutions to the remaining questions in English:

6) Given that $y = 2x^2 - 3x + 1$ . Find the value of $y$ when $x = -2$ .

Substitute $x = -2$ into the given equation.
$y = 2(-2)^2 - 3(-2) + 1$
Perform the calculations following the order of operations (PEMDAS/BODMAS).
$y = 2(4) - (-6) + 1$ $y = 8 + 6 + 1$ $y = 15$
The value of $y$ when $x = -2$ is $\boxed{15}$ .

7) Solve the equation $3(x - 2) = 12$ .
Distribute the 3 on the left side of the equation.
$3x - 6 = 12$
Add 6 to both sides of the equation to isolate the term with $x$ .
$3x = 12 + 6$ $3x = 18$
Divide both sides by 3 to solve for $x$ .
$x = \frac{18}{3}$ $x = 6$
The solution to the equation is $\boxed{x = 6}$ .

8) A bag contains 5 red balls, 3 blue balls, and 2 green balls. A ball is picked at random from the bag. Find the probability that the ball picked is:

a) Red

b) Not green
Calculate the total number of balls in the bag.
Total number of balls = $5 (\text{red}) + 3 (\text{blue}) + 2 (\text{green}) = 10$ balls.

a) Red
Determine the number of red balls.
Number of red balls = 5.
Calculate the probability of picking a red ball.
$P(\text{Red}) = \frac{\text{Number of red balls}}{\text{Total number of balls}}$ $P(\text{Red}) = \frac{5}{10} = \frac{1}{2}$
The probability of picking a red ball is $\boxed{\frac{1}{2}}$ .

b) Not green
Determine the number of balls that are not green.
Number of not green balls = Total number of balls - Number of green balls = $10 - 2 = 8$ .
Calculate the probability of picking a ball that is not green.
$P(\text{Not green}) = \frac{\text{Number of not green balls}}{\text{Total number of balls}}$ $P(\text{Not green}) = \frac{8}{10} = \frac{4}{5}$
The probability of picking a ball that is not green is $\boxed{\frac{4}{5}}$ .

9) Simplify $\frac{x^2 - 4}{x + 2}$ .
Factor the numerator using the difference of squares formula, $a^2 - b^2 = (a - b)(a + b)$ .
Here, $x^2 - 4 = x^2 - 2^2 = (x - 2)(x + 2)$ .
Substitute the factored form into the expression.
$\frac{(x - 2)(x + 2)}{x + 2}$
Cancel out the common factor $(x + 2)$ from the numerator and the denominator (assuming $x \neq -2$ ).
$x - 2$
The simplified expression is $\boxed{x - 2}$ .

10) Find the equation of a straight line passing through the points $(1, 2)$ and $(3, 8)$ .
Calculate the slope ( $m$ ) of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Let $(x_1, y_1) = (1, 2)$ and $(x_2, y_2) = (3, 8)$ .
$m = \frac{8 - 2}{3 - 1}$ $m = \frac{6}{2}$ $m = 3$
Use the point-slope form of a linear equation, $y - y_1 = m(x - x_1)$ .
Using the point $(1, 2)$ and the calculated slope $m = 3$ :
$y - 2 = 3(x - 1)$
Convert the equation to the slope-intercept form, $y = mx + c$ , by simplifying.
$y - 2 = 3x - 3$ $y = 3x - 3 + 2$ $y = 3x - 1$
The equation of the straight line is $\boxed{y = 3x - 1}$ .

Please treat it in english

Step-by-step solution

Substitute $x = -2$ into the given equation.

Perform the calculations following the order of operations (PEMDAS/BODMAS).

Distribute the 3 on the left side of the equation.

Add 6 to both sides of the equation to isolate the term with $x$ .

Divide both sides by 3 to solve for $x$ .

Calculate the total number of balls in the bag.

Determine the number of red balls.

Calculate the probability of picking a red ball.

Determine the number of balls that are not green.

Calculate the probability of picking a ball that is not green.

Factor the numerator using the difference of squares formula, $a^2 - b^2 = (a - b)(a + b)$ .

Substitute the factored form into the expression.

Cancel out the common factor $(x + 2)$ from the numerator and the denominator (assuming $x \neq -2$ ).

Calculate the slope ( $m$ ) of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

Use the point-slope form of a linear equation, $y - y_1 = m(x - x_1)$ .

Convert the equation to the slope-intercept form, $y = mx + c$ , by simplifying.

Still stuck on this one?

More English Questions

Please treat it in english

Step-by-step solution

Substitute x=−2x = -2x=−2 into the given equation.

Perform the calculations following the order of operations (PEMDAS/BODMAS).

Distribute the 3 on the left side of the equation.

Add 6 to both sides of the equation to isolate the term with xxx.

Divide both sides by 3 to solve for xxx.

Calculate the total number of balls in the bag.

Determine the number of red balls.

Calculate the probability of picking a red ball.

Determine the number of balls that are not green.

Calculate the probability of picking a ball that is not green.

Factor the numerator using the difference of squares formula, a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b)a2−b2=(a−b)(a+b).

Substitute the factored form into the expression.

Cancel out the common factor (x+2)(x + 2)(x+2) from the numerator and the denominator (assuming x≠−2x \neq -2x=−2).

Calculate the slope (mmm) of the line using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​.

Use the point-slope form of a linear equation, y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1​=m(x−x1​).

Convert the equation to the slope-intercept form, y=mx+cy = mx + cy=mx+c, by simplifying.

Still stuck on this one?

More English Questions

Substitute $x = -2$ into the given equation.

Add 6 to both sides of the equation to isolate the term with $x$ .

Divide both sides by 3 to solve for $x$ .

Factor the numerator using the difference of squares formula, $a^2 - b^2 = (a - b)(a + b)$ .

Cancel out the common factor $(x + 2)$ from the numerator and the denominator (assuming $x \neq -2$ ).

Calculate the slope ( $m$ ) of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

Use the point-slope form of a linear equation, $y - y_1 = m(x - x_1)$ .

Convert the equation to the slope-intercept form, $y = mx + c$ , by simplifying.