Evaluate a² + ab -b² +5 when a =2 and b = 3. is the answer A. 0 B. 1 C. 6 D. 11

1) 2 (x+3) +3 (5-x)=

Ugo [173]

Answer:

Below

Step-by-step explanation:

1. 2 (x+3) +3 (5-x)=

Simplifying

2(x + 3) + 3(5 + -1x) = 0

Reorder the terms:

2(3 + x) + 3(5 + -1x) = 0

(3 * 2 + x * 2) + 3(5 + -1x) = 0

(6 + 2x) + 3(5 + -1x) = 0

6 + 2x + (5 * 3 + -1x * 3) = 0

6 + 2x + (15 + -3x) = 0

Reorder the terms:

6 + 15 + 2x + -3x = 0

Combine like terms: 6 + 15 = 21

21 + 2x + -3x = 0

Combine like terms: 2x + -3x = -1x

21 + -1x = 0

Solving

21 + -1x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-21' to each side of the equation.

21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0

0 + -1x = 0 + -21

-1x = 0 + -21

Combine like terms: 0 + -21 = -21

-1x = -21

Divide each side by '-1'.

x = 21

Simplifying

x = 21

2. 3 (y+2) -4y=-24y

Simplifying

3(y + 2) + -4y = -24y

Reorder the terms:

3(2 + y) + -4y = -24y

(2 * 3 + y * 3) + -4y = -24y

(6 + 3y) + -4y = -24y

Combine like terms: 3y + -4y = -1y

6 + -1y = -24y

Solving

6 + -1y = -24y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '24y' to each side of the equation.

6 + -1y + 24y = -24y + 24y

Combine like terms: -1y + 24y = 23y

6 + 23y = -24y + 24y

Combine like terms: -24y + 24y = 0

6 + 23y = 0

Add '-6' to each side of the equation.

6 + -6 + 23y = 0 + -6

Combine like terms: 6 + -6 = 0

0 + 23y = 0 + -6

23y = 0 + -6

Combine like terms: 0 + -6 = -6

23y = -6

Divide each side by '23'.

y = -0.2608695652

Simplifying

y = -0.2608695652

3. -(x+2) -2(1-x)=

Simplifying

-1(x + 2) + -2(1 + -1x) = 0

Reorder the terms:

-1(2 + x) + -2(1 + -1x) = 0

(2 * -1 + x * -1) + -2(1 + -1x) = 0

(-2 + -1x) + -2(1 + -1x) = 0

-2 + -1x + (1 * -2 + -1x * -2) = 0

-2 + -1x + (-2 + 2x) = 0

Reorder the terms:

-2 + -2 + -1x + 2x = 0

Combine like terms: -2 + -2 = -4

-4 + -1x + 2x = 0

Combine like terms: -1x + 2x = 1x

-4 + 1x = 0

Solving

-4 + 1x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.

-4 + 4 + 1x = 0 + 4

Combine like terms: -4 + 4 = 0

0 + 1x = 0 + 4

1x = 0 + 4

Combine like terms: 0 + 4 = 4

1x = 4

Divide each side by '1'.

x = 4

Simplifying

x = 4

4. whats ? is the equation

6 0

3 years ago

It is known that the point P(-9,18) belongs to the graph of the function y=k/x. Find k.

riadik2000 [5.3K]

Answer:

$k = (-162)$ .

Step-by-step explanation:

A point of the form $(x_{0},\, y_{0})$ belongs to the graph of this function, $y = k / x$ , if and only if the equation of this function holds after substituting in $x = x_{0}$ and $y = y_{0}$ .

The question states that the point $(-9,\, 18)$ belongs to the graph of this function. Thus, the equation of this function, $y = k / x$ , should hold after substituting in $x = (-9)$ and $y = 18$ :

$y = k / x$ .

$18 = k / (-9)$ .

Solve this equation for the constant $k$ :

$\begin{aligned}k &= 18 \times (-9) \\ &= (-162)\end{aligned}$ .

Thus, $k = (-162)$ .

6 0

2 years ago

Nina asked 30 of her friends what they thought about a new movie.

Sunny_sXe [5.5K]

No, this is not a random group of students. Because Nina asked her friends if they liked the movie. For her to ask a random group of people, she would have to go and ask people that she did not know.

4 0

3 years ago

Read 2 more answers

The values of 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-gr

postnew [5]

Answer:

Only 60 is an identified outlier

Step-by-step explanation:

Given

Age group: 40 to 50

$Min = 60$ $Q_1 = 70$ $Median= 73$