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3 years ago

TJ solved a quadratic equation. His work is shown below, with Step 3 missing.

Mathematics

1 answer:

Yanka [14]3 years ago

4 0

Answer:

The value of x are -11 and -1.

Step-by-step explanation:

The quadratic equation is:

2 (x + 6)² - 5 = 45

Compute the value of x as follows:

2 (x + 6)² - 5 = 45

2 (x + 6)² = 50

(x + 6)² = 25

x² + 12x + 36 = 25

x² + 12x + 11 = 0

x² + 11x + x + 11 = 0

x (x + 11) + 1 (x + 11) = 0

(x + 11) (x + 1) = 0

If (x + 11) = 0, then x = -11.

If (x + 1) = 0, then x = -1.

Thus, the value of x are -11 and -1.

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Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points.

ddd [48]

Answer:

a) The slope of the line is parallel to the another line m=4

b) The slope of the line is perpendicular to the another line m= $\frac{-1}{4}$

Step-by-step explanation:

Step1:-

Slope of a line :-

If θ is the inclination of a line 'l' then tanθ is called the slope or gradient of the line 'l'.The slope of a line is denoted by m=tanθ

The slope of a line given two points m= $\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

Parallel lines:-

Two non-vertical lines are parallel if and only if their slopes are parallel

Perpendicular lines:-

Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

Step 2:-

a)The slope of a line when given two points (-1,-4) and (0,0)

$m = \frac{0-(-4)}{0-(-1)} =4$

Two non-vertical lines are parallel if and only if their slopes are parallel

$m_{1} = m_{2}$

Therefore the slope of the line that is parallel to the another line

$m_{1} =m_{2} =4$

Step 3:-

b) Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

$m_{2} =\frac{-1}{4}$

Therefore the slope of the line is perpendicular to the another line is

$m=\frac{-1}{4}$

3 0

3 years ago

Read 2 more answers

What is the slope of the line shown? -7/9 9/7 7/9 -9/7

SpyIntel [72]

To find slope, we must find the change in y values divided by the change in x values, also called the rise/run. This is modeled below:

Slope = m = (y1 - y2)/(x1-x2) = (6-(-3))/(1 - (-6)) = (6+3)/(1+6) = 9/7

We can check that this answer is correct by consulting the graph. The graph shows a positive correlation (means that the slope should be positive), and if you count the graph unit squares, you get that the graph moves up 9 squares and over 7 squares between the two points shown, letting us know we got the right answer.

Hope this helps!

7 0

3 years ago

The coordinates of A on a grid are (-2,-4.Point A is reflexed across the y-axis to obtain.The coordinates of point B are?

Valentin [98]

Answer:

(2,-4)

Step-by-step explanation:

when reflecting across the Y-axis from quadrant 3 to quadrant 4, a sign change from (-,-) to (+,-) would occur.

3 0

3 years ago

Identify the constant term in this expression 7p - 3p + 9 + x

ANEK [815]

Answer:

the constant in this expression is 9 because it is not a coefficient of any variable

7 0

3 years ago

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39*10*100*1,000*0+37???? HELPPP

FromTheMoon [43]

Answer:

Step-by-step explanation:

Anything multiplied by 0 is 0 then you just add the 37

5 0

2 years ago