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2 years ago

Find the gradient of the line segment between the points (-4,4) and (0,12)

Mathematics

1 answer:

Likurg_2 [28]2 years ago

7 0

Answer:

Hope that will help you

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Solve each quadratic equation by completing the square. 6. x2 + 2x = 8 7. x2 - 6x = 16 8. x2 - 18x = 19 9. x2 + 3x = 3 10. x2 +

Andrei [34K]

Lets get started :)

These questions have asked us to solve by completing the square.
How do we? I have attached a picture, which will explain

6. x² + 2x = 8
→ b is the coefficient of x, which is 2
→ We take half of 2 and square it. Then, we add it to either side

x² + 2x $+ (\frac{2}{2} )^2 = 8 + ( \frac{2}{2})^2$
x² + 2x + 1 = 8 + 1
( x + 1 )( x + 1 ) = 9
( x + 1 )² = 9
$\sqrt{( x + 1 )^2} = \sqrt{9}$
x + 1 = + 3 or x + 1 = - 3
x = 2 or x = - 4

7. x² - 6x = 16

→ We do the same thing we did in the previous question

x² - 6x + $(\frac{6}{2})^2 = 16 + (\frac{6}{2})^2$
x² - 6x + 9 = 16 + 9
(x - 3)² = 25
$\sqrt{(x-3)^2} = \sqrt{25}$
x - 3 = + 5 or x - 3 = - 5
x = 8 or x = - 2

8. x² - 18x = 19

x² - 18x + $( \frac{18}{2} )^2 = 19 + ( \frac{18}{2})^2$
x² - 18x + 81 = 19 + 81
( x - 9 )( x - 9 ) = 100
( x - 9 )² = 100
$\sqrt{(x-9)^2} = \sqrt{100}$
x - 9 = + 10 or x - 9 = -10
x = 19 or x = - 1

9. x² + 3x = 3

x² + 3x + $( \frac{3}{2} )^2 = 3 + (\frac{3}{2} )$
$x^2 + 3x + \frac{9}{4} = 3 + \frac{9}{4}$
$x^{2} + 3x + \frac{9}{4} = \frac{21}{4}$
$(x^2 + \frac{3}{2} ) ( x^2 + \frac{3}{2} ) = \frac{21}{4}$
$( x^2 + \frac{3}{2} )^2 = \frac{21}{4}$
$\sqrt{ x^2 + \frac{3}{2} } = \sqrt{ \frac{21}{4} }$
x + $\frac{3}{2}$ = + $\frac{ \sqrt{21} }{2}$ or x + $\frac{3}{2} = - \frac{ \sqrt{21} }{2}$
x = $\frac{-3+ \sqrt{21} }{2}$ or x = $\frac{-3 - \sqrt{21}}{2}$

7 0

3 years ago

Solve the equation.

Hitman42 [59]

(x+4)(x+6)=0
x = -4, x=-6

The answer is C.

4 0

2 years ago

Mrs Tay had 425 cookies at first.

yKpoI14uk [10]

Answer:

425-65=360

360-65=295

Mrs Chan had at first 295 cookies

3 0

3 years ago

Read 2 more answers

If the price of a gallon of gas was $0.89 in 1984 and was $3.59 in 2014, what was the average rate of change in the price per ga

mylen [45]

Answer:

0.09

Step-by-step explanation:

avg rate of change is: change in y/ change in x

so it´d be 3.59 - 0.89 / 2014 - 1984

= 2.7/ 30

= 0.09

note:

The slope formula and the average rate of change formula are the same, just written a bit different, so you could also use:

y2 - y1 / x2 - x1

8 0

2 years ago

What is 1 over 40 in decimals

Sindrei [870]

Answer:

0.025

Step-by-step explanation:

you can divide 1/40 and should get 0.025

7 0

3 years ago

Read 2 more answers