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3 years ago

I need help with these 2 questions

Mathematics

1 answer:

bagirrra123 [75]3 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

(a)

x² - 6x + 4 = 0 ( subtract 4 from both sides )

x² - 6x = - 4

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = - 4 + 9

(x - 3)² = 5 ( take the square root of both sides )

x - 3 = ± $\sqrt{5}$ ( add 3 to both sides )

x = 3 ± $\sqrt{5}$ ← exact solutions

(b)

4x² + 16x + 9 = 0

To complete the square

The coefficient of the x² term must be 1

Factor out 4 from 4x² + 16x

4(x² + 4x) + 9 = 0

add/subtract ( half the coefficient of the x- term )² to x² + 4x

4(x² + 2(2)x + 4 - 4 ) + 9 = 0

4(x + 2)² - 16 + 9 = 0

4(x + 2)² - 7 = 0 ( add 7 to both sides )

4(x + 2)² = 7 ( divide both sides by 4 )

(x + 2)² = $\frac{7}{4}$ ( take the square root of both sides )

x + 2 = ± $\sqrt{\frac{7}{4} }$ = ± $\frac{\sqrt{7} }{2}$ ( subtract 2 from both sides )

x = - 2 ± $\frac{\sqrt{7} }{2}$ ← exact solutions

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goblinko [34]

Answer:

$\huge\boxed{A=60\pi cm^2}$

Step-by-step explanation:

The formula of an area of a elipse:

$A=\pi ab$

We have:

$2a=10cm\to a=5cm\\\\2b=24cm\to b=12cm$

Substitute:

$A=\pi\dot5\cdot12=60\pi(cm^2)$

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2 years ago

Clara created a coordinate grid of her city. The bowling alley is located at (10, 12) and the skating rink is located at (-6, -4

yulyashka [42]

First we need to know the coordinates of the movie theater, we can do this applying the midpoint formula:

$\begin{gathered} P(BA,SR)=(\frac{10-6}{2},\frac{12-4}{2})\text{ = (}\frac{4}{2},\frac{8}{2}) \\ \Rightarrow P(BA,SR)=(2,4) \end{gathered}$

We have that the movie theater is located at (2,4). Now we use this coordinates to find the location of Clara's house using again the midpoint formula:

$\begin{gathered} P(MT,SR)=(\frac{-6+2}{2},\frac{4-4}{2})=(-\frac{4}{2},0) \\ \Rightarrow P(MT,SR)=(-2,0) \end{gathered}$

Therefore, Clara's house is located at (-2,0)

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1 year ago

Isaac keeps track of the amount of money in his savings certificate each month. He has accumulated the following data:

Dafna1 [17]

Answer:

d. The common ratio is 1.1

Step-by-step explanation:

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In this case, since $60.5 - 55 \neq 55 - 50$ , it has a common ratio.