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3 years ago

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 2x = 17

1 answer:

7 0

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Equation Given
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x² + 2x = 17

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Add the constant to make it perfect square
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x² + 2x + (2/2)² - ²(2/2)² = 17

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Evaluate the brackets
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x² + 2x + (1)² - ²(1)² = 17

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Form the perfect square
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(x + 1)² - 1 = 17

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Add 1 to both sides
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(x + 1)² = 17 + 1
(x + 1)² = 18

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Square root both sides
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√(x + 1)² = $\pm$ √18

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Solve for x
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x = 4.24 - 1 or - 4.24 -1

x = 3.24 or - 5.24 (nearest hundredth)

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Answer: x = x = 3.24 or - 5.24
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Nookie1986 [14]

Answer:

£29.6

Step-by-step explanation:

37/5=7.4

37-7.4=29.6

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3 years ago

Bailey has a teddy bear collection. 5 of the bears are pink this is 25% of all of her bears. How many total bears does she have

Elden [556K]

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3 years ago

Read 2 more answers

The general solution to the second-order differential equation y′′+10y=0 is in the form y(x)=c1cosβx+c2sinβx. Find the value of

allsm [11]

Answer:β=√10 or 3.16 (rounded to 2 decimal places)

Step-by-step explanation:

To find the value of β :

we will differentiate the y(x) equation twice to get a second order differential equation.
We compare our second order differential equation with the Second order differential equation specified in the problem to get the value of β

y(x)=c1cosβx+c2sinβx

we use the derivative of a sum rule to differentiate since we have an addition sign in our equation.

Also when differentiating Cosβx and Sinβx we should note that this involves function of a function. so we will differentiate βx in each case and multiply with the differential of c1cosx and c2sinx respectively.

lastly the differential of sinx= cosx and for cosx = -sinx.

Knowing all these we can proceed to solving the problem.

y=c1cosβx+c2sinβx

y'= β×c1×-sinβx+β×c2×cosβx

y'=-c1βsinβx+c2βcosβx

y''=β×-c1β×cosβx + (β×c2β×-sinβx)

y''= -c1β²cosβx -c2β²sinβx

factorize -β²

y''= -β²(c1cosβx +c2sinβx)

y(x)=c1cosβx+c2sinβx

therefore y'' = -β²y

y''+β²y=0

now we compare this with the second order D.E provided in the question

y''+10y=0

this means that β²y=10y

β²=10

B=√10 or 3.16(2 d.p)

5 0

3 years ago

Find the volume of the cylinder

goblinko [34]

Answer: 769.3ft³

Step-by-step explanation:

V = $\pi$ r²h

V = (3.14)(7)²(5)

V = 769.3ft³

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3 years ago

For f(x) = 4x+1 and g(x) = x2 - 5, find (f - g)(x).

Lostsunrise [7]

Answer:

Step-by-step explanation:

Simply substitute the equations f(x) and g(x) for f and g.

(4x+1)-( $x^{2}$ -5)

4x+1- $x^{2}$ +5

Do some rearranging and:

$-x^{2}$ +4x+6

Hope this helped!

3 0

3 years ago