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3 years ago

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 3x – 5 = 0

Mathematics

2 answers:

KatRina [158]3 years ago

6 0

Answer: The required solution is

$x=1.19,~-4.19.$

Step-by-step explanation: We are given to solve the following quadratic equation by the method of completing the square :

$x^2+3x-5=0.$

We have

$x^2+3x-5=0\\\\\Rightarrow x^2+3x=5\\\\\Rightarrow x^2+2\times x\times \dfrac{3}{2}+\left(\dfrac{3}{2}\right)^2=5+\left(\dfrac{3}{2}\right)^2\\\\\\\Rightarrow \left(x+\dfrac{3}{2}\right)^2=5+\dfrac{9}{4}\\\\\\\Rightarrow x+\dfrac{3}{2}=\pm\dfrac{\sqrt{29}}{2}\\\\\\\Rightarrow x=-\dfrac{3}{2}\pm\dfrac{\sqrt{29}}{2}\\\\\\\Rightarrow x=\dfrac{-3\pm\sqrt{29}}{2}\\\\\Rightarrow x=\dfrac{-3\pm5.38}{2}\\\\\\\Rightarrow x=\dfrac{2.38}{2},~~\dfrac{-8.38}{2}\\\\\\\Rightarrow x=1.19,~-4.19$

Thus, the required solution is

$x=1.19,~-4.19.$

RoseWind [281]3 years ago

3 0

The answer is x = 1.19 and x = -4.19

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A ladder 40 feet in length rests against a vertical wall. The foot of the ladder is 7 feet from the wall. What angle, θ, does th

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3 years ago

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You have drawn a simple random sample of 36 college students, asking each student how much rent they pay per month. You obtain a

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Answer:

$573-1.690\frac{22}{\sqrt{36}}=566.8033$

$573+1.690\frac{22}{\sqrt{36}}=579.1967$

And the 90% confidence interval would be between [566.80 and 579.20]

Step-by-step explanation:

Information given

$\bar X=573$ represent the sample mean

$\mu$ population mean (variable of interest)

s=22 represent the sample standard deviation

n=36 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are given by:

$df=n-1=36-1=35$

The Confidence level is 0.90 or 90%, the significance would be $\alpha=0.1$ and $\alpha/2 =0.05$ , and the critical value for this case would be $t_{\alpha/2}=1.690$

And replacing we got:

$573-1.690\frac{22}{\sqrt{36}}=566.8033$

$573+1.690\frac{22}{\sqrt{36}}=579.1967$

And the 90% confidence interval would be between [566.8033 and 579.1967]

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3 years ago

Lily is buying candy for party favors. She needs 1.5 pounds of chocolates, 0.75 pounds of mints, and 15 lollipops. What is the t

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Answer:

<h2>The answer is B. $8.82</h2>

Step-by-step explanation:

given data

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chocolates $4.70 per pound

lollipops $0.07 each

cost of each items based on the amount item

mints $0.96*0.75= 0.72

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total cost= 0.72+7.05+1.05

total cost=$8.82

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2 years ago

In Marissa's calculus course, attendance counts for 15% of the grade, quizzes count for 20% of the grade, exams count for

Alexandra [31]

Answer:

Her average was 87.35% on this course.

Step-by-step explanation:

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Attendance counts for 15% of the grade and she has 100% average on that. So we have:

attendance = weight*(Marissa's average)

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Quizzes = weigth*(Marissa's average)

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Exams = weigth*(Marissa's average)

Exams = 50%*(82/100) = 41%

The final exam counts for 15% of the grade and she has a average of 85% on that so we have:

Finals = 15%*(85/100) = 12.75%

So her grade is the sum of all the cattegories:

Course's average = 15+18.6+41+12.75 = 87.35 %

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So 0.03 is your answer

<span>Hope I Helped!!!</span>

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2 years ago