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Llana [10]
4 years ago
9

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

Mathematics
2 answers:
KatRina [158]4 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]4 years ago
3 0
The answer is x = 1.19 and x = -4.19
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Write an equation of the circle with center (-7, 4) and radius 8.
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answer

(x+7)^2 + (y-4)^2 = 64

set up equation

the equation of a circle is (x - h)^2 + (y - k)^2 = r^2

where h is the center x coordinate and k is the center y coordinate

values

from the point (-7,4) we know that h = -7 and k = 4

since the radius is 8, r^2 = 8^2 = 64

plug in values

now that we have all the values, we plug them into (x - h)^2 + (y - k)^2 = r^2

(x - h)^2 + (y - k)^2 = r^2

(x - (-7))^2 + (y-4)^2 = 64

(x+7)^2 + (y-4)^2 = 64

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3 years ago
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4 0
3 years ago
I don’t understand please help!
JulijaS [17]
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5 0
3 years ago
The traffic engineer for a large city is conducting a study on traffic flow at a certain intersection near the city administrati
AlexFokin [52]

Options

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B. The number of pedestrians crossing the intersection in one hour

C. The number of bicyclists crossing the intersection in one hour

D. The number of food trucks that park within four blocks of the intersection

E. The number of minutes for a car to get from the intersection to the administration building

Answer:

The number of minutes for a car to get from the intersection to the administration building

Step-by-step explanation:

A variable is said to be discrete if and only if it has a countable number of values. While a variable is said to be continuous if it can take infinitely many values.

Option a to d contains discrete variables (1 hour) and (4 blocks), so they can't be regarded as the right option. 1 hour and 4 blocks are specified values and they can't take any other fraction of values aside 1 and 4 respectively.

Looking at option e, the variable, number of minute as stated in this option is a continuous variable. This is so because at any two interval of minutes, fractions and lots of a minute can always be recorded by the engineer to study the traffic flow

5 0
3 years ago
When Nayeli goes bowling, her scores are normally
Ber [7]

Using the normal distribution, it is found that she scores less than 128 in 28.1% of her games.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, the mean and the standard deviation are given, respectively, by \mu = 135, \sigma = 12.

The proportion of games in which she scores less than 128 is the <u>p-value of Z when X = 128</u>, hence:

Z = \frac{X - \mu}{\sigma}

Z = \frac{128 - 135}{12}

Z = -0.58

Z = -0.58 has a p-value of 0.281.

She scores less than 128 in 28.1% of her games.

More can be learned about the normal distribution at brainly.com/question/24663213

#SPJ1

3 0
2 years ago
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