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3 years ago

What is the value of c so that y=x^2+15x+c is a perfect square.

Mathematics

2 answers:

Verizon [17]3 years ago

7 0

Divide 15 by 2, then square the amount.

(15/2)^2 = 225/4

dimulka [17.4K]3 years ago

5 0

Answer: The correct option is (D) $\dfrac{225}{4}.$

Step-by-step explanation: We are give to find the value of c so that the following expression becomes a perfect square.

$y=x^2+15x+c~~~~~~~~~~~~~~~~~~~(i)$

We have

$y\\\\=x^2+15x+c\\\\\\=x^2+2\times x\times \dfrac{15}{2}+c\\\\\\=x^2+2\times x\times \dfrac{15}{2}+\left(\dfrac{15}{2}\right)^2+c-\left(\dfrac{15}{2}\right)^2\\\\\\=(x+\dfrac{15}{2})^2+c-\dfrac{225}{4}.$

So, for the given function (i) to be a perfect square, we must have

$c-\dfrac{225}{4}=0\\\\\\\Rightarrow c=\dfrac{225}{4}.$

Thus, the required value of c is $\dfrac{225}{4}.$

Option (D) is correct.

You might be interested in

Determine the intercepts of the line that passes through the following points

shepuryov [24]

Answer:

(2,0) - x -intercept

(0, 1.5) - y-intercept

Step-by-step explanation:

The slope of the points can be found by writing a ratio of vertical change to horizontal change. It can be found in the table by subtracting y values from each other and subtracting x values from each other. The y values decrease by 3 each time or -6 - -3 = -6 + 3 = -3.

The x values increase by 4.

So the rate of change is -3/4.

This means if you go backwards on the table the previous point would be (2, 0). This is the x-intercept.

To find the y-intercept, you must go further back. Going back 2 more units would make the table appear as:

x y

-2 3

0 ???

2 0

6 -3

10 -6

14 -9

Since the y values decrease by 3 each time and we went back half the usual amount, then the value would be 1.5.

5 0

3 years ago

Help...,..........please..............

IgorLugansk [536]

Here, Add both the equations in order to eliminate y,
5x = 10
x = 10/5
x = 2

Now, substitute it in 1st equation,
8(2) - 4y = -32
-4y= -32- 16
y = -48/-4
y = 12

In short, Your Answer would be (2, 12)

Hope this helps!

5 0

3 years ago

a) A large hotel in Miami has 900 rooms (all rooms are equivalent). During Christmas, the hotel is usually fully booked. However

Olegator [25]

Answer:

14.69% probability that this happens

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

1000 people were given assurance of a room.

This means that $n = 1000$

Let us assume that each customer cancels their reservation with a probability of 0.1.

So 0.9 probability that they still keep their booking, which means that $p = 0.9$

Probability more than 900 still keeps their booking:

$n = 1000, p = 0.9$

$\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{1000}} = 0.0095$

901/1000 = 0.91

So this is 1 subtracted by the pvalue of Z when X = 0.91.

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

By the Central Limit Theorem

$Z = \frac{0.91 - 0.9}{0.0095}$

$Z = 1.05$

$Z = 1.05$ has a pvalue of 0.8531

1 - 0.8531 = 0.1469

14.69% probability that this happens

3 0

2 years ago

O the<br> What is the x-coordinate of the point plotted below?

chubhunter [2.5K]

Answer:

The x coordinate is 2

Step-by-step explanation:

Since the point is on 2 of the x-axis. The exact coordinates of that point is (2,0)

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3 years ago

Find the outlier of the data set<br> 3.1, 5.3, 4.3, 0.7, 5.6, 5.2, 5.8, 5.4

Lelechka [254]

An outglier is a data item which is much bigger/smaller than other data items.

The data item arranged is 0.7, 3.1, 4.3, 5.2, 5.3, 5.4, 5.6, 5.8
From the data 0.7 is much smaller than other data items.

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3 years ago