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3 years ago

Example 1

Mathematics

1 answer:

katovenus [111]3 years ago

8 0

Answer:

The answer to your question is getting the center and the radius of the polynomial we conclude that the data given are correct.

Step-by-step explanation:

x² - 2x + 1 + y² - 4y + 4 = 25

First, factor the first three terms as a perfect square trinomial

(x - 1)² + y² - 4y + 4 = 25

Second, factor the last terms as a perfect square trinomial

(x - 1)² + (y - 2)² = 25

Get the numbers of each factor and change their signs

Ex (x -1)² = 1

(y - 2)² = 2

These numbers are the center of the circle (1, 2)

Get the square root of 25

$\sqrt{25} = 5$ This is the radius

Then center = (1, 2) and radius = 5

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SAVE ME. Please Answer my Questions Clevers.

Vladimir [108]

Answer:

See below

Step-by-step explanation:

Q1. if a counting number is selected at random from a set of whole number less than or equal to 20 find the probability of getting:

Counting numbers are Natural numbers: $\mathbb{N}$

Also, we have Whole numbers. Despite not having an official symbol, I usually denote the set as $\mathbb{Z}_{\ge 0}$

Whole numbers less than or equal to 20: $A\leq 20, A \subset \mathbb{Z}_{\ge 0} \\\implies A=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}$

A. Prime numbers

From the set A, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19.

Once we have 21 numbers in total and 8 prime numbers, the probability is:

$P=\frac{8}{21} \approx 40\%$

B. Composite numbers

From the set A, the composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20.

Once we have 21 numbers in total and 11 composite numbers, the probability is:

$P=\frac{11}{21} \approx 52\%$

C. Divisible by three

From the set A, the numbers divisible by three are 3, 6, 9, 12, 15, 18.

Once we have 21 numbers in total and 6 numbers divisible by three, the probability is:

$P=\frac{6}{21} \approx 30\%$

D. Square of 2

From the set A, the numbers square of 2 are 0, 1, 4, 9, 16.

$\sqrt{0} =0$

$\sqrt{1} =1$

$\sqrt{4} =2$

$\sqrt{9} =3$

$\sqrt{16} =4$

Once we have 21 numbers in total and 5 numbers square of 2 , the probability is:

$P=\frac{5}{21} \approx 24\%$

Q2. The opposite angle of acyclic quadrilaterals is in the ratio of 2:3. Find the degree measure of each opposite angle?

Once they're opposite, they add up to 180º

$2x+3x=180 \implies 5x=180 \implies x=36$

The first angle is 72º

The second angle is 108º

Q3. what is the solution set of 9x-4<13x-7 (domain, x e z) ?

$x \in \mathbb{Z}\\$

$x>\frac{3}{4}$

$x\in \left(\frac{3}{4},\infty \right)$

Q4. if three fourth of a number is one tenths, what is the number?

$\frac{3}{4} x =\frac{1}{10} \implies 3x=\frac{4}{10} \implies \boxed{x = \frac{2}{15}}$

Q5. which one is the equation of the line passing through the origin and having a slope 4?

$y=mx+b$

$m: \text{slope}$

$b: \text{y-intercept}$

B. Y= 4x

7 0

3 years ago

What is 9 2/5-8 1/3 I need to know for math tomorrow

patriot [66]

Answer:

$1\frac{1}{15}$

Step-by-step explanation:

Let's use a start by using common denominators. $9\frac{2}{5} = 9\frac{6}{15}$ and $8\frac{1}{3} = 8 \frac{5}{15}$

Now, replace the original equation with the common denominators. $9\frac{6}{15} - 8\frac{5}{15}$

Solve! $9\frac{6}{15} - 8\frac{5}{15} = 1\frac{1}{15}$

8 0

3 years ago

Help please I beg if you can

MAVERICK [17]

Answer:

24.30 Difference, sale price 56.70

Step-by-step explanation:

30% off 81.00 is 56.70

The difference is 24.30

7 0

3 years ago

The maxwell family goes out for dinner and the price of the meal is $60 the sales tax on the meal is 7% and they also want to le

sukhopar [10]

So we start with the $60 untouched.

Then we add the tax which is $60•0.07= 4.20 that is the tax

Then add the tax to the total $60 + $4.20= $64.20

Next we must add the tip so $60•0.15= 9.

Then $64.20 + $9.00 = $73.20

Total cost of meal $73.20

Any questions? :)

4 0

3 years ago

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In a study of 225 adults, the mean heart rate was 72 beats per minute. Assume the population of heart rates is known to be appro

Aleonysh [2.5K]

The lower and upper bounds of the confidence intervals must be equally distanced from the mean
so it will be
70.9 - 73.1
hope it helps

3 0

3 years ago

Read 2 more answers