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[tex]\large\bold{{Question :-}}[/tex]The sum of the Squares of three consecutive number is 110. Then determine the Three Numbers.

[tex]\large\bold\red{\underline{Answer :-}}[/tex]

So, First of all The Question is to find out three consecutive Numbers .

First of all let's learn a little about Consecutive Numbers. So, Consecutive Numbers are the Numbers which follows each other. For example :- 1,2,3,4 are consecutive Numbers.

Let's start with Our Question :-

So,

[tex]:\pink\implies[/tex] [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(x + 1)^{2}}}[/tex] + [tex]\bold{{(x + 2)^{2}}}[/tex] = [tex]\bold{{110}}[/tex]

[tex]:\pink\implies[/tex] [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(1)^{2}}}[/tex]+ [tex]\bold{{2x}}[/tex] +[tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(4)}}[/tex]+ [tex]\bold{{(4x)}}[/tex] = [tex]\bold{{110}}[/tex]

[tex]:\pink\implies[/tex] [tex]\bold{{3x^{2}}}[/tex] + [tex]\large\bold{{6x}}[/tex] + [tex]\bold{{5}}[/tex] - [tex]\large\bold{{110}}[/tex] = [tex]\bold{{0}}[/tex]

[tex]:\pink\implies[/tex] [tex]\bold{{3x^{2}}}[/tex] + [tex]\bold{{6x}}[/tex] - [tex]\bold{{105}}[/tex] = [tex]\bold{{0}}[/tex]

By taking 3 Out as Common, we are left with the Quadratic Equation :—

[tex]:\pink\implies[/tex] [tex]\large\bold{{1x^{2}}}[/tex]+ [tex]\large\bold{{2x}}[/tex] - [tex]\large\bold{{35}}[/tex] = [tex]\large\bold{{0}}[/tex]

x = -b ± √(b)^2— 4 × a × c / 2a

x = -2 ± √(2)^2— 4 × 1 × -35 / 2×1

x = -2 ± √144/2

[ As we know that "144" is square of 12 ]

x = -2 ± 12/2

Hence, x = +5

x +1 = 5+1 = +6

x+2 = 5+2 = +7

Hence, x = -7

x+1 = -7+1 = -6

x+2 = -7+2 = -5

Answer:

Step-by-step explanation:

Let the three consecutive numbers be denoted as :

Identity

It is given that the sum of the squares of these numbers add up to 110.

Taking x = 5

Taking x = -7

Solution

Answer:

Option1 : Domain and range for both functions are all real numbers

Step-by-step explanation:

Answer:

It should be a kilogram.

Gram = too small

milligram = too small

meter = distance

Answer:

1/3

Step-by-step explanation:

probability = favorable events / total num of events

here total num of events is 3 and favorable is 1 since there is only one odd number.

therefore, p(odd) = 1/3

Answer:

[tex]\huge\boxed{\bf\:\frac{1}{3}=0.33}[/tex]

Step-by-step explanation:

Odd numbers are numbers that end with the digits [tex]\rightarrow 1,3,5,7,9[/tex], whereas even numbers are numbers that end with the digits [tex]\rightarrow 0,2,4,6,8[/tex].

Here, we can see that,

Therefore,

Probability of getting an odd number (3) card

= Number of odd number cards / Total number of cards

= ⅓ = 0.33

[tex]\rule{150pt}{2pt}[/tex]

Independent: r- the length of the route

[tex]\bull\:[/tex][tex]\sf{x^2+y^2 -10x+8y + 1= 0}[/tex]

[tex]\\[/tex]

The general form of circle is given by the equation by the equation -

[tex]\green{ \underline { \boxed{ \sf{x^2+y^2 + 2gx+2fy + c = 0}}}}[/tex]

in which

❀ Comparing given equation with general form of circle -

So, Center of Circle = (-(-5), -4)

➥ (5, -4)

[tex]\\[/tex]

Also, radius of circle = [tex]\sqrt{(-5)^2+4^2-1}[/tex]

➥ [tex]\sqrt{25+16-1}[/tex]

➥ [tex]\sqrt{40}[/tex]

➥ [tex]2\sqrt{10}[/tex] units .

Step-by-step explanation:

Answer:

597

Step-by-step explanation:

711-114=597

Hope it helps you

Answer:

576

Step-by-step explanation: multiply 48 by 12 and you should get 576

Answer:

8

Step-by-step explanation:

(n−2) × 180°= 1080

=> n = 1080 / 180  + 2

Answer:

The first one with 8 points.

Step-by-step explanation:

It's an octagon.

Answer: 129.33 g

Step-by-step explanation:

[tex]$$Let $p=A \cdot e^{n t}$ \\$(p=$ present amount, $A=$ initial amount, $n=$ decay rate, $t=$ time)[/tex]

[tex]\begin{aligned}&\Rightarrow \text { Given } p=\frac{A}{2} \ a t \ t=1590 \\&\Rightarrow \frac{1}{2}=e^{1590n} \Rightarrow n=\frac{\ln (1 / 2)}{1590}=-0.00043594162\end{aligned}[/tex]

[tex]$$If $A=200 \mathrm{mg}$ and $t=1000$ then,$$\begin{aligned}P &=200 e^{\left(\frac{\ln \left(1/2\right)}{1590}\right) \cdot 1000} \text \\\\&=129.33 \text { grams}\end{aligned}$$[/tex]

Answer:

E: since irrational is non-terminating and the ... means it goes on forever which cannot be represented by a fraction

Answer:

6.53

Step-by-step explanation:

cos(theta)= adjacent/hypotenuse

cos(40)= 5/h

H= 5/cos(40)

=6.527

Rounded to the nearest hundredth will be 6.53

Answer:

  x = 2

Step-by-step explanation:

These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.

__

The usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.

  [tex]\sqrt{x+2}+1=\sqrt{3x+3}\qquad\text{given}\\\\(x+2)+2\sqrt{x+2}+1=3x+3\qquad\text{square both sides}\\\\2\sqrt{x+2}=(3x+3)-(x+3)=2x\qquad\text{isolate the root term}\\\\x+2=x^2\qquad\text{divide by 2, square both sides}\\\\x^2-x-2=0\qquad\text{write in standard form}\\\\(x-2)(x+1)=0\qquad\text{factor}[/tex]

The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.

  x = -1: √(-1+2) +1 = √(3(-1)+3)   ⇒   1+1 = 0 . . . . not true

  x = 2: √(2+2) +1 = √(3(2) +3)   ⇒   2 +1 = 3 . . . . true . . . x = 2 is the solution

__

Another way to solve this is using substitution for one of the radicals. We choose ...

  [tex]u=\sqrt{x+2}\qquad\text{requires $u\ge0$}\\\\u^2-2=x\qquad\text{solve for x}\\\\u+1=\sqrt{3(u^2-2)+3}\qquad\text{substitute for x in the original equation}\\\\(u+1)^2=3u^2-3\qquad\text{square both sides, simplify a little}\\\\2u^2-2u-4=0\qquad\text{subtract $(u+1)^2$}\\\\2(u-2)(u+1)=0\qquad\text{factor}[/tex]

Solutions to this equation are ...

  u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution

The value of x is ...

  x = u² -2 = 2² -2

  x = 2 . . . . the solution to the equation

_____

Additional comment

Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.

Answer:

1. 15.49 cm

2. 14.39 cm

3. 17.32 cm

4. 11.53 cm

5. 5 cm

Step-by-step explanation:

In the given problem, you can solve the unknown side of the triangle using either Pythagorean Theorem or SOA CAH TOA method. In Trigo, you can use the Pythagorean Theorem if the triangle has 90 degrees, or it is a right triangle.

In the given problem, the angle of the triangles are unknown, therefore to solve the unknown side of triangles, we will you use the SOA CAH TOA.

In this case, since the given side are b and c, we can use CAH (Cos Teta equals Adjacent over Hypotenuse), and TOA ( Tan Teta equals Opposite over Adjacent)

Lets provide the solution for the number, and the rest have the same solutions and process.

b= 17, c= 3, let u is the angle

Cosu= 17/23, to get the angle, use inverse cosine.

The result will be 42.34°, and to get the unknown side, use TOA

Tanu=a/17, a=17Tanu

It will give you 15.49 cm

In the number 2 and 5, it will be the same when you rotate the triangle.

Read more about the concept of SOA CAH TOA at

https://brainly.com/question/22767551

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Applying the inscribed angle theorem, since x and 31° are subtended by the same arc in the given circle, then x = 31°.

The inscribed angle theorem states that if two inscribed angles are subtended by the same arc, the measure of both inscribed angles are equal.

Inscribed angle = 1/2(measure of intercepted arc)

Based on the inscribed angle theorem, x = 31° because they are both subtended by the same arc.

Learn more about inscribed angle theorem on:

https://brainly.com/question/3538263

Answer:

-2 ± √19

Explanation:

Quadratic formula

Hope this helps!

Answer:

30 ants are in the ant farm.

---------------------------------------

If there are 40 ants on the second part of the scale,

multiply 5 by 8 to get 40 because there are 5 ants for each row, and 8 rows total

and there are 10 ants visible on the first side of the scale, the second part of the scale would have the majority and there would be a big inbalance. To fix that, we could say there are 30 ants in the ant farm, because there are 10 ants on the scale. [tex]10 + 30 = 40[/tex], so that would make the scale balanced.

Using the combination formula, it is found that you can select 2 boys and 5 girls in 2,520 ways.

In this problem, Joao and Elisa would be the same team as Elisa and Joao, hence the order is not important and the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem:

Hence:

[tex]T = C_{5,2}C_{10,5} = \frac{5!}{3!2!} \times \frac{10!}{5!5!} = 2520[/tex]

You can select 2 boys and 5 girls in 2,520 ways.

More can be learned about the combination formula at https://brainly.com/question/25821700

#SPJ1

Answer:

Option B, There are no real solutions

Step-by-step explanation:

Step 1:  Square root both sides

[tex]x^2 = -49[/tex]

[tex]\sqrt{x^2} = \sqrt{-49}[/tex]

Since we are trying to square root a negative it would cause imaginary solutions so in conclusion we have no real solutions.

Answer: Option B, There are no real solutions

Make things easier by expanding J(v) first:

[tex]J(v) = (v^3-2v) \left(\dfrac1{v^4}+\dfrac1{v^2}\right) = \dfrac1v - \dfrac2{v^3} - \dfrac2v + v = v - \dfrac1v - \dfrac2{v^3}[/tex]

Now differentiate term-by-term (power rule):

[tex]J'(v) = \boxed{1 - \dfrac1{v^2} + \dfrac6{v^4}}[/tex]

In case you're supposed to use the product rule first, we have

[tex]J'(v) = (3v^2 - 2) \left(\dfrac1{v^4} + \dfrac1{v^2}\right) + (v^3-2v) \left(-\dfrac4{v^5} - \dfrac2{v^3}\right)[/tex]

Expanding and simplifying will yield the same result as before.

Answer:

see below

Step-by-step explanation:

The three sides add to 51

n      +    4n-4    +   4n-8   = 51

9n -12 = 51

9n = 63

n = 7        4n-4 = 24      4n-8 = 20  

Answer:

that means the answer is c

Answer: 0.65

Step-by-step explanation:

the probability is high

The probability that at least one of the next five birds sees is a song sparrow will be 0.65

Probability is chance that a given event will occur

The steps are as follows:

05716 16803 96568 33855 76635 88864 05943 77510 74051 97895 86481 94036 24005

P=(number of occurrence/number of simulation)

∴ P=13/20

∴ P=0.65

There is 0.65 probability that at least one of the next five birds Cory sees is a song sparrow

Learn more about probability here:

https://brainly.com/question/25870256

#SPJ2

Answer:

$5.00

Step-by-step explanation:

10 × 50/100

Discount = 10 x 0.5

You save = $5.00

The spinner of Maddi's game is an illustration of probability, and it is expected that the number of spins is 28

The number of sections in the spinner is given as:

Sections = 4

The letter C is given as:

Letter C = 1

The expected appearance of letter C is given as:

Expected appearance = 7

The expected number of letter C is calculated using

Expected = Letter C/Sections * Number of spins (n)

So, we have:

7 = 1/4 * (n)

Multiply both sides by 4

n = 28

Hence, it is expected that the number of spins is 28

#SPJ1

Read more about expected values at:

brainly.com/question/15858152

Answer:

a.) 23.6

b.) 40/3

Step-by-step explanation:

Answer: 3x + 28 > 200

Step-by-step explanation:

[tex]$$Let $x$ be the amount each friend received. Since there are 3 friends, then $3 x$ is the amount of money they split evenly. The amount of money they split evenly was the amount left over after paying their parent's $\$ 28$. Therefore $3 x+28$ is the total amount they earned.[/tex]

Answer:

0

Step-by-step explanation:

The answer is 1/12