La suma dels quadrats de tres nombres naturals consecutius i múltiples de 3 és igual a 450. Planteja una equació de segon grau i calcula els tres nombres.

Answers

Answer 1

Answer:

The 3 numbers are 9, 12, and 15.

Step-by-step explanation:

I will answer in English, below the answer you can see a translation in Catalan.

This can be translated to:

The sum of the squares of three consecutive and multiple natural numbers of 3 is equal to 450. Pose a quadratic equation and calculate the three numbers.

First, a multiple of 3 can be written as:

3*n

The consecutive multiple of 3 is:

3*n + 3

The consecutive multiple of 3 is:

3*n + 3 + 3

Then the sum of their squares is:

(3*n)^2 + (3*n + 3)^2 + (3*n + 6)^2

And we know that this is equal to 450, then we need to solve the equation:

(3*n)^2 + (3*n + 3)^2 + (3*n + 6)^2 = 450

let's solve this:

9*n^2 + (9*n^2 + 2*(3*n)*3 + 9) + (9*n^2 + 2*(3*n)*6 + 36) = 450

27*n^2 + 54*n + 45 = 450

we can write this as:

27*n^2 + 54*n + 45 - 450 = 0

27*n^2 + 54*n - 405 = 0

The solutions of this equation are given by the Bhaskara's formula, and the solutions are:

[tex]n = \frac{-54 \pm \sqrt{54^2 -4*27*(-415)} }{2*27} = \frac{-54 \pm 216 }{54}[/tex]

we know that our numbers are naturals, then the numbers are positives, which means that we only care for the positive solution of n, which is:

n = (-54 + 216)/54 = 3

Then the 3 numbers are:

3*n = 3*3 = 9

(3*n + 3) = (3*3 + 3) = 12

(3*n + 6) = (3*3 + 6) = 15

In Catalan:

En primer lloc, es pot escriure un múltiple de 3 com:

3 * n

El múltiple consecutiu de 3 és:

3 * n + 3

El múltiple consecutiu de 3 és:

3 * n + 3 + 3

Llavors, la suma dels seus quadrats és:

(3 * n) ^ 2 + (3 * n + 3) ^ 2 + (3 * n + 6) ^ 2

I sabem que això és igual a 450, llavors hem de resoldre l’equació:

(3 * n) ^ 2 + (3 * n + 3) ^ 2 + (3 * n + 6) ^ 2 = 450

resolem això:

9 * n ^ 2 + (9 * n ^ 2 + 2 * (3 * n) * 3 + 9) + (9 * n ^ 2 + 2 * (3 * n) * 6 + 36) = 450

27 * n ^ 2 + 54 * n + 45 = 450

podem escriure això com:

27 * n ^ 2 + 54 * n + 45 - 450 = 0

27 * n ^ 2 + 54 * n - 405 = 0

Les solucions d’aquesta equació vénen donades per la fórmula de Bhaskara, i les solucions són:

[tex]n = \frac{-54 \pm \sqrt{54^2 -4*27*(-415)} }{2*27} = \frac{-54 \pm 216 }{54}[/tex]

sabem que els nostres nombres són naturals, aleshores els nombres són positius, cosa que significa que només ens importa la solució positiva de n, que és:

n = (-54 + 216) / 54 = 3

Llavors els 3 nombres són:

3 * n = 3 * 3 = 9

(3 * n + 3) = (3 * 3 + 3) = 12

(3 * n + 6) = (3 * 3 + 6) = 15


Related Questions

The sides of a right triangle are used to construct three squares, as shown below. The number of square units, representing area, is shown in two of the squares. A represents the area of the largest square.

Answers

1. We know that the distance formula will be be d=√((x_2-x_1)²+(y_2-y_1)²), then we can do x2-x1=3. Y2-Y1=5. 3x3+5x5=34, the square root of 34 is around 5.83. The answer is F.

The person with that spam is rude and wasted your time, sorry for that.

The solution is Option D.

The area of the square with the side having the hypotenuse of the triangle as the side is 34 units²

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the area of the square A be = S

Let the triangle be represented as ΔABC

The base of the triangle BC = 5 units

The height of the triangle AB = 3 units

So , the hypotenuse of the triangle AC = Side of the square A

And , from the Pythagoras theorem

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substituting the values in the equation , we get

AC² = AB² + BC²

AC² = 5² + 3²

AC² = 25 + 9

AC² = 34 units²

AC² = Area of the square A with side AC

Therefore , the value of S is 34 units²

Hence , The area of the square with the side having the hypotenuse of the triangle as the side is 34 units²

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Find the perimeter and area of the shape.

Answers

Answer:

The perimeter is 41

Step-by-step explanation:

The perimeter of a shape is just the sum of all its sides added up. In this case, that would mean the perimeter is:

12 + 9 + 9 + 4.6 + 6.4  = P30 + 11 = P41 = P

Hope this helps!

The answer to the question is 41

Determine the area of the following trapezoids.
(Hint): A = 1/2(b1 + b2)(h)

Answers

Look at the link they gave!! Very helpful!

if y varies inversely as x, and y =35 when x =14, find x when y =15.

Answers

Answer:

[tex]x = 32 \frac{2}{3} [/tex]

Step-by-step explanation:

[tex]y = \frac{k}{x} ,where \: k \: is \: a \: constant.[/tex]

Let's find the value of k first.

When y= 35, x= 14,

[tex]35 = \frac{k}{14} [/tex]

k= 14(35)

k= 490

Substitute the value of k into the equation:

[tex]y = \frac{490}{x} [/tex]

When y= 15,

[tex]15 = \frac{490}{x} [/tex]

15x= 490

x= 490 ÷15

[tex]x = 32 \frac{2}{3} [/tex]

LM is a common tangent. PL=10, QM=2, and LM=20. Find the measure of LN.

Answers

Answer:

25cm

Step-by-step explanation:

using similar triangles.

10/2 = (20+y)/y

where y is length of MN

10y = 40+2y

40= 8y

y= 5.

LN = LM + MN

= 20+5

25cm

Fill in the missing number on the table, based on the graph?

Answers

Answer:

0.5

Step-by-step explanation:

sana panget kayong lahat

PLEASE HELP!!! I WILL RATE YOU BRAINLIEST
The first laptop ever was sold was the Osborne 1. It came onto the market in 1981, and it had a mass of 11 kg. Suppose that since 1981 the mass of laptops has decreased at an average rate of 4.7% per year. What was the approximate weight of a laptop in 2019?

a. 6.43 kg
b. 8.10 kg
c. 4.62 kg
d. 1.76 kg

Answers

Answer: (d)- 1.76 kg

Step-by-step explanation:

Given

The first laptop mass was 11 kg

The rate of mass decreases by 4.7% per year

In 1982, it was

[tex]\Rightarrow 11-11\times 4.7\%=11-11\times 0.047\\\Rightarrow 11(1-0.047)\ kg[/tex]

In 1983, it was

[tex]\Rightarrow 11(1-0.047)-11(1-0.047)\times 0.047=11(1-0.047)^2[/tex]

In 2019 i.e. after 38 years, it is

[tex]\Rightarrow 11(1-0.047)^38=11\times 0.953^{38}=1.76\ kg[/tex]

Please help me answer question number 1 ?

Answers

Answer:

8820.26 yd

Explanation:

the formula for finding the area of a circle is π × radius². since the diameter of the circle is given, we can simply divide it by 2 to find the radius.

106 ÷ 2 = 53

now, we can substitute this into the formula:

π × radius²

= 3.14 × 53²

= 8820.26 yd

i hope this helps! :D

Pls help me i will give u brainlist

Answers

Answer:

y  < or= -3/2

Step-by-step explanation:

Answer:

< or= -3/2

Step-by-step explanation:

Resuelve usando el método de sustitución o el de eliminación. Para un juego de baloncesto se vendieron 1,850 boletos. Se recaudo un total de $ 8,800. Si los boletos de niños cuestan $ 4 y los de adultos cuestan $ 6. ¿Cuántos boletos de cada clase se vendieron?

Answers

Answer:

Se vendieron 700 boletos para adultos y 1,150 boletos para niños.

Step-by-step explanation:

Primero tenemos que definir dos variables:

x = número de boletos de niños vendidos

y = número de boletos de adultos vendidos.

Entonces podemos escribir la recaudación total como:

x*$4 + y*$6

Y sabemos que la recaudación total fue $8,800, entonces:

x*$4 + y*$6 = $8,800

También sabemos que se vendieron 1,850 boletos, entonces:

x + y = 1,850

Entonces tenemos el sistema de ecuaciones:

x*$4 + y*$6 = $8,800

x + y = 1,850

En este caso podemos utilizar el método de sustitución, para ello primero debemos aislar una de las variables en una de las ecuaciones.

Si aislamos x en la segunda ecuación tenemos:

x = 1,850 - y

Ahora podemos sustituir esto en la otra ecuación para obtener:

(1,850 - y)*$4 + y*$6 = $8,800

Ahora podemos resolver esto para y.

$7,400 - y*$4 + y*$6 = $8,800

y*$2 = $8,800 - $7,400 = $1,400

y = $1,400/$2 = 700

Entonces se vendieron 700 boletos para adultos.

Ahora podemos usar la ecuación x = 1,850 - y para obtener el valor de x.

x = 1,850 - y

x = 1,850 - 700 = 1,150

Se vendieron 1,150 boletos para niños.

Find the missing sides and angles of this triangle

Answers

The missing angle is 180 -(70+90)
The third angle is 20 degrees

6.6^2 + x^2= 7^2
43.56+x^2=49
X^2 = 5.44
X= 2.33. Is the other side

which expression is equal to 24x^2-22x+5

Answers

Answer: (12x−5)(2x−1)

Step-by-step explanation: Hope this help :D

Answer:

24(x^2)-22x+5

=24(x^2)-(12+10)x+5

=24(x^2)-12x-10x+5

=12x(2x-1)-5(2x-1)

=(2x-1)(12x-5)

I really need help Please and thank you ​

Answers

la B s la correcta por que es el que esta mas serca :)

Urgent please help..

Answers

Answer:

30cm

Step-by-step explanation:

The perimeter of the triangle is the sum of all of its sides

Since the triangle is an isosceles triangle, then AC = BC

Since AC = 3cm + 9cm = 12cm, then;

AC = BC = 12cm

For AB;

AB = 3cm + 3cm

AB = 6cm

Perimeter of the polygon = AC+BC + AB

Perimeter of the polygon = 12cm + 12cm + 6cm

Perimeter of the polygon =30cm

hello please help i’ll give brainliest

Answers

Answer:

-8/6 is equivalent to the -8.(1/6).

Step-by-step explanation:

third an forth options are correct

[tex] - \frac{1}{6} \times 8[/tex]

[tex] - \frac{8}{6} [/tex]

solve the equation b - 7 - 6 = 15 + 5b

Answers

Answer:

b = -7

Step-by-step explanation:

b - 7 - 6 = 15 + 5b

b - 13 = 15 + 5b

4b = -28

b = -7

what is the negative solution to this equation? 4x^2+12x=135​

Answers

Answer:

[tex]-\frac{15}{2}[/tex]

Step-by-step explanation:

[tex]\mathrm{Subtract\:}135\mathrm{\:from\:both\:sides}[/tex]

[tex]4x^2+12x-135=135-135[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]4x^2+12x-135=0[/tex]

[tex]x1, 2=−b±√b2−4ac2a For a=4, b=12, c=−135x1, 2=−12±√122−4· 4(−135)2· 4[/tex]

Find the product of (x+6)(x−4).

Answers

Step-by-step explanation:

(x+6)(x−4)

x²- 4x+6x - 24

x² + 2x - 24

Answer:

x²+2x-24

Step-by-step explanation:

see attachment below

Please help.
Is algebra.

Answers

The answer for question 4 is C and the answer for question 5 is D.

HELP PLEASE ILL GIVE BRAINLIEST

Answers

Answer:

y=3x+3

Step-by-step explanation:

First find put the intersect point at the end then find slope.

easy

PLS HELP WITH THIS I NEED A GOOD GRADE

Answers

Step-by-step explanation:

4.5 approximately is the answer.

1. the area of a circle is 132.7 square inches. find the radius. round to the nearest tenth

2. in terms of pi, find the area of a 120 degree sector in a circle with a 6m radius

Answers

Answer:

no ):(

Step-by-step explanation:

Answer:

1. r ≈ 6.5in

2. 132

Step-by-step explanation:

1. A=πr2

Solving for r

r=A

π=132.7

π≈6.49921 in

2. = 120°/ 360° x 22/7 x 6²

= 1/3 x 22/7 x 6 x 6

= 22 x 6 x 6 / 7 x 3

= 22 x 6

= 462

What is a linear function in the form y=mx+b for the line passing through (2, -4) with y-intercept 2?

Answers

Answer:

A linear function in the form y = m·x + b for the line passing through the point (2, -4) with y-intercept 2 is;

y = -3·x + 2

Step-by-step explanation:

From the question, it is required to find the a linear equation passing through the point (2, - 4) with a y-intercept 2 in the form y = m·x + c

Given that the y-intercept is the point at which the line cuts the y-axis, we have, x = 0

Therefore, we have the point on the line representing the y-intercept is (0, 2)

Therefore, the slope of the graph is given as follows;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Therefore, we have;

[tex]Slope, \, m =\dfrac{2-(-4)}{0-2} = \dfrac{6}{-2} = -3[/tex]

The equation of the graph in point and slope is given as follows;

y - 2 = -3 × (x - 0) = -3 × x

Therefore, the equation of the line in the form y = m·x + c is given as follows;

y - 2 + 2 = -3 × x + 2

∴ y = -3·x + 2

The equation of the line in the form y = m·x + c is y = -3·x + 2.

pls help me with this math​

Answers

Answer: C

Step-by-step explanation:

Based on the diagram, what is sin A
Enter your answer in the boxes.
sin A =

Answers

Answer:

sin A = a/c

Step-by-step explanation:

2.Use the digits given below to make the largest possible number
without repetition off digits. .Then round off nearest ten, hundred and
thousand
a) 2, 5,4 , 3, 6, 7

b) 0 ,9, 8, 7 ,6, 4

Answers

Answer:

1)765432

Nearest ten: 765430

Nearest hundred: 765400

Nearest thousand: 765000

2) 987640

Nearest ten: 987640

Nearest hundred: 987600

Nearest thousand: 988000

Not sure if this is what you want.

Nancy, Bryan and Jamie combined their money to purchase a laptop. Together, they paid a total of 490 dollars for the laptop, including tax.
Nancy paid 50 dollars more than Bryan paid.
Bryan paid twice as much as Jamie paid. How much did Nancy paid

Answers

Answer:

226 dollars

Step-by-step explanation:

Bryan = 176

Jamie = 88

Nancy = 226

Since Nancy paid 50 dollars more than Bryan paid that is 226.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Nancy, Bryan and Jamie combined their money to purchase a laptop. Together, they paid a total of 490 dollars for the laptop, including tax.

The total = 490 dollars

Given that Nancy paid 50 dollars more than Bryan paid and Bryan paid twice as much as Jamie paid.

Bryan = 2 x Jamie

Nancy = 50 + Bryan

Let Jamie = J

J + 2J + 50 + 2J = 490

5J + 50 = 490

5J = 440

J = 88

Therefore, Bryan = 176

Jamie = 88

Nancy = 226

Hence, Since Nancy paid 50 dollars more than Bryan paid that is 226.

Learn more about the unitary method;

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Answer this question to get marked as brainliest!!!!

Answers

Answer:

Diameter is the second option

Radius is the first option

Circumference is the third option

Area is the sixth option.

Step-by-step explanation:

Diameter is the distance between two circles from one end to another.

Radius is from the center to any part of the circle

To find cirumfrnce it’s diameter*π

To find area is πr^2 or in this case π*radius*radius

Jenny bought scrapbooking supplies for $70.75. She paid $5.66 in sales tax. What was the sales tax rate on the supplies? If necessary, round your answer to the nearest tenth.

Answers

Answer:

8%

Step-by-step explanation:


2) Zaria rolls a dice and flips a coin. What is the
probability that she will get a number greater
than 3 and heads?

Answers

Step-by-step explanation:

probability of dice

3/6 or 1/2

probability of coin

1/2

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