Answer:
1) 135 y 137, 2) 13 y 15, 3) El lado del cuadrado es de 14 unidades, 4) Se necesita 350 metros de valla, 5) El niño tiene 6 años de edad.
Step-by-step explanation:
1) El conjunto de los números naturales comprende al subconjunto de los números reales que son enteros y positivos. El enunciado se puede traducir con la siguiente expresión numérica:
[tex]x + (x+n) = 272[/tex]
Donde [tex]x[/tex] y [tex]n[/tex] son números naturales. Se despeja [tex]x[/tex]:
i) [tex]2\cdot x + n = 272[/tex] Propiedad asociativa/Definición de adición
ii) [tex]2\cdot x = 272-n[/tex] Compatibilidad con la adición/Existencia del inverso aditivo/Propiedad modulativa/Definición de sustracción
iii) [tex]x = \frac{272-n}{2}[/tex] Compatibilidad con la multiplicación/Existencia del inverso multiplicativo/Propiedad modulativa/Definición de división
iv) [tex]x = \frac{272}{2}-\frac{n}{2}[/tex] [tex]\frac{x+y}{z} = \frac{x}{z} + \frac{y}{z}[/tex]
v) [tex]x = 136 - \frac{n}{2}[/tex] Definición de división/Resultado
Puesto que [tex]x[/tex] y [tex]n[/tex] son números naturales, [tex]\frac{n}{2}[/tex] también debe ser entero y para garantizar la consecución entre los números, [tex]n[/tex] debe ser el elemento natural más pequeño posible. El número natural más pequeño es 1, por tanto, el valor mínimo de [tex]n[/tex] es 2. En consecuencia, el valor de [tex]x[/tex] es:
[tex]x = 136-\frac{2}{2}[/tex]
[tex]x = 136-1[/tex]
[tex]x = 135[/tex]
Los dos números naturales consecutivos son 135 y 137.
2) El enunciado se puede traducir en las siguientes dos ecuaciones matemáticas:
[tex]x+y = 28[/tex]
[tex]x^{2}-y^{2} = 56[/tex]
Se despeja una de las variables de la primera ecuación y se elimina la variable correspondiente en la segunda ecuación:
[tex]x = 28-y[/tex]
[tex](28-y)^{2}-y^{2} = 56[/tex]
Se expande la ecuación resultante por álgebra de reales:
[tex]784-56\cdot y +y^{2}-y^{2} = 56[/tex]
[tex]784-56\cdot y = 56[/tex]
[tex]56\cdot y = 784-56[/tex]
[tex]56\cdot y = 728[/tex]
[tex]y = 13[/tex]
Finalmente, se halla el valor de la variable restante:
[tex]x = 28-13[/tex]
[tex]x = 15[/tex]
Los dos números naturales son 13 y 15.
3) Las fórmulas para el área ([tex]A[/tex]) y el perímetro del cuadrado ([tex]p[/tex]) son, respectivamente:
[tex]A = l^{2}[/tex]
[tex]p = 4\cdot l[/tex]
Donde [tex]l[/tex] es la longitud del lado del cuadrado.
De acuerdo con el enunciado, existe la siguiente condición:
[tex]A + p = 252[/tex]
[tex]l^{2}+4\cdot l = 252[/tex]
[tex]l^{2}+4\cdot l -252 = 0[/tex]
La ecuación resultante es un polinomio de segundo orden, cuyas raíces se obtienen por la Fórmula Cuadrática:
[tex]l_{1} = 14[/tex] y [tex]l_{2} = -18[/tex]
La primera raíz es la única solución razonable para la condición dada.
El lado del cuadrado es de 14 unidades.
4) Dado que la finca tiene una área rectangular y que se conoce la medida de la diagonal así como la diferencia entre el largo y el ancho, se puede determinar las variables restantes a partir del Teorema de Pitágoras:
[tex]d^{2} = l^{2}+w^{2}[/tex]
Donde:
[tex]d[/tex] - Diagonal, medida en metros.
[tex]l[/tex] - Largo, medido en metros.
[tex]w[/tex] - Ancho, medido en metros.
Además, las relaciones son las siguientes:
[tex]l = w + 25\,m[/tex]
[tex]d = 125\,m[/tex]
Se desarrolla y simplifica la identidad pitagórica hasta obtenerse un polinomio de segundo orden:
[tex]125^{2} = (w+25)^{2}+w^{2}[/tex]
[tex]2\cdot w^{2}+50\cdot w -15000 = 0[/tex]
Las raíces del polinomio se hallan con ayuda de la Fórmula Cuadrática:
[tex]w_{1} = 75[/tex] y [tex]w_{2} = -100[/tex]
Solo la primera raíz ofrece una solución razonable, el ancho del rectángulo es de 75 metros. Por último, se halla el largo de la figura:
[tex]l = 75\,m+25\,m[/tex]
[tex]l = 100\,m[/tex]
El largo del rectángulo es de 100 metros.
El perímetro del rectángulo ([tex]p[/tex]), medido en metros, es calculado por la siguiente fórmula:
[tex]p = 2\cdot (w+l)[/tex]
[tex]p = 2\cdot (75\,m+100\,m)[/tex]
[tex]p = 350\,m[/tex]
Se necesita 350 metros de valla.
5) Sea [tex]x[/tex] la edad actual del niño y [tex]l[/tex] el lado del cuadrado. Entonces:
[tex]x + 3 = l^{2}[/tex]
[tex]x -3 = l[/tex]
Se reemplaza el lado del cuadrado en la primera ecuación con ayuda de la segunda ecuación:
[tex]x+3 = (x-3)^{2}[/tex]
[tex]x +3 = x^{2}-6\cdot x + 9[/tex]
[tex]x^{2}-7\cdot x+6 = 0[/tex]
Las raíces se obtienen por factorización:
[tex](x-6)\cdot (x-1) = 0[/tex]
[tex]x = 6 \,\wedge \,x = 1[/tex]
Ambas raíces son parecen razonables, se comprueba cada una para ver si satisfacen las condiciones del enunciado:
x = 1
[tex]1+3 = l^{2}[/tex]
[tex]4 = l^{2}[/tex]
[tex]1-3 = l[/tex]
[tex]-2 = l[/tex]
Si bien está matemáticamente bien, no lo es en lo que respecta a edad.
x = 6
[tex]6+3 = l^{2}[/tex]
[tex]9 = l^{2}[/tex]
[tex]6-3 = l[/tex]
[tex]3 = l[/tex]
Esta solución es correcto en cuanto a matemática y edad.
El niño tiene 6 años de edad.
Over one weekend the fast florist makes 368 deliveries of one dozen roses. Did the fast florist deliver more then or less than 4,000 roses? Explain. That's my question ^ please help
Answer:
The florist delivered more than 4000 roses
Step-by-step explanation:
One dozen is 12 roses, so the fast florist delivered a total of 368 x 12 = 4416 roses. That is more than 4000 roses, so the answer is More than 4000 roses
What is the solution to the equation One-third (x minus 2) = one-fifth (x + 4) + 2? x = 12 x = 14 x = 16 x = 26
Answer:
x = 26
Step-by-step explanation:
Given
[tex]\frac{1}{3}[/tex] (x - 2) = [tex]\frac{1}{5}[/tex] (x + 4) + 2
Multiply through by 15 to clear the fractions
5(x - 2) =3(x + 4) + 30 ← distribute and simplify both sides
5x - 10 = 3x + 12 + 30, that is
5x - 10 = 3x + 42 ( subtract 3x from both sides )
2x - 10 = 42 ( add 10 to both sides )
2x = 52 ( divide both sides by 2 )
x = 26
Cynthia besch  wants to buy a rug for a room that is 21 feet wide and 29 feet long. she wants to leave a uniform strip floor around the rug. she can afford to buy 345 square fee of carpeting. what dimensions should the rug have
Step-by-step explanation:
Let x be the width of the uniform strip floor around the rug.
Then the width of the rug is (21 - 2x) and the length of the rug is (29 - 2x).
(21 - 2x)(29 - 2x) = 345
609 - 100x + 4x^2 = 345
4x^2 - 100x + 264 = 0
x^2 - 25x + 66 = 0
(x - 22)(x - 3) = 0
x = 3 or x = 22 (rejected as x must be less that the width of the room)
Hence the width of the rug is 21 - 2(3) = 15 feet and the length of the rug is 29 - 2(3) = 23 feet.
Write the coordinates of the vertices after a translation 5 units right and 2 units up.
101
Y
- 10
0
10
F
E
10
с
D
C(-4, 10)
)
D(2, -10)
D'C
E(2,-2)
→ El
F(-4,-2) - FC
Answer:
c=(1,-8)
d=(7,-8)
e=(7,0)
f=(1,0)
Step-by-step explanation:
It super simple, just just move each point to the right 5 lines/units, and up 2 lines/units.
The coordinates of the vertices after a translation 5 units right and 2 units up. C =(1,-8), D =(7,-8), E =(7,0) and F =(1,0)
How to draw a shifted figure if the shifts are provided?Suppose the graph is drawn on the coordinate plane.
Let the shifting be (x,y) → (x+a, y+b)
Then, add 'a' to all x coordinates of the graph's points. Add 'b' to all y coordinates of the graph's points.
The resultant set of new points will be plotted.
Thus it is called origin shift since we think of it as the origin was picked and placed at the point (a,b)(in this case) along with those two axes (x and y axes) and now everything will be measured from this new axes' frame.
Therefore, the coordinates of the vertices after a translation 5 units right and 2 units up.
C =(1,-8)
D =(7,-8)
E =(7,0)
F =(1,0)
Learn more about area of a triangle from its vertices' coordinates here:
https://brainly.com/question/2532574
#SPJ2
16. A newspaper surveyed its subscribers as to which section of the paper they read first. The results are below. Is it reasonable to conclude that 39.1% of the paper's subscribers read the business or sports sections first?
Section
%
Front Page 25.0
Sports
25.2
Business 13.9
Comics 22.1
Horoscope 13.8
Answer:
j
Step-by-step explanation:n
3 . 072 > 3 . 2 Choose...
Answer:
The answer is 3.2.
Step-by-step explanation:
Answer:
the statement above is false a
Step-by-step explanation:
3.2 is greater than 3.072
Solve the formula for the indicated variable.
D = ABC for A
A=
Divide 2 over 3 ÷ 1 over 6 = ____. Numerical Answers Expected! Answer for Blank 1:
Answer: the answer is 4
Step-by-step explanation:
2/3 / 1/6
change the places of 1/6 to 6/1
2/3 / 6/1
the division sign changes to multiplication
2/3 * 6/1
cancel out the 3 and 6 to give
2/1 * 2/1
=4
what is the answer please helppp
Answer:
v is less than negative 8
Step-by-step explanation:
-8 and -6 is -14 so it has to be less than -8 to be greater than -14
What is the Absolute value of |-9-8|?
Answer:
17
Step-by-step explanation:
|-9-8|
Solve what is inside the absolute value
|-17|
Then take the non negative result
17
Answer:
17
Step-by-step explanation:
The answer is 17 there u go
3t+5+t=5+4t
Please help find each solution set
Answer:
This equation has infinite solutions
Step-by-step explanation:
3t + 5 + t = 5 + 4t
4t + 5 = 4t + 5
4t = 4t
t = t
Infinite solutions
Answer:
3t+5+t=5+4t.
3t+t-4t=5-5.
0=0.
The answer is 0
Question 10 of 10
Classify the following triangle. Check all that apply.
A. Right
B. Acute
C. Equilateral
D. Isosceles
E. Obtuse
F. Scalene
I hope this helps you
The triangle is an isosceles and an obtuse triangle
What Is an Isosceles Triangle?A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
The three types of Isosceles Triangles are :
Isosceles acute triangle
Isosceles right triangle
Isosceles obtuse triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of ∠ABC = 120°
So , it is an obtuse triangle with angle > 90°
Now , the measure of sides AB = measure of BC
So , an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base
Therefore , it is an Isosceles obtuse triangle
Hence , the triangle is isosceles
To learn more about isosceles triangles click :
https://brainly.com/question/1900674
#SPJ7
IS THIS CORRECT, THANKS!
Answer:
Step-by-step explanation:
y + 3 < -1
y < -4
why is math really hard
Answer:
Actually it is not hard. It is just the mentallity or attitude that u have towards it. Stop saying and believing that it is hard........just start doing more practice per topic everyday, 2 to 3 sums a day in a topic that u have not understood will do the trick. And above all, believe in yourself and start seeing yourself as a little math genius and never give up trying.
Step-by-step explanation:
Answer:
Math is hard because it wants us to fail.
Step-by-step explanation:
Also someone says that math stands for Mental Abuse To Humans. So...
Q:Evaluate -15 + (-4)
Answer Choices:
1) -11
2) 19
3) -19
4) 11
Answer: -19
Step-by-step explanation:
-15-4=-19 olur. İyi dersler!
An athlete goes to the gym to train for 90 minutes each day for as many days as possible. Write an equation that relates the number of days, d, that the athlete spends training if the athlete trains for 540 minutes.
Answer:
23
Step-by-step explanation:
Find the mode and range of the information.
Answer:
please like it wild be a lot to me
Step-by-step explanation:
ddyruxcdgjkgd cycrlcrylruclvtistnugfsjvdsnhcd
A rectangular yard is enclosed by 100 meters of fencing. The table shows some possible values for the length and width of the yard.
>The area is in square meters<
Length (meters): Width (meters): Area:
10 40 400
20 30 _
25 25 625
35 15 525
40 _ _
1. Complete the table with the missing values
Answer:
what did you put for question 2 and 3?
Step-by-step explanation:
2.If the values for length and area are plotted, what would the graph look like?
3.How is the relationship between the length and the area of the rectangle different from other kinds of relationships we’ve seen before?
An investor earned 5 times the profits of what she earned last year. If she made \(\$613801.5599999999\) total for both years, how much did she earn in profits each year?
Answer:
Profit earn 1st year = $102,300.26
Profit earn 2nd year = $511,501.3
Step-by-step explanation:
Given:
Total profit earn = $613801.5599999999 = $613801.56
Find:
Profit earn each year
Computation:
Assume,
Profit earn 1st year = x
Profit earn 2nd year = 5x
Total profit earn = Profit earn 1st year + Profit earn 2nd year
x + 5x = 613,801.56
6x = 613,801.56
x = 102,300.26
Profit earn 1st year = $102,300.26
Profit earn 2nd year = 5x = 5(102,300.26)
Profit earn 2nd year = $511,501.3
-1 3/8 divided by (-1 4/7) simplified in a fraction form
Someone please help me with this
Answer:
C
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = [tex]x^{4}[/tex] + 7 ( subtract 7 from both sides )
y - 7 = [tex]x^{4}[/tex] ( take the fourth root of both sides )
[tex]\sqrt[4]{y-7}[/tex] = x
Change y back into terms of x where x is g(x)
g(x) = [tex]\sqrt[4]{x-7}[/tex] , x ≥ 7
1/16 + 3/16 + 11/16 =
Hurry
Secondary School work, find the height of capsule B
⚠️⚠️PLEASE⚠️⚠️
Brainliest will be marked ;) )
Answer:
[tex](\frac{1}{k} )^{10}[/tex]
Step-by-step explanation:
When making a negative a positive, all you need to do is flip it, in this case, making it a fraction.
~theLocoCoco
Point B is on line segment \overline{AC}
AC
. Given AB=4x-6,AB=4x−6, AC=2x+10,AC=2x+10, and BC=4,BC=4, determine the numerical length of \overline{AC}.
AC
Answer:
AC= 22
Step-by-step explanation:
see photo
The numerical length of AC is 22 units.
What is a line segment?In geometry, a line segment is a part of a line that is bounded by two distinct end points,and contains every point on the line that is between its endpoints.
Now it is given that,
Point B is on line segment AC
AB = 4x-6
AC = 2x+10
BC = 4
now since Point B is on line segment AC, therefore
AC = AB + AC
⇒ 2x + 10 = 4x - 6 + 4
⇒ 2x + 10 = 4x - 2
⇒ 2x = 12
⇒ x = 6
Put the value of x in AC, we get
AC = 2(6) + 10
or, AC = 12 + 10
or, AC = 22 units.
Hence, the numerical length of AC is 22 units.
More about line segment :
https://brainly.com/question/14326939
#SPJ2
Find the length of the line segment joining the points J(-4,2) and G(146,52). Round your answer to the nearest tenth if necessary
A.155.0
B.151.9
C.150.5
D.141.4
E.158.1
Answer:
The answer is option E.Step-by-step explanation:
The length of a line segment or the distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
J(-4,2) and G(146,52)
The the length of the line segment joining the points is
[tex] |JG| = \sqrt{ ({ - 4 - 146})^{2} + ({2 - 52})^{2} } \\ = \sqrt{ ({ -150})^{2} + ({ -50})^{2} } \\ = \sqrt{22500 + 2500} \\ = \sqrt{25000} \\ = 50 \sqrt{10} \\ = 158.11388[/tex]
We have the final answer as
158.1 to the nearest tenthHope this helps you
How would you write -5.6 x 10-3 in standard form?
Answer:
negative five point six times ten minus three
Step-by-step explanation:
write the number out with letters
Answer:
-0.0056
Step-by-step explanation:
Hope this helped
2.4+10m=6.89 what does m equal
Answer:
m = 0.449
Step-by-step explanation:
Isolate the variable, m. Note the equal sign, what you do to one side, you do to the other. Remember to do the opposite of PEMDAS.
PEMDAS is the order of operation & =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, subtract 2.4 from both sides:
2.4 (-2.4) + 10m = 6.89 (-2.4)
10m = 6.89 - 2.4
10m = 4.49
Divide 10 from both sides:
(10m)/10 = (4.49)/10
m = 4.49/10
m = 0.449
0.449 is your answer for m.
~
Answer:
m = 0.449
Step-by-step explanation:
[tex]2.4+10m=6.89\\\\\mathrm{Subtract\:}2.4\mathrm{\:from\:both\:sides}\\2.4+10m-2.4=6.89-2.4\\\\Simplify\\10m=4.49\\\\\mathrm{Divide\:both\:sides\:by\:}10\\\frac{10m}{10}=\frac{4.49}{10}\\\\Simplify\\m=\frac{4.49}{10}\\\\\left(\mathrm{Decimal}:\quad m=0.449\right)[/tex]
When Matthew eats pizza, he always eats a whole slice at a time with no bites left over. Which graph best represents this situation?
Answer:
B
Step-by-step explanation:
i just took the assignment
Answer:
its b
Step-by-step explanation:
i did the assignment
A survey showed that 4 out of 5 students own a bicycle. Based on this result, how many of the 800 students in a school own a bicycle? Use any strategy to solve.
Answer:
640 students
Step-by-step explanation:
We are told in the question that 4 out of every 5 students owns a bicycle
This also means , out of every 5 students only 1 does not have bicycle
Then we have a ratio of 4 : 1
This means a fraction of 4/5 students own a bicycle in a school
Based on this result, how many of the 800 students in a school own a bicycle?
This calculated as:
4/5 × 800
= 640 students
Therefore, 640 students out of 800 students own a bicycle