Answer:
x=2
Step-by-step explanation:
-3x+12=-18
-3x=-18+12
-3x=-6
x=-6/-3
x=2
Answer:
x=10
Step-by-step explanation:
We are given the equation:
[tex]-3x+12= -18[/tex]
and asked to solve for x. Therefore, we must isolate x on one side of the equation.
12 is being added to -3x. The inverse of addition is subtraction. Subtract 12 from both sides of the equation.
[tex]-3x+12-12= -18 -12[/tex]
[tex]-3x= -18-12[/tex]
[tex]-3x=-30[/tex]
x is being multiplied by -3. The inverse of multiplication is division. Divide both sides of the equation by -3.
[tex]-3x/3=-30/-3[/tex]
[tex]x= -30/-3[/tex]
[tex]x=10[/tex]
Let's check our solution. Plug 10 in for x and solve.
[tex]-3x+12=-18[/tex]
[tex]-3(10)+12=-18[/tex]
Multiply -3 and 10.
[tex]-30+12=-18[/tex]
Add 12 to -30.
[tex]-18=-18[/tex]
This checks out, so we know our solution is correct.
The solution -3x+12=-18 is x=10.
1) El producto de dos números naturales consecutivos es 272. ¿Cuáles son esos números?
2) Hallar dos números naturales tales que su suma es 28 y la diferencia de sus cuadrados es 56.
3) Halla el lado de un cuadrado tal que la suma de su área más su perímetro es numéricamente igual a 252.
4) Se quiere vallar una finca rectangular que tiene de largo 25 m más que de ancho y cuya diagonal mide 125 m. ¿Cuántos metros de valla se necesitan?
5) La edad de un niño será dentro de tres años un cuadrado perfecto, y hace tres años que su edad era precisamente la raíz cuadrada de este cuadrado. ¿Qué edad tiene?
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.
what’s 2+2+2+1000 drop ur ig for some points :)
Answer:
1,006
Step-by-step explanation:
Answer:
1006
Step-by-step explanation:
_plexstyx
2. The rule for a translation will show values added to x and/or y
True
False
Answer:
it should be true well it has to be
PLEASE HURRY!!!!! GIVEN 135 MPH, convert to INCHES PER SECOND.
Answer:
2376
Step-by-step explanation:
given 135MPH
convert it inches per second
as 1MPH=7.6 inches per second
so
135×7.6
2376 inches per second
Answer:
LOL, its Shuhuai from Accelerated Science. I just finished the question and copy and pasted it to check it. I'm like, nobody is going to answer this because my teacher just made it up. And I see the top result is your comment, but hey at least I got the question correct. But yeah, i just thought it was a bit coincidental lol.
Step-by-step explanation:
You're making lunches for school and you want to pack chips. You
can purchase Funyuns in a 7 oz bag for $2.49. What is the price per
ounce?
Answer : The price per ounce of funyuns is $0.356.
Step-by-step explanation :
As we are given that the price of 7 ounce bag of funyuns is $2.49.
Now we have to determine the price per ounce.
According to the question,
As, 7 ounce bag of funyuns = $2.49
So, 1 ounce bag of funyuns = [tex]\frac{1\text{ ounce}}{7\text{ ounce}}\times \$ 2.49[/tex]
= $0.356
Therefore, the price per ounce of funyuns is $0.356.
Find the value of x in each case: b)
I will give 20 Brainly points if answered within 30 minutes!!!!!!
Answer:
15 DEGREES
Step-by-step explanation:
OK SO BASICALLY, USING THE EXTERIOR ANGLES THEOREM, YOU FIND THAT 9x = 5x + something. That something is 4x so:
9x = 5x + 4x
THEN YOU FIND THAT 8x = 5x + something. That something is 3x so:
8x = 5x + 3x
4x and 3x and 5x are the interior angles of the triangle (ABC)
Then you use triangle theorem and get 4x + 3x + 5x = 180
Then: 12x = 180 and so you get x = 15
kaziyah josey
The x-axis is the line of reflection for a reflection over the x-axis.
O True
O False
7 + 22 x 4 - 31 = 85
This is for order of operations I don’t know how to do any of this
Answer:
64
Step-by-step explanation:
7 + 22 × 4 - 31 = 64
How the answer is 64:
Use BODMAS (Bracket, Of, Division, Multiplication, Addition, Subtraction) for order of operation.
22 × 4 is first which is equal to 88
7 + 88 is next which is 95
95 - 31 is last which is 64.
The answer is 64, not 85.
1.32 rewrite as a simplified fraction
Answer:
33/25 should be the answer
Step-by-step explanation:
Given segment XZ and point Y that lies on XZ, find XY if XZ = 37 and YZ = 18
Answer:
XZ=19
Step-by-step explanation:
the total length of the segment is 37, and half of the segment is 18, so to find the other half of the segment, you would subtract the half from the total amount: 37-18=19
hope this helps
6x+4 = -6+ 4x +18 solve for x
Answer:
4
Step-by-step explanation:
6x+4=12+4x6x-4x=12-42x=8x=4Answer:
7/4 or 1.75 or 1 3/4
Step-by-step explanation:
try to use a scientific calculator and then that will be your answer that I came up with.
raise 7 to the 3rd power, then find the product of the result and m
Answer:7³=343
343 × M = 343m
Step-by-step explanation:
7×7×7=343
Write an equation in slope-intercept form for the line parallel to y= -7x-9 that passes through the point (4,9). Show your work. Thank you :)
Answer: y=-7x + 37
Step-by-step explanation:
Parallel lines will have the same slope but different y-intercepts so again we can use the coordinates to determine the y intercept of the new equation.
So we know that the slope intercept formula is y=mx + b where m is the slope and b is the y-intercept so we will input the x and y coordinates to solve for b.
9 = -7(4) + b
9 = -28 + b
+28 +28
b = 37
The equation will be y= -7x + 37
The equation of line passes through the point (4, 9) will be;
⇒ y = - 7x + 37
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (4, 9).
And, The parallel line is,
⇒ y = - 7x - 9
Now,
Since, The equation of line passes through the point (4, 9).
So, We need to find the slope of the line.
Since, The slope of the parallel line is same.
Hence, Slope of the line is,
y = - 7x - 9
m = dy/dx = - 7
m = - 7
Thus, The equation of line with slope - 7 is,
⇒ y - 9 = -7 (x - 4)
⇒ y - 9 = - 7x + 28
⇒ y = - 7x + 28 + 9
⇒ y = - 7x + 37
Therefore, The equation of line passes through the point (4, 9) is,
⇒ y = - 7x + 37
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ2
Solve for x. 20x + 5 = 5x + 65
Answer:
x=4
Step-by-step explanation:
move the variable to the left side and change its sign
20x-5x=65-5
collect like terms
15x=65-5
15x=60 divide both side by 15
x=4
On average, it takes a shoe factory 21 minutes, with a standard deviation of 3 minutes, to manufacture a pair of running shoes. How often will it take the factory more than 27 minutes to manufacture a pair of running shoes?
Answer:
The number of times it would take more than 27 minutes to manufacture a pair of running shoes is 2.275 times or approximately 2 times per every 100 shoes
Step-by-step explanation:
The average time it takes to manufacture a pair of shoes = 21 minutes;
The standard deviation = 3 minutes
To find how often it takes more than 27 minutes to manufacture a pair of running shoes, we have;
Standard score, given as follows;
[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]
Where;
x = The raw score = 27 minutes
μ = The average score = 21 minutes
σ = The standard deviation = 3 minutes
From which we have;
[tex]Z=\dfrac{27-21 }{3 } = 2[/tex]
Therefore, it is borderline unusual with a p value of P(z>2) = 1 - 0.97725 = 0.02275
Therefore, the number of times out of 100 that it would take more than 27 minutes to manufacture a pair of running shoes = 100 × 0.02275 = 2.275 times which is approximately 2 times in every 100 shoes.
The quotient of 35 and a number is 7.
Answer:
number=5
Step-by-step explanation:
35/7=5
quotient is the answer to a division problem
Steps to solve:
35/n = 7
~Multiply 1/35 to both sides
35/n * 1/35 = 7 * 1/35
~Simplify
n = 5
Best of Luck!
Which of the following represents the area of a rectangle whose length is x - 7 and whose width is x + 12?
Length of rectangle = x - 7
Width of rectangle = x + 12
We have to find area of rectangle[tex].[/tex]
_________________________________
[tex]:\implies\sf\:Area=Length\times Width[/tex]
[tex]:\implies\sf\:Area=(x-7)(x+12)[/tex]
[tex]:\implies\sf\:Area=x^2+12x-7x-84[/tex]
[tex]:\implies\bf\:Area=x^2+5x-84[/tex]
A trangle has a 30 angle and a 55angle .what is the other angle ？how do you know？
Answer:
95°
Step-by-step explanation:
Sum of 3 angles of a triangle equals to 180°Here we have angles of 30° and 55°, so the remaining angle is:
180° -(30° + 55°) = 95°can some one help me !? please.
Answer:
y=3/4x+45
Step-by-step explanation:
Answer:
the equation is 1/3x + 2
It takes 45 minutes to drive to the nearest bowling alley taking city streets going 30 miles per hour
(mph). How long will it take to get there using the freeway going 65mph if the distance is the same?
(Round to the nearest minute).
HELLLLPPPPPPP
Answer:
The time it will take to get to the bowling alley while driving at 65 mph on the freeway is approximately 20.8 minutes
Step-by-step explanation:
The given parameters are;
The time it takes through the streets to drive to the nearest bowling alley = 45 minutes
The speed of driving through the streets = 30 miles per hour (mph)
The speed of driving through the freeway to the bowling alley = 65 mph
From the speed of driving through the streets and the time taken we have;
The formula for speed, S, is S = Distance/Time
Therefore, 30 mph = Distance/45 minutes
Where, 1 hour = 60 minutes, 45 minutes = 1/60×45 hour = 3/4 hour
30 mph = Distance/45 minutes = Distance/(3/4 hour)
30 mph = Distance/(3/4 hour)
Distance = 30 mph × 3/4 hour = 22.5 miles
Given that the distance through the freeway and through the streets are the same, we have from speed = Distance/Time;
Time = Distance/Speed
The speed through the freeway = 65 mph while the distance remain 22.5 miles
Therefore;
Time = 22.5 miles/(65 mph) ≈ 0.346 hour ≈ 20.8 minutes
The time it will take to get to the bowling alley while driving at 65 mph on the freeway is approximately 20.8 minutes.
Based on the pattern, what are the next two terms of the sequence? 9, 15, 21, 27, . . .
Answer: The next two terms are 33 and 39
Step-by-step explanation:
9,15,21,27
First determine how you get from one value to the other.
To get from 9 to 15 you add 6.
To get from 15 to 21 you add 6 to 15.
And to get from 21 to 27 you add 6 to 21
So to get to the next term add 6 and another 6 to the value you get.
27 + 6 = 33
33 + 6 = 39
Which is the best type of graph to model the speed of a roller coaster over the full two minutes it takes to complete the ride?
Step-by-step explanation:
I would say a speed/time line graph because those types of graphs are usually used for these scenarios in Physics problems.
Hope this helped!
Helllp find each measure.
Answer:
6)44
7)64
8)121
9)23
Step-by-step explanation:
6)5z-16=3z+8
z=12
7)4w+4=2w+22
w=9
8)9x-5=10x-19
x=14
9)3y-1=y+15
y=8
-8 ÷ (—4) =?
you have to divide it, if you can figure it out thanks!
Answer:
I believe it's positive 2
How do you simplify the answer for 185/200
Answer: 37/40
Step-by-step explanation:
divide 185 by 5 and same with 200 so your answer is 37/40
please mark me brainliest :)
Q11. The ratio of angles of a quadrilateral are
in 3: 5:9:13. Find the angles.
Step-by-step explanation:
Let us take ratio constant as 'x'
Therefore ratio of angles
3x:5x:9x:13x
Sum of interior angles of quadrilateral is 360 degree.
3x+5x+9x+13x=sum of interior angles of quadrilateral
=>3x+5x+9x+13x=360
=>30x=360
=>x=12
PLEASE HELP I HAVE 21 POINTS PLEASE Part A: The sun produces 3.9 ⋅ 10^33 ergs of radiant energy per second. How many ergs of radiant energy does the sun produce in 3.25 ⋅ 10^3 seconds? (5 points) Part B: Which is the more reasonable measurement of the distance between the tracks on a railroad: 1.435 ⋅ 10^−3 mm or 1.435 ⋅ 10^3 mm? Justify your answer. (5 points)
Answer:
Step-by-step explanation:
Part A;
[tex]\frac{3.9\times10^3^3}{1} = \frac{x}{1.44\times 10^7} \\Cross\Multiply\\x = 3.9\times 10^3^3 \times 1.44 times 10^7\\\\x = 6.045\times 10^4^0[/tex]
Part B ;
[tex]1.435 \times 10^3 \:mm = 1.4\m\\1.435 \times 10^-^3\: mm = 0.001435\m[/tex]
The more reasonable one is 1.4m .0.001435 is too small(its not even up to 1)
Answer:
1.2675 × 10^37.
Step-by-step explanation:
you would have to multiply 3.9 x 3.25= 12. 675 and it is not in scientific notation so you would do 1.2675 x 10^37
Hope it helps!
What are the roots of the equation 25x^2 - 50x + 26 = 0 in simplest a + bi form? Complex Roots
Answer:
Hope this is helpful for you
What is the equivdent
equation to: –6=3y
Answer:
-2 is the answer
Step-by-step explanation:
mark as me brainlist
13 - (this number) - (this number) = -6 The numbers have to be the same when subtracting
Answer:
9.5
Step-by-step explanation:
13-x-x=-6
13+6=2x
19=2x
9.5=x
Answer:9
Step-by-step explanation:
13 - 9 - 9