find the perimeter please it said it has to be 20 characters long don’t mind this
Answer:
[tex]16x^2 + 18y[/tex] units
Step-by-step explanation:
The perimeter of a rectangle is [tex]2l+2w[/tex], where l and w are the length and width respectively. Since we know the value of the length and width, we can substitute inside the equation.
[tex]2(x+5y) + 2(8x^2 - x + 4y)\\\\2x + 10y + 16x^2 - 2x + 8y[/tex]
We can now combine like terms to get [tex]16x^2 + 18y[/tex].
Hope this helped!
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.
Jacob is training for a marathon. His plan is to run the same distance for 3 days a week, then increase that distance
by the same amount each week of training. During week 6, Jacob runs 14 miles per day, which is 1.5 miles more per
day than he ran during week 5. Which equation represents the daily running distance, in miles, as a function of time,
t, in weeks?
Answer: The answer should be
C) f(t)=1.5t+5
Two brothers Steven and Walter each inherit 41000. Steven invests his inheritance in a savings account with an annual return of 2.7% while Walter invests his inheritance in a cd paying 6.4% annually. How much more money than Steven does Walter have after 1 year
Answer:
Walter earns $1,517 more than Stevens in one year.
Step-by-step explanation:
Giving the following information:
Two brothers Steven and Walter each inherit $41,000
Steven:
Annual return= 2.7%
Walter:
Annual return= 6.4%
To determine the future value for the brothers, we need to use the following formula:
FV= PV*(1+i)^n
Steven:
FV= 41,000*1.027= $42,107
Walter:
FV= 41,000*1.064= $43,624
Difference= 43,624 - 42,107= $1,517
Walter earns $1,517 more than Stevens in one year.
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.
In what order should you stack the machines so that
when 6 is dropped into the first machine, and all four
machines have had their effect, the last machine's
output is 11 ?
f(x)=√x
g(x) -(x - 2)2
h(x) = 2X-7
k(x) = - - 1
Order the functions below so that you use all four
functions.
= k(
k(x) = -2 -1
h(x)=2x - 7
Answer:
[tex]g(x) = -(x - 2)^2[/tex]
[tex]k(x) = -\frac{x}{2} - 1[/tex]
[tex]h(x) = 2^x - 7[/tex]
[tex]f(x) =\sqrt{x}[/tex]
Step-by-step explanation:
Given
Input = 6
Expected Output = 11
Process:
[tex]f(x) =\sqrt{x}[/tex]
[tex]g(x) = -(x - 2)^2[/tex]
[tex]h(x) = 2^x - 7[/tex]
[tex]k(x) = -\frac{x}{2} - 1[/tex]
Required
Arrange the processes to give an output of 11
To answer this question, I'll make use of trial by error methods.
After some attempts, the following is the order of the processes;
Set x = 6
Substitute 6 for x in g(x)
[tex]g(x) = -(x - 2)^2[/tex]
[tex]g(6) = -(6 - 2)^2[/tex]
[tex]g(6) = -(4)^2[/tex]
[tex]g(6) = -16[/tex]
Substitute -16 for x in k(x)
[tex]k(-16) = -\frac{-16}{2} - 1[/tex]
[tex]k(-16) = -(-8) - 1[/tex]
[tex]k(-16) = 8 - 1[/tex]
[tex]k(-16) = 7[/tex]
Substitute 7 for x in h(x)
[tex]h(x) = 2^x - 7[/tex]
[tex]h(7) = 2^7 - 7[/tex]
[tex]h(7) = 128 - 7[/tex]
[tex]h(7) = 121[/tex]
Substitute 121 for x in f(x)
[tex]f(x) =\sqrt{x}[/tex]
[tex]f(121) = \sqrt{121}[/tex]
[tex]f(121) = 11[/tex]
Hence, the processes is:
[tex]g(x) = -(x - 2)^2[/tex]
[tex]k(x) = -\frac{x}{2} - 1[/tex]
[tex]h(x) = 2^x - 7[/tex]
[tex]f(x) =\sqrt{x}[/tex]
What are the coordinates
of the midpoint, P, of QT
with endpoints Q(-2,-8)
and T(1,5)?
Thank you!
Answer:
(-1/2 , -3/2)
Step-by-step explanation:
midpoint formula:
(x₁ + x₂) / 2 , (y₁ + y₂) / 2
(-2 + 1) / 2 , (-8 + 5) / 2
P: (-1/2 , -3/2)
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.
Solve -1/2w - 3/5 = 1/5w
Answer:
w = -6/7
Step-by-step explanation:
Step 1:
-5/10w - 6/10 = 2/10w
Step 2:
-6/10 = 7/10w
Step 3:
-6/10 × 10/7w
Answer:
w = -6/7
Hope This Helps :)
Which of the following is an equivalent form of the compound inequality −44 > −2x − 8 ≥ −8?
Select one:
a. −2x − 8 > −44 and −2x − 8 ≥ −8
b. −2x > −44 and −8 ≥ −8
c. −2x − 8 < −44 and −2x − 8 ≤ −8
d. −2x − 8 < −44 and −2x − 8 ≥ −8
Answer:
C.
Step-by-step explanation:
Find the missing exponent
Answer:
where is the rest of the context?
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
What has the same value as |-5| ?
Answer:
5
Step-by-step explanation:
This is because |-5| is equal to 5
Answer:
It is 5
Step-by-step explanation:
The absolute value sign means how many spots that number is away from the 0 on the number line so it makes all numbers positive except if there is a negative sign on the outside of the absolute value sign
f(x) = 4x + 5; Find f(8)= Evaluate
Answer:
f(8)=4(8) +5
=32 +5
=37
are 2d and 4d like terms
Answer: Yes they are like terms
They both have the same variable so that is why they are like terms.
We can think of 'd' representing something like "dogs" maybe
d = 1 dog
2d = 2 dogs
3d = 3 dogs
4d = 4 dogs
and so on
Adding 2d with 4d gets us 2d+4d = 6d meaning we have 6 dogs overall if we started with 2 and added on 4 more. This is one way to help see why we can combine like terms.
In contrast, something like 2c+4d cannot be combined since having 2 cats and 4 dogs doesn't result in 6 cats or 6 dogs. We just simply leave it as 2c+4d.
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]
Find the smallest value of n such that the LCM of n and 15 is 45
Answer:
n=9
Step-by-step explanation:
LCM(n,15)=45
LCM(9,15)=45
Which Venn diagram correctly describes the relationship between Set R and Set Q?
Answer:
D. because all irrational numbers are real numbers.
Step-by-step explanation:
Real numbers include virtually all numbers we can come up with, either negative or positive, rational or irrational, decimals, etc. They are not imaginary numbers.
Irrational numbers include all numbers that cannot be written as a quotient of two integers. They are numbers whose decimals are never terminating. Examples include π, √2 etc.
Irrational are a subset of real numbers.
Therefore, the correct venn diagram that shows this relationship between Set R {real numbers} and Set Q {irrational numbers} is the venn diagram in option D (last option), because, all irrational numbers are real numbers.
FIRST TO ANSWER WILL GET BRAINLIEST At a local fitness center, members pay a $6 membership fee and $3 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
Answer:
c represents the number of classes
6 + 5c = 6c
Can you solve for c and answer?
i need the answer now plz
Answer:
Area= 4,200 square feet
Step-by-step explanation:
If I read your question correctly, I'm assuming the dots (".") mean a multiplication sign ("x").
If they are all being multiplied, use PEMDAS to solve this. First, find to value for any exponents you have (in this case, it's [tex]2^3[/tex] and [tex]5^2[/tex]).
[tex]2^3=2*2*2=8\\5^2=5*5=25[/tex]
Now that you have the values for these two exponents, multiply all the numbers together.
8 x 3 x 25 x 7 = 4,200
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 :)
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.
Kelly berjoging di sekeliling taman sebanyak tiga kali dalam seminggu. Taman itu berbentuk segi empat sama dan menpunyai sisi yang berukuran 80m. Cari jumlah jarak Kelly berjoging dalam seminggu
3 x 80(4) = 960
80 multiply with 4 as the length of the sisi of the square is 80m and has four sisi.
3 multiply 80(4) as Kelly jog three times a week
Where is (2,-6) located on the coordinate plane?
Is it y-Axis or A-axis and what quadrant ?
Answer:
(2, -6) 2 is on the x-axis and -6 is on the y-axis.
Step-by-step explanation: X-Axis is horizontal and Y is vertical. X can also be remembered as left to right. Y-axis runs up and down. It would be in the IV (fourth) quadrant.
Answer:
Step-by-step explanation:
its in the forth box
If s(x) = 2 – x2 and t(x) = 3x, which value is equivalent to (s t)(-7)? A. -439 B. -141 C. 153 D. 443 please answer quick this test is timed!
We're trying to find [tex]s(t(-7))[/tex].
[tex]t(-7)=3(-7)[/tex]
[tex]t(-7)=-21[/tex]
[tex]s(-21)=2-(-21)^2[/tex]
[tex]s(-21)=2-441[/tex]
[tex]s(-21)=-439[/tex]
Hope this helps.
頑張って!
At the beginning of the week, Yolanda withdrew $75.00 from her savings account. She then used her debit card to buy groceries for $30.89 and gas for $21. At the end of the week, she deposited $100 into her savings account.
Answer:
226.89
Step-by-step explanation:
Answer:
(-) withdraw/earn
(+) deposit/spend
$75.00 - $30.89 - $21.00 + $100 = $123.11
$75 - $30.89 = $44.11
$44.11 - $21.00 = $23.11
$23.11 + $100 = $123.11
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!
A stack of logs has 17 logs on the bottom layer. Each subsequent layer has 3 fewer logs than the previous layer. If the top layer has two logs, how many total logs are in the pile?
Answer:
152 logs
Step-by-step explanation:
This question is an Arithmetic progression question
A stack of logs has 17 logs on the bottom layer.
First term = a1 = 17
We are told that: each subsequent layer has 3 fewer logs than the previous layer.
Common difference = 3
Hence, Second term = 17 - 3 = 14
Third term = 14 - 3 = 11
If the top layer has two logs,
Last term = 2
Step 1
We find the number of layers of logs present
Number of logs in the bottom layer - number of logs in the first layer + 1
= 17 - 2 +1
= 16 layers
Step 2
We are asked in the question to find , how many total logs are in the pile?
This means, we are to find the sum of terms in the Arithmetic progression.
The formula is given as
Sn = n/2(a + l)
Where a = First term = 17
l = Last term = 2
Sn = n/2(17 + 2)
Sn = 16/2(19)
Sn = 8 × 19
Sn= 152 logs
What does x represent in f-1(x) = 30? What is the value of x?
What is the equivdent
equation to: –6=3y
Answer:
-2 is the answer
Step-by-step explanation:
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