Answer: a^2 + 2ab + b^2
Step-by-step explanation:
(a+b)²=
(a+b)(a+b)=
a*a + a*b + b*a + b*b=a^2 + 2ab + b^2
Write a system of equations and solve. A chemist wants to make a 10% solution of fertilizer. How much water and how much of a 30% solution should the chemist mix to get 30 L of a 10% solution?
Answer:
x=10 L of .30 solution
x+y=30
y=20 L water
Step-by-step explanation:
The perimeter of a rectangle is 37cm find X
find the partimater of (-3,-2), (-5,-5), (1,-5), (3,-2)
The perimeter of the given rectangle is, 19.2112
Given that, the vertices of the rectangle are A(-3,-2), B(-5,-5), C(1,-5), D(3,-2) .
to find the perimeter through the given vertices, we need to calculate the distance from the vertices AB,BC,CD,DA.
we already know that the sum of all sides of the rectangle is known as the perimeter of the rectangle.
Using distance formula between 2 vertices , √[(x2-x1)²+(y2-y1)²]
AB = √[(-5+3)²+(-5+2)²]
= √[(-2)²+(-3)²]
= √[4+9]
= √[13]
= √13
AB = 3.6056
BC = √[(1+5)²+(-5+5)²]
= √[(6)²+(0)²]
= √[36+0]
= √[36]
= √36
BC = 6
CD = √[(3-1)²+(-2+5)²]
= √[(2)²+(3)²]
= √[4+9]
= √[13]
= √13
CD = 3.6056
DA = √[(-3-3)²+(-2+2)²]
= √[(-6)²+(0)²]
= √[36+0]
= √[36]
= √36
DA = 6
Therefore perimeter of the rectangle with given vertices is ,
= AB+BC+CD+DA
= 3.6056+6+3.6056+6
= 19.2112
= 19 (rounded to nearest tenth).
Therefore the perimeter of the rectangle with given vertices is 19.2112
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An architect built a scale model of a sports stadium using a scale in which 2 inches represents 30 feet. The height of the sports stadium is 180 feet. What is the height of the scale model in inches?
Answer:
12 inchesStep-by-step explanation:
Given the conversion factor;
2inches = 30feet
if the height of the building is 180feet, we are to find the height of the scale model in inches.
Let x = 180 feet.
Equating both;
2inches = 30feet
x inches = 180feet
Cross multiply;
30 * x = 2 * 180
30x = 360
x = 360/30
x = 12inches
Hence the height of the scale model in inches is 12inches
Answer: 60 in
Step-by-step explanation:Let x = 180 feet.
Equating both;
2 inches = 30 feet
x inches = 180 feet
Cross multiply;
30 * x = 2 * 180
30 x = 360
x = 360/30
x = 60 inches
Dany has a business selling bracelets for 7.50 each. She only has enough material to make 5 bracelets. If x represents the number of bracelets sold and y represents the total cost, what is the range for this situation.
Answer:
The range is [0,37.5]
Step-by-step explanation:
We start by writing the equation that links x and y
From the question;
y = 7.5x
Now, she has enough material to make 5 only
When we talk of range, we are referring to the values on the y-axis
So the lowest y value is 0
and since the highest number of bracelets is 5;
The total cost of the 5 is 7.5(5) = 37.5
So the range is [0,37.5]
Please help asap! I attached the image.
Step-by-step explanation:
[tex] {5}^{2} = {x}^{2} + {x}^{2} \\ {5}^{2} = {x}^{4} \\ 5 = \sqrt{ {x}^{4} } \\ 5 = {x}^{2} \\ x = \sqrt{5} =2.236068\\ [/tex]
A parallelogram is drawn such that the diagonals are congruent. Which shape below would not fit this description?
The shape that would not fit this description is a trapezoid.
What is a trapezium?It is a quadrilateral that has one pair of parallel sides and a height.
The area is calculated as 1/2 x the sum of the parallel sides x height.
Examples:
Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.
Area = 1/2 x (3 + 4) x 5
Area = 1/2 x 7 x 5
Area = 35/2 = 17.5 cm^2
We have,
A parallelogram is a four-sided shape where opposite sides are parallel and congruent.
If a parallelogram has diagonals that are congruent, it must be a rectangle.
Therefore, the shape that would not fit this description is any shape that is not a rectangle.
Out of the shapes given,
A trapezoid is not a rectangle and does not have diagonals that are congruent.
Therefore,
The shape is a trapezoid.
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Find the first four terms of the sequence given by the following.
a₁ = -3.5"-1 n=1, 2, 3
the first four terms of the sequence is 51,51.8,52.6,53.4
we can find first four terms by using formula given by
[tex]a_{n} =a_{1} +(n-1) *d[/tex]
[tex]a_{n}[/tex] = the nᵗʰ term in the sequence
[tex]a_{1[/tex] = the first term in the sequence
d = the common difference between terms
Arithmetic progression is a progression in which every term after the first is obtained by adding a constant value, called the common difference (d). So, to find the nth term of an arithmetic progression, we know an = a1 + (n – 1)d. a1 is the first term, a1 + d is the second term, the third term is a1 + 2d, and so on
an=51 + (n-1)*0.8, n=1, 2, 3...
a1 = 51 + (1 -1 ) * 0.8
a1 = 51
a2 = 51 + (2 - 1)*0.8
a2 = 51 + 0.8
a2 = 51.8
a3 = 51 + (3 - 1)*0.8
a3 = 51 + 2*0.8
a3 = 51 + 1.6
a3 = 52.6
a4 = 51 + (4 - 1)*0.8
a4 = 51 + 2.4
a4 = 53.4
Hence , the first four terms of the sequence is 51,51.8,52.6,53.4
the complete question is
Find the first four terms of the sequence given by the following.
an=51 + (n-1)*0.8, n=1, 2, 3...
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YOU HAVE A SWELLING INJURY. DO YOU USE….
Heat or ice?
Answer:
Ice would be the correct answer.
Answer:
if u want go to the doctor but use ice but if its to cold use a little heat not too much tho
Step-by-step explanation:
If you have injured your neck and are experiencing swelling, you should ice the area for at least 72 hours. After icing, you can use heat to help any lingering pain. Tight neck muscles and old injuries can benefit from heat only, as long as there isn’t any swelling.
1. Un representante de ventas debe visitar 6 ciudades durante un viaje. a) Si hay 10 ciudades en el área geográfica que va a visitar ¿Cuántos grupos diferentes de seis ciudades podrá seleccionar? b) Suponga que las seis ciudades por visitar han sido designadas, pero no la secuencia en que se han de visitar ¿Cuántas secuencias posibles existen para las seis ciudades designadas?
Answer:
a) Hay 210 grupos diferentes de seis ciudades que el representante de ventas podrá seleccionar.
b) Hay 720 secuencias posibles existen para las seis ciudades designadas.
Step-by-step explanation:
a) Se llama combinaciones de m elementos tomados de n en n a todas las agrupaciones posibles que pueden hacerse con los m elementos de forma que no entran todos los elementos , no importa el orden y no se repiten los elementos. La combinación se calcula como:
[tex]C=\frac{m!}{n!*(m-n)!}[/tex]
En este caso m corresponde a las 10 ciudades en el área geográfica que va a visitar, mientras que n corresponde a las 6 ciudades que debe visitar un representante de venta durante un viaje.
Entonces:
[tex]C=\frac{10!}{6!*(10-6)!}=\frac{10!}{6!*4!}[/tex]
Considerando que el factorial ! indica que se deben multiplicar todos los números enteros y positivos que hay entre el número que aparece en la fórmula y el número 1, entonces la combinación dará como resultado:
C= 210
Hay 210 grupos diferentes de seis ciudades que el representante de ventas podrá seleccionar.
b) Se llama permutación de n elementos a cada una de las diferentes ordenaciones que se pueden hacer con esos elementos.
Si se tiene un grupo de n objetos distintos, el número de maneras diferentes que podemos tomar un número r de objetos (r < n) del grupo, está dado por la fórmula de la permutación:
[tex]P=\frac{n!}{(n-r)!}[/tex]
Si m=n para calcular el total de permutaciones se utiliza la fórmula:
P= n!
En este caso se utiliza esta última expresión, ya que se desea calcular las permutaciones de 6 ciudades en 6 posiciones:
P=6!
P=720
Hay 720 secuencias posibles existen para las seis ciudades designadas.
If Ms. Akers has 84 candy canes and 72 packets of hot cocoa. What is the greatest amount of groups can she make that have the same amount of candy canes and the same amount of hot cocoa packets?
Answer:
12
Step-by-step explanation:
HELPPPP!!!!!!! TIMEDDDDD!!!!!!!! ASPPP!!!!!!
Which of the following is an arithmetic sequence?
3, 4, 6, 9, 13
1, 3, 6, 10, 15, 21
2, 5, 8, 11, 14
1, 2, 4, 8, 16
Answer:
1, 2, 4, 8, 16
Step-by-step explanation:
Each gets higher everytime you multiply by 2
Answer:
C or 3
Step-by-step explanation:
It is the only one going in a pattern or arithmetic sequence
2 + 3 = 5
5 + 3 = 8
8 + 3 = 11
11 + 3 = 14
The relationship is 3
pls answer I give brainliest
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
please mark brainiest
the difference of 3 times a number and 7 is written how ?
victor was asked to simplify this expression into exponential form: 8^0 + 12^0.
he says the answer is 2. do you agree with victor? explain your reasoning.
Answer:
yes, because anything to the 0 power is 1 so the equation would simplify to 1+1 which is equal to 2
Step-by-step explanation:
Find the common ratio
6.) -1, -6, -36, -216,
A.) r=5
B.) r=6
C.) r=-6
D.) r=4
Answer:
6
Step-by-step explanation:
try mulyipling each sequence by 6
alex is w years old. His sister claudia is three years younger than Alex. The product of their ages is 180 a) set up an equation to represent this information b) solve your equation (from a) to find alex's age
Answer: The equation is w*(w-3)= 180 & Alex is 15 years old
Step-by-step explanation:
Alex= w years old
Claudia= (w-3) years old
a) Equation, w*(w-3)= 180
b) Now,
w*(w-3)= 180
⇒ w²-3w-180= 0
⇒ (w+12)*(w-15)= 0
⇒ w= 15
Alex is 15 years old
Claudia is (15-3) = 12 years old
There are 12800 films on Netflix. 9% of the films are horror. How many films are horror?
Answer:
1152
Step-by-step explanation:
You multiply the 12800 films by 9% to get your answer.
Answer:
1152
Step-by-step explanation:
Step 1: Our output value is 9.
Step 2: We represent the unknown value with $x$.
Step 3: From step 1 above,$9=100\%$.
Step 4: Similarly, $x=12800\%$.
Step 5: This results in a pair of simple equations:
$9=100\%(1)$.
$x=12800\%(2)$.
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
$\frac{9}{x}=\frac{100\%}{12800\%}$
Step 7: Again, the reciprocal of both sides gives
$\frac{x}{9}=\frac{12800}{100}$
$\Rightarrow x=1152$
Therefore, $12800\%$ of $9$ is $1152$
this took a really long time
What is 54/72 in simplest form?
Answer:
3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
x intercepts of -12x^2+108x=h and the y intercept
Answer:
x: 0 or 9
y-int: 0
A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 50 nails and each large box has 400 nails. The contractor bought six more small boxes than large boxes, which altogether had 1200 nails. Create a system of equations to represent this situation. Define the variables that you use to write the system.
Answer:
https://brainly.com/question/14526835?referrer=searchResults#
some one already answered the question you have
Step-by-step explanation:
state if the three numbers can be the lengths of the sides of a triangle 7, 19, 9
Answer:
Well i am not sure on that but i do know that the angle measures have to add up to 180 degrees hope that helps at least a little
Step-by-step explanation:
Find the scale factor!
Answer:
1.8
Step-by-step explanation:
Answer:
satingin ko 1.8 yan lang
sana makatulong
Please help me with this question
Answer:
37
add all of them together then divide it by two
A line contains the points (82, −96) and (87, −86).
What is the slope of the line in simplified form?
Answer:
The slope is 2.
Step-by-step explanation:
ΔX = X2 - X1 = 87 - 82 = 5
ΔY = Y2 - Y1 = -86 - (-96) = -86 + 96 = 10
ΔY/ΔX = 10/5 = 2/1 = 2
what is 200 times 350=
pleser help
Answer:
70000
Step-by-step explanation:
At costco food court a family can purchase 4 hot dog meals for 6$ what is the cost per person
Answer:
$1.50
Step-by-step explanation:
Answer:
$1.5
Explanation:
6 / 4?
You have $50,000 to invest (YAY!). You need $350,000 in the account to retire in 30 years. At what continuously compounded interest rate would you need to invest to reach your goal?
What formula will you be using? Type your answer in the first math box below.
In the following math boxes, make your substitutions and show the ALGEBRAIC steps to your solution.
Answer:
You need to invest at a continuous compound interest rate of 6.701355026%
Step-by-step explanation:
The formula to use is the compound interest formula:A=P(1+r/100)^t
where A=Total amount at the end of the investment period
P=Principal amount
R=Rate of interest
T=Investment tenor/time
Now,
350,000=50000(1+r/100)^30 is what needs to be simplified to 6.701355026%
is 1/2(2p+9)=-p+5 a one solution or infinite solution or no solution
Your inequality has one solution which is p = 1/4
need help with this question
Answer:
1. He added 5 instead of subtracted 5.
2. He should have subtracted 5.
3. 2 2/3
Step-by-step explanation:
3x+5=13
subtract 5 to both sides 3x=8
divide both sides by 3 x=8/3 or 2 2/3
Answer:
3x + 5 =13 is the error
Step-by-step explanation: