Queremos encontrar dos números enteros tales que su diferencia sea de 6 y la suma de sus cuadrados sea igual a 260.
Veremos que los dos números son 8 y 14.
Primero, podemos definir esos números como A y B.
Entonces tenemos que:
A - B = 6
A^2 + B^2 = 260
Esto es un sistema de ecuaciones.
Para resolverlo, el primer paso es aislar una de las variables en una de las ecuaciones, vamos a hacer esto en la primera.
A - B = 6
A = 6 + B
Ahora reemplazamos esto en la otra ecuación.
A^2 + B^2 = 260
(6 + B)^2 + B^2 = 260
36 + 12*B + B^2 + B^2 = 260
36 + 12*B + 2*B^2 = 260
Ahora podemos resolver esto para B:
2*B^2 + 12*B + 36 - 260 = 0
2*B^2 + 12*B - 224
Las soluciones estan dadas por la formula de Bhaskara:
[tex]B = \frac{-12\pm \sqrt{12^2 - 4*2*(-224)} }{2*2} \\\\B = \frac{-12 \pm 44 }{4}\\\\B = (-3 \pm 11)[/tex]
Entonces las dos soluciones son:
B = -3 + 11 = 8
B = -3 - 11 = -14
Sabemos que los números son positivos, asi que elejimos la primera, entonces tenemos:
B = 8.
Con esto podemos calcular el valor de A como:
A - B = 6
A = 6 + B = 6 + 8 = 14
Entonces los dos números son:
8 y 14.
Si deseas aprender más, puedes leer:
https://brainly.com/question/24761554
Which is not a way to write the answer to this problem?
Answer:
D) .
Step-by-step explanation:
913 ÷ 29 ≈ 31
x:y=2:3 and x+y=10.Find value of x and y
Answer:
We know that x is 2
Whilst y is 3
this can be changed due to it’s ratio
So in this code x+y=10
2+3=10
We can do it this way.
2+3=5 (add the ratios)
10/5=2 (Divide the sum by the number needed)
2*2=4 (multiply the quotient for each ratio)
3*2=6 (multiply the quotient for each ratio)
x is 4
y is 6
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day!!
We can solve this problem in two steps, Comprehension and Solving
I'll start off with comprehension.
Comprehension
We know that ratios are basically fractions as they both show comparison, so we can make x:y into [tex]\frac{x}{y}[/tex].
We also have another equation, making this problem a system of equations.
Now that we know what to do, we can begin solving!
Solving
We can solve this by first getting our two equations.
[tex]\frac{x}{y}=\frac{2}{3}[/tex]
We can simplify the 2nd equation so that we know what one variable is.
[tex]x+y=10\\x=10-y[/tex]
We can now input our second equation into the first equation.
[tex]\frac{10-y}{y}=\frac{2}{3}\\3(10-y)=2y\\30-3y=2y\\30=5y\\y=6[/tex]
If y is six, then we can use the second equation to solve for x.
[tex]x+6=10\\x=4[/tex]
We know that x is 4 and y is 6.
We can now check our answers.
1st Equation
[tex]\frac{4}{6}=\frac{2}{3}?\\[/tex]
[tex]\frac{2}{3}=\frac{2}{3}[/tex]
2nd Equation
[tex]4+6=10?\\10=10[/tex]
We've proven our answers to be right, therefore, x is 4 and y is 6.
HELP ME ASAP i could rly use it
Answer:
B-at the second line
Step-by-step explanation:
hope it can help you lovelots
#LEARN WITH BRAINLY
[tex]x^2 +6x +18 =0\\\\\implies x^2 + 2 \cdot 3 \cdot x + 3^2 -3^2 +18 =0\\\\\implies (x+3)^2 -9 +18 =0\\\\\implies (x+3)^2 +9 =0\\\\\implies (x+3)^2 =-9[/tex]
you could give away 70 coffee mugs without charging anything.
If you charge $10.00, nobody will buy the coffee mugs. You also figured out that your sales will be decreasing
following straight line. Your job is to find the maximum possible revenue from selling the coffee mugs.
Answer the following questions:
1. Graph the linear relationship between the price of coffee mugs p, and the number of coffee mugs sold S.
Hint: To give away 70 coffee mugs means when the price p=0, S(0) = 70. Plot that point on the graph. Find one
more point using the other given condition. Keep in mind S(p) is a linear function. Be careful what will be
represented on the x-axis, and what will be represented on the y-axis.
2. Find the equation of the linear function S(p) that describes the quantity sold as a function of the price p.
3. The revenue is determined by R = Sp. Express the revenue as a function of the price p.
Help: You may look at the examples from the power point for section 2.6
4. Graph the revenue function. Make sure to label the x - and the y - axis with the appropriate units.
5. At which price per coffee mug do you not make any money?
6. Find the price per coffee mug that makes the most revenue.
7. How many coffee mugs must be sold to maximize the revenue?
8. What is the maximum revenue?
9. What price per coffee mug you should charge to collect at least $70 in revenue?
Your project will be graded based on the following:
1. Turned in a hard copy, and an electronic version as a PDF file on Blackboard on time (due date Dec 7
or before ) (5pts. deduction per day)
2. Completeness (no missing part, show all of your work, calculations, formulas used etc.
3. Precision ( correct answers )
4. Complete graph
the graph has a title
the axes are labeled ( make sure you have included the units of measurement)
-
At $ 10 per mug you will not get any money; the maximum possible revenue is $ 175, which will be obtained by selling the mugs for $ 5; and to get at least $ 70 in revenue the mugs must be sold for $ 2.
Since you could give away 70 coffee mugs without charging anything, and if you charge $ 10.00, nobody will buy the coffee mugs, and you also figured out that your sales will be decreasing following straight line, and your job is to find the maximum possible revenue from selling the coffee mugs, to determine at which price per coffee mug do you not make any money; the price per coffee mug that makes the most revenue; how many coffee mugs must be sold to maximize the revenue; what is the maximum revenue; and what price per coffee mug you should charge to collect at least $ 70 in revenue; the following calculations must be performed:
70 = 0 0 = 10 35 = 5 63 x 1 = 63 56 x 2 = 112 49 x 3 = 147 42 x 4 = 168 35 x 5 = 175 28 x 6 = 168
Therefore, at $ 10 per mug you will not get any money; the maximum possible revenue is $ 175, which will be obtained by selling the mugs for $ 5; and to get at least $ 70 in revenue the mugs must be sold for $ 2.
Learn more about quantities in https://brainly.com/question/25797049
find two positive numbers A and B with A less than or equal to B whose sum is 52 and whose product is mazimized
Answer:
26 and 26
Step-by-step explanation:
Let's call the two numbers x and 52-x.
Their product is [tex]p(x) = x(52-x)=52x-x^2[/tex]. Now, if you know calculus, you take it's derivative, see where it goes to 0, and determine what kind of critical point is that. Or - especially if you don't know what a derivative is - you stare at it long enough, and realize that that's the equation of a parabola. pointing downward. It means it has a maximum at its vertex, and the vertex has its first coordinate in the point [tex]x_v= -\frac{b}{2a} = -\frac{52}{2)(-1)} = 26[/tex] The two numbers are, then 26 and 52-26=26.
(X-3)(X-12)
Expand and simplify
Answer:
x^2-15x+36
Step-by-step explanation:
x(x-12)-3(x-12)
x^2-12x-3x+36
x^2-15x+36
Answer: X^2 -15x + 36
Step-by-step explanation:
(X-3) (x-12)
Multiply each term in the first bracket by each term in the second bracket
X^2 -12x -3x + 36
Collect like terms
X^2 -15x + 36
Question involving derivatives and limits...
What is the limit as x approaches 2 of (3 f(x) - 15) / (x-2)... where f(2) is 5. The answer is not 0, I checked.
the derivative f'(2) is 1/8 in case that's needed
it can be either 3/8, , 3.545, or 3/2
Answer:
undefined
Step-by-step explanation:
F = 1/5 gh^2
solve for h
Answer:
First of all, let's multiply both sides by 5, clearing the denominators:
Then, as long as g is not zero, we can divide by g, and let's read right to left:
At this point, assuming F and g are either both positive or both negative, we can take the square root of both sides:
If h represent a quantity that is positive by it's nature (ie, the length of a segment) you can consider only the positive root, ie ignoring the plus or minus sign.
How do i find the value of x in this equation?
Answer:
5x-10=60
5x=70
x=14
Hope This Helps!!!
Answer: 14
Step-by-step explanation:
Thr two angles are equal, so we can write:
5x-10 = 60
5x = 70
x = 14
(I’m having trouble with this question, it would be greatly appreciated if I could have some help, thank you)
What is the equation of a line that is parallel to – 2x + 3y = -6 and passes through the point (-2, 0)?
Answer:
y = 2/3x + 4/3
Step-by-step explanation:
you need to know the slope of the line -2x + 3y = -6 because parallel lines have the same slopes
let's put the equation in y=mx+b format (slope-intercept format)
-2x + 3y = -6
add 2x to each side to get:
3y = 2x - 6
divide each side by 3 to get:
y = 2/3x - 2
the equation now shows us the slope is 2/3 and the y-intercept is (0,-2)
now we use y=mx+b again and use the point (-2,0) and the m=2/3 to get the y-intercept ('b' value) of the equation that is parallel:
0 = 2/3(-2) + b
0 = -4/3 + b
b = 4/3
equation would be:
y = 2/3x + 4/3
The show gave a 10% discount for students. The full ticket price is $30. How much was the students price?
Answer:
$27
Step-by-step explanation:
You can get the equation 30 - 30 * 1/10 = x, and x is what we are looking for. Simplifying gives 30 - 3, so x is 27. So, the answer is $27.
Answer:
$3
Step-by-step explanation: 10%= 0.10 divide that by 30, 30 ÷ 0.10 = 3
help with this plesseee
Answer:
the length and width of rectangle could be (3cm and 7 cm ) & (1cm and 21cm) respectively.
Cuanto es 1/3 + 5/8 + 1/2
Answer:
35/24
Step-by-step explanation:
1/3 + 5/8 + 1/2
8/24 + 15/24 + 12/24
Hola!
Primero, debes asegurarte de que todas las funciones compartan el mismo denominador.
4(1/2)= 4/8
1/3 + 5/8 + 4/8
1/3 + 9/8
Ahora necesitamos encontrar un denominador común de 3 y 8.
El mínimo común múltiplo de 3 y 8 es 24.
8(1/3)= 8/24
3(9/8)= 27/24
8/24 + 27/24= 35/24
Entonces tu respuesta es 35/24!!
Lo siento si mi español no es bueno.
HELP PLEASE 100 POINTS
Answer:
118 is the answer.Step-by-step explanation:
All pentagons angles = 540
540 - 107 - 100 - 96 - 119 = 118
118 is the answer.Hope it helped!
Kavitha
Answer:
The answer above is in fact correct
Step-by-step explanation:
107+100+96+119+118=540
Can someone please help me
Answer:
Step-by-step explanation:
1) Statements Reasons
ABCD is a trapezoid Given
AD ║ BC bases of trapezoid are parallel
∠AED = ∠CEB vertically opposite angles are equal
∠EBC = ∠ADE alternate interior angles are equal and BD is transversal
∠ECB = ∠EAD alternate interior angles are equal and AC is transversal
ΔAED ~ ΔCEB ∠ECB = ∠EAD & ∠AED = ∠BEC & ∠EBC = ∠ADE
all angles are same and their shape is same, so similar
2) hope you can write 2nd one as above two column proof
T is the mid point of QR
U is the mid point of QS
V is the mid point of RS
Definition: The segment of line joining the middle points of two sides of a triangle is called middle segment.
Inference: A middle segment of a triangle is parallel to the third side and its lengths is half the third side's.
so here TU ║ RV and TU = RV
UV ║ TR and UV = TR
so TUVR becomes a parallelogram
∠TUV = ∠TRV --------> condition 1
same goes with parallelogram TQUV
∠TQU = ∠UVT ----------> condition 2
same goes with parallelogram TUSV
∠UTV = ∠USV ------------> condition 3
from the above 3 conditions we can say
ΔQRS ~ ΔVUT
3) see the below figure for graph
in both triangles ∠B is common
AC and TS are parallel lines
BC and BA are transversals
∠C ∠S are equal --> corresponding angles
∠A ∠T are equal ---> corresponding angles
so ΔABC & ΔTBS are similar
Examine the solution to the equation
-6(x + 5) + 3 = -2(x + 4) - 4x
-6x - 30 + 3 = -2x - 8 - 4x
-6x-27 = -6x - 8
Which statements accurately describe this equation?
Check all that apply.
This equation has one solution.
This equation has no solution.
This equation has infinitely many solutions.
Any input value for the variable will generate a true
equation
O Any input value for the variable will generate a false
equation.
-27 = -8
Answer:
option (2) and (5) is correct.
2) This equation has no solution.
5) Any input value for the variable will generate a false equation.
Step-by-step explanation:
Given a solution to the equation,
-6( x + 5) + 3 = -2( x + 4) - 4x
⇒ –6x – 30 + 3 = –2x – 8 – 4x
⇒ –6x – 27 = –6x – 8
⇒ –27 = – 8
Which is false statement as -27 is never equal to -8.
Thus, This equation has no solution.
Also, if we substitute any value of x , then also the equality never hold.
For example lets put x = 1 in -6( x + 5) + 3 = -2( x + 4) - 4x , we get,
⇒ -6( 1 + 5) + 3 = -2( 1 + 4) - 4(1)
⇒ -6( 6) + 3 = -2(5) - 4
⇒ -36 + 3 = -10 - 4
⇒ -33 = -14
Still the value is false as -33 is never equal to -14.
Any input value for the variable will generate a false equation.
Thus, option (2) and (5) is correct.
who my fav celeb who ever can guess it close to the name gets brainest
Answer:
john cena
Step-by-step explanation:
i have no idea lol
which algebraic expression represents the total area of a cube each dimension of which is 1.5x
Answer:
okkkkkkkķkkkkkkkkkkkkk
Answer:
Step 1: Remove parentheses by multiplying factors.
= (x * x) + (1 * x) + (2 * x) + (2 * 1)
Step 2: Combine like terms by adding coefficients.
(x * x) = x2
(1 * x) = 1x
(2* x) = 2x
Step 3: Combine the constants.
(2 * 1) = 2
Step 4: Therefore, Simplifying Algebraic Expression is solved as
= x2 + 3x + 2.
Step-by-step explanation:
A cube is 3- dimensional shape with 6 equal sides, 6 faces, and 6 vertices in geometry. ... In 3 – dimension, the cube's sides are; the length, width, and height.
Find an equation of the circle that has center (-6,2) and passes through (1,-2).
Answer:
(x+6)^2+(y-2)^2=65
Step-by-step explanation:
Answer:
Should be (x+6)^2+(y-2)^2=65
the number after the carrot represents an exponent
hope it helps
What is a simple way to find 12 mod 7 + 12 mod 7 + 12 mod 7 + 12 mod 7?
12 ≡ 7 + 5 ≡ 5 (mod 7)
so
12 + 12 + 12 + 12 ≡ 4•12 ≡ 4•5 ≡ 20 ≡ 14 + 6 ≡ 6 (mod 7)
Johnny ate seven apples, his bus comes around 3 in the morning, the neighbors dog took a dump on the ground weighing 2.67 kilograms. Whats the mass of the sun??
Answer:
mass if the sun is 123
Step-by-step explanation:
I saw the dog take a dump
The proportion of the total area under a normal curve between two z-scores corresponds to the ______ of that range of scores.
Answer:
For any normal distribution, the mean and the median will have the same value. For any normal distribution, the proportion corresponding to scores greater than z = +1.00 is exactly equal to the proportion corresponding to scores less than z = -1.00.
Step-by-step explanation:
I need help asap please!
what is the output when in the input is 7
Answer:
If the input is 7 then output is:-Tiny Small. Explaination: - 7 is smaller than 10 so output is tiny.
Which statement about the function f(x)=x2−x−20 is true?The expression x2−x−20 has factors (x−5) and (x+4), and f(x) has zeros at x=−5 and x=4.The expression x 2 − − x − − 20 has factors ( x − − 5 ) and ( x + 4 ) , and f ( x ) has zeros at x = − − 5 and x = 4 .The expression x2−x−20 has factors (x−5) and (x+4), and f(x) has zeros at x=−4 and x=5.The expression x 2 − − x − − 20 has factors ( x − − 5 ) and ( x + 4 ) , and f ( x ) has zeros at x = − − 4 and x = 5 .The expression x2−x−20 has factors (x−4) and (x+5), and f(x) has zeros at x=−5 and x=4.The expression x 2 − − x − − 20 has factors ( x − − 4 ) and ( x + 5 ) , and f ( x ) has zeros at x = − − 5 and x = 4 .The expression x2−x−20 has factors (x−4) and (x+5), and f(x) has zeros at x=−4 and x=5.The expression x 2 − − x − − 20 has factors ( x − − 4 ) and ( x + 5 ) , and f ( x ) has zeros at x = − − 4 and x = 5 .
Answer: its C
Step-by-step explanation:
The lines represented by the equations y + 3/2x = -6 and 3y – 2x = -24 are
parallel
neither parallel nor perpendicular
perpendicular
the same line
Answer:
Neither Parallel nor Perpendicular
Step-by-step explanation:
Convert 3y - 2x = -24 to slope - intercept form
3y - 2x = -24
3y = -24 + 2x
3y = 2x - 24
y = 2/3x - 8
They are neither parallel or perpendicular
Parallel lines have the same slope, but these are different
Perpendicular lines have the opposite inverse (negative reciprocal) slope, but these are just reciprocals
-Chetan K
Edwin and Franklin share money in the ratio 3:7 Franklin received $20 more than Edwin. Find the amount shared and what each of them received.
Step-by-step explanation:
We have,
Edwin and Franklin share money in the ratio 3:7.Franklin received $20 more than Edwin.We've to find the amount shared and what each of them received.
★ Amount Shared = Amount received by Edwin + Amount received by Franklin ★
As, Edwin and Franklin share money in the ratio 3:7. So, let's say that,
Amount received by Edwin = $ 3xAmount received by Franklin = $ 7xAlso, Franklin received $20 more than Edwin. So,
→ Amount received by Franklin = 20 + Amount received by Edwin
→ 7x = 20 + 3x
Solving the equation further.
→ 7x - 3x = 20
→ 4x = 20
→ x = 20/4
→ x = 5
Hence,
→ Amount received by Edwin = $ 3x
→ Amount received by Edwin = $ 3(5)
→ Amount received by Edwin = $ 15 [Ans]
And,
→ Amount received by Franklin = $ 7x
→ Amount received by Franklin = $ 7(5)
→ Amount received by Franklin = $ 35 [Ans]
Lastly,
→ Total amount shared = 3x + 7x
→ Total amount shared = $35 + $15
→ Total amount shared = $50 [Ans]
Hence, solved!whats 2 + 2 ??!?!?!?!?!?!?!?
Answer:
4 duhh... Ur kidding me??
Answer:
22 because 2+2
Step-by-step explanation:
if we put 2 near 2 it will be 22 so the answer is 22
Tim's phone service charges $24.25 plus an additional $0.18 for each text message sent per month. If Tim's phone bill was $28.75, which equation could be used to find how many text messages, x, Tim sent last month?
Help me please I need to pass this class
Answer:
The answer is C
Step-by-step explanation:
I know this because if you 5 plus 3 is 8 right not the other ones so if you just add zero's it will be 50 plus 30 and then that will equal 80 so it is for every 5 question's he got 3 wrong.
Hope this helps ('o')
Given : In the recent maths test, Jeremy answered 48 questions correct out of 80 total questions. Which statement is correct ?
Solution :
As we know that total no. of questions is 80
Now, as per the options we get 80/5 = 16
However the third option seems to be the accurate as 3(16) = 48
So, we get to know that option C is correct
Out of every 5 questions, Jeremy answered 3 correctly.