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:
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A line that includes the points ( – 4, – 6) and (5,v) has a slope of – 2/9 . What is the value of v?
Answer:
v is -8
Step-by-step explanation:
The form of a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).
We are given the slope, so let's write:
y = -(2/9)x + b
We can find b by using the one fully given point, (-4, -6).
y = -(2/9)x + b
-6 = -(2/9)(-4) + b
b = -6 - (8/9)
b = -(62/9)
Now we have y = -(2/9)x - (62/9)
We want the value of y when x is 5 to find v in (5,v):
y = -(2/9)x - (62/9)
y = -(2/9)(5) - (62/9)
y = -(10/9) - (62/9)
y = -(72/9)
y = -8
v is -8
which of the following is an example of a polynomial equation?
Writing quadratic functions
Answer:
So, y = x^2 is a quadratic equation, as is y = 3x^2 + x + 1. All of these are polynomial functions of degree 2. Often you will be given the quadratic ...
Find a point-slope form for the line with slope
and passing through the point (-4,-7).
Answer:
[tex]\displaystyle y + 7 = \frac{1}{5}(x + 4)[/tex]
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Identify variables.
Point (-4, -7)
Slope m = [tex]\displaystyle \frac{1}{5}[/tex]
Step 2: Find Equation
Substitute in variables [Point-Slope Form]: [tex]\displaystyle y - -7 = \frac{1}{5}(x - -4)[/tex]Simplify: [tex]\displaystyle y + 7 = \frac{1}{5}(x + 4)[/tex]If A={s, t, a, r} and B={m, a, t, h}, find A ∩ B.
A ∩ B = { t,a }
This is because it is asked to find the common elements present in both sets.
We need to write only the same elements present in both sets.
Therefore, A ∩ B = { t,a } is the answer.
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Answered by Benjemin ✍️
Could you please help with this
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
14. They are symbols that denote silence and give the performer time to relax. * O a. notes O b.rests O c. time signatures
Answer:
b.rests
Step-by-step explanation:
HOPE IT'S HELP
#PHILIPPINES
HELP 25 POINTS LIKE HELP SOLVE THIS ASAP!!!
Answer:
nahhhh why did you report me I did nun wrong
Step-by-step explanation:
You are finding the total distance of a road trip by measuring the distance on a map. On the map the distance between 3 towns measure 2 7/16 inch, 1 5/8 inch, and 3 3/4 inch, repectively. What is the total distance of the trip on the map?
Answer:
The answer would be 7 and 13/16
Step-by-step explanation:
Hope this helps.
Solve pls brainliest
Answer:
If u double both numerator & denominator, this ration is 46/100
This answer is 46%
Mountain ranges often appear on the edges of continents. What theory does this support?
Mountains were formed when Earth’s crust cooled and Earth shrank.
Mountain ranges were formed when continents collided.
Mountain ranges did not exist millions of years ago.
Mountain ranges were formed only by glaciers.
Answer: Its B!
Step-by-step explanation:
i just got it right :)
Answer: b. Mountain ranges were formed when continents collided.
Step-by-step explanation:
solve x. 24-8x=-16 and have a bless day
Answer:
x = 5
Step-by-step explanation:
24 - 8x = -16
Subtract 24 from both sides.
-8x = -40
Divide both sides by -8.
x = 5
Answer:
5
Step-by-step explanation:
24 - 8x = -16
24 + 16 = 8x
8x = 40
x = 40/8
= 10/2
= 5
5x + 7y = 5 10x + 14y = 10 solve by elimination
The answer is:
x= 46/5
y= 5/7
I need help plzzzzzzzz
Answer:
51
Step-by-step explanation:
Given:
c=3
d = 7
thus just substitute it in.
15+(3)^2 * (7) - (3)^3
15 + 9*7-27
15+63-27
=51
You have 64 coins, consisting of pennies, nickels, and quarters. The value of the coins is $4.60. You also know that you have three times as many nickels as quarters. Find the quantity of each type of coins
Number of pennies =
Number of nickels =
Number of quarters =
Answer:
There are 20 pennies, 33 nickels and 11 quarts.
Step-by-step explanation:
Total number of coins = 64 Amount of money = $4.60 = 460 cents
x = pennies y = nickels x = quarters
y x 3 = x
x + y + z = 64 coins
x + 5y + 25z
x + 4z = 64
x + 40z = 460
x = 20 z = 11
y = 3z = 33
What is the missing numerator?
blank over seven minus three-eighths equals twenty-seven fifty sixths
4
5
6
7
Answer:
6
Step-by-step explanation:
6/7 - 3/8= 27/56
Answer:
it is 6
Step-by-step explanation:
6.
Identify the vertex of the parabola.
A. (−4, 0)
B. (−3, 1)
C. (1, −3)
D. (−1, −3)
Step-by-step explanation:
the vertex is the point, where the parabola turns around. it is (depending on its orientation, if it is opening upwards or downwards) the maximum or the minimum of the curve.
so, as we can see on the grid, that point is x = -3, y = +1 = (-3, 1).
so, B is correct
Answer:
B. (−3, 1)
Step-by-step explanation:
-3, 1 is the vertex I believe
-3,1 should be the one
pls help quick :( worth 20 pts
Answer:
Answer A
Step-by-step explanation:
From the image, it looks like the answer is y<1/2x+2 because the shading of the line is below, as well as the points of interception are 4 and 2. I hope this helps!
The binomial (x + 5) is a factor of x2 + 8x + 15. What is the other factor?
(x + 3)
(x + 7)
(x + 12)
(x + 13)
Answer:A
Step-by-step explanation:
Please help I’m begging you
Answer:
y = 9
Step-by-step explanation:
The line "y = 9" is parallel to the x-axis and passes through (0,9).
Evaluate each function for the given value of x, and write the input x and
output f(x) as an ordered pair.
18,20,22,24
Answer:
18) 3
20) -65
22) 12/5
24) -5/2
Step-by-step explanation:
18) f(-5) = -[2(-5)+1] / 3
= -(-10+1)/3
= -(-9)/3
= 3
20) f(7) = -9(7)-2
= -63-2
= -65
22) f(-1) = -[(12 · -1)]÷5
= -(-12)÷5
= 12/5 or 2 2/5
24) f(9) = 2/9(9) - 9/2
= 2 - 9/2
= 4/2 - 9/2
= -5/2 or -2 1/2
what is 8 x ( 4 x 2 ) = ?
Answer:
64
Step-by-step explanation:
4*2 is 8
Multiply 8*8
Answer:
the answer is 64
Step-by-step explanation:
8(4*2)
=8*8
=64
Billy wants to save $3,720 so that he can buy the car he wants. If Billy can save $30 per day, how many days will it take him to save enough money?
Answer:
The Answer Above Is Right =)
Step-by-step explanation:
(x-4)^2-(x-4)(x+3)=35
Answer:
Step-by-step explanation:
(a - b)² = a² - 2ab + b²
(x -4)² - (x - 4)(x +3) = 35
x² - 8x + 16 - [ x(x +3) - 4(X +3)] = 35
x² - 8x + 16 - [x² + 3x - 4x - 12 ] = 35
x² - 8x +16 - [ x² -x - 12] = 35
x² - 8x + 16 -x² + x + 12 = 35
x² - x² - 8x + x + 16 + 12 = 35 {Combine like terms}
-7x + 28 = 35
-7x = 35 -28
-7x = 7
x = 7/-7
x = -1
(-1, 5) (3,y) m=5 whats the value of my and whats the slope <3
Answer:
slope: 5
y = 25
Step-by-step explanation:
slope is m, and m = 5, so slope is 5.
y-5=5(x+1)...........set up point slope form
y-5=5x+5............distribute 5
y=5x+10..............add 5 to both sides
y=5(3)+10............plug in 3
y=25.....................simplify
Step-by-step explanation:
I am not sure you posted the question correctly.
m is the slope already. this comes from the point slope form
y - y1 = m(x - x1)
where x1, y1 are the coordinates of a point on the line.
so, the slope is 5 (and cannot be <3).
so, using the first point we get
y - 5 = 5(x - -1) = 5(x + 1) = 5x + 5
therefore
y = 5x + 10
for (3, y) we put 3 in as x
y = 5×3 + 10 = 15 + 10 = 25
it is (3, 25) for m = 5.
x^8+8x^7+15x^6−9x^5−72x^4−135x^3+8x^2+64x+120 Factor completely given the following factors: (x+5) and (x+3) There should be 6 factors (2 given, 2 binomials, and 2 trinomials.) show steps
Answer:
(×+3)(×+5)(×2)(×-1) (×^2+2×+4)(×^2+×+)Step-by-step explanation:
Where the given one is bolded the 2 binomials is italicized Ang the 2 trinomials is underlinedpa BRAINLEST pls
When the Johnson family lights candles at 5:00 PM, each candle is 8 inches tall. The height of each candle changes by -3/4 inch for each hour that it burns. How tall will each candle be at 11:00 PM when the Johnsons put the candles out for the night?
Each candle will be___inches tall.
From the information given, it can be deduced that the length of the candle at 11:00PM will be 3.5 inches tall.
Since the family lights candles at 5:00 PM and offs them by 11:00PM, the difference in hours will be 6 hours.
Therefore, the length of the candles at 11:00PM will be:
= 8 - (3/4 × 6)
= 8 - 4.5
= 3.5
In conclusion, the correct option is 3.5 inches tall.
Read related link on:
https://brainly.com/question/25711376
Answer: 3.5
just did it
Step-by-step explanation:
if the sum of two consecutive odd number is 12 find them
Answer:
5 and 7
Step-by-step explanation:
Fast and loose: 12 is written as a sum of two odd numbers as 1+11; 3+9; 5+7. The only consecutive pair is 5 and 7
Let's use algebra: let's call 2n+1 the first and 2n+3 the second.
Their sum is 2n+1 +2n+3 = 4n+4 = 12. Thus, n+1=3 and n= 2. It means the 2 numbers are 2x2+1 =5 and 2x2+3 =7
a group can plant 3/4 acres in 1 7/8. What os the unit rate in acres per day? Write your answer in simplest form.
Sam buys one bag of flour for $2.50, three packages of shredded cheese for $3.00 each, and x packages of mushrooms for $3.50 each. If Sam paid $18.50 in all, how many packages of mushrooms did Sam buy?
Answer:
The answer is 1 pack of mushroom
Step-by-step explanation: