john has 1 chicken jake took one how much does john have left

Answer:

[tex]38[/tex] and [tex]68[/tex].

Step-by-step explanation:

Let [tex]x[/tex] be the smaller one of the two number.

[tex]x[/tex] must be a positive integer. The other number would be [tex](x + 30)[/tex].

The question states that the product of the two numbers is [tex]2584[/tex]. In other words:

[tex]x\, (x + 30) = 2584[/tex].

Rearrange this equation and solve for [tex]x[/tex]:

[tex]x^{2} + 30\, x - 2584 = 0[/tex].

The first root of this quadratic equation would be:

[tex]\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}[/tex].

Similarly, the second root of this quadratic equation would be:

[tex]\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}[/tex].

Since the question requires that both numbers should be positive, [tex]x > 0[/tex]. Therefore, only [tex]x = 38[/tex] is valid.

Hence, the two numbers would be [tex]38[/tex] and [tex](38 + 30)[/tex], which is [tex]68[/tex].

9514 1404 393

Answer:

  38 and 68

Step-by-step explanation:

Let x represent the average of the two numbers. Then their product is ...

  (x -15)(x +15) = 2584

  x^2 = 2584 +225 = 2809 . . . . . . use relation (x -a)(x +a) = x^2 -a^2; add a^2

  x = √2809 = 53

Then the two numbers are ...

  53 +15 = 68

and

  68 -30 = 38

The two numbers are 38 and 68.

_____

Additional comment

Solving the problem in this way is equivalent to writing the quadratic equation for the smallest (or largest) number and solving that by completing the square. The "solution" x = -53 is not relevant in this problem.

Answer:

3rd, y=-1/5x

Step-by-step explanation:

-7/10 + (-5/6) = -(7/10 + 5/6) =

= -(21/30 + 25/30) = -46/30 =

= -1 16/30 = -1 8/15 ← the end

Answer:

the answer is "B"

the "a" (as in ax^2) is negative thus the parabola "goes downward"

Step-by-step explanation:

The equation of parabola is,

y = - 1/2x²

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.

We have to given that;

In a parabola,

Vertex = (0, 0)

Since, We know that;

Standard form of equation of parabola is,

y = a (x - h)² + k

Where, (h, k) = (0, 0) = vertex

Hence, We get;

y = a (x - 0)² + 0

y = ax²

Here, A point on parabola is, (2, - 2)

- 2 = a (2)²

a = - 2 / 4

a = - 1/2

Hence, The equation of parabola is,

y = - 1/2x²

Learn more about parabola visit:

https://brainly.com/question/29635857

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Answer:

5 more matches was won by yu-na kim

Answer:

m = -1

Step-by-step explanation:

Find the equation in slope intercept form [ y = mx + b ] for line AB. Find the slope using the formula [ y2-y1/x2-x1 ].

8-5/7-4

3/3

1

Find the y-intercept.

5 = 1(4) + b

5 = 4 + b

1 = b

So the equation of the line AB is y = x + 1.

The slope of a perpendicular line is the opposite reciprocal of the original line.

1 -> -1/1 -> -1

Best of Luck!

Answer:

3=g/-4  -5

3+5=g/-4

8= g/-4

8x(-4)=g

g=-32

Step-by-step explanation:

Answer:

1360

Step-by-step explanation:

there are 1200 seconds in 20 minutes. if Ella can do 17 jumps in 15 seconds, you would divide 1200 by 15 (which equals 80) because that would be the number of 15 seconds in 20 minutes. then you would divide 80 by 17, which gives you your final answer of 1360 jumps in 20 minutes.

Answer:

23.8 years

Step-by-step explanation:

Assuming this is compound interest, we'll use the compound interest formula

A = P(1 + r)ⁿ

A = Final amount (2000)

P = Initial amount (500)

r = Annual interest rate (.06)

n = ?

Our equation will look like this

2000 = 500(1.06)ⁿ

First, divide both sides by 500

2000/500 = (500(1.06)ⁿ)/500

(1.06)ⁿ = 4

Then we have to take the log₁.₀₆ out of both sides

n = log₁.₀₆(4)

n = 23.79132