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blondinia [14]
3 years ago
10

Jonah has a large collection of marbles he notices that if he borrows five marbles from a from a friend he can arrange the marbl

es in rows of 13 inch what is the remainder when he divides original number of marbles by 13
Mathematics
1 answer:
olga nikolaevna [1]3 years ago
5 0

Answer:

The remainder is 8

Step-by-step explanation:

Let Jonah's Marble=x

If he arranges x marbles into y rows of 13 each, and there are remainders(R)

Then:

x/13=y+(R/13).....(I)

If he borrows 5 marbles from a friend, there will be no remainder. However, the number of rows y, will be increased by 1

New Total Marbles=x+5

(x+5)/13=y+1.....(ii)

x+5=13(y+1)

x=13y+13-5

x=13y+8

From (I)

x=13y+R

Comparing the values of x derived from (I) and (ii)

13y+R=13y+8

Therefore the Remainder, R= 8

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Expand and simplify (X+5) (x+7)
Hoochie [10]

Answer:

x^2+12x+35

Step-by-step explanation:

x(x+7)+5(x+7)

x^2+7x+5x +35

x^2+12x+35

4 0
3 years ago
Given B = {a, l, g, e, b, r} and C = {m, y, t, h}, find B ∪ C. {} {a} {a, b, e, g, h, l, m, r, t, y}
sertanlavr [38]
1. A ∪ B = { x | x ∈ A or x ∈ B} ==> Ans C. 
<span>2. B ∪ C = { x | x ∈ B or x ∈ C} ==> Ans C</span>
3 0
3 years ago
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Simplifying products and quotients of powers
lesantik [10]

Answer:

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Step-by-step explanation:

5 0
2 years ago
Require full steps working for this question
Ray Of Light [21]

I let the computer do the graphing.  

f(x) = x(x + 3)²(1 - x) / 3

We see obvious zeros at x=0, x=-3 and x=1.

f(x) = x(x + 3)²(1 - x) / 3

f(x) = x(x^2 + 6x + 9)(1 - x)/3

f(x) = x(x^2 + 6x + 9 - x^3 - 6x^2 - 9x)/3

f(x) = x(- x^3 - 5x^2 -3x +9)/3

f(x) = (-x^4 - 5x^3 -3x^2 +9x)/3

f'(x) = (-4x^3 - 15x^2 -6x + 9)/3

We know there's f'(-3)=0 so x+3 must be a factor here,

f'(x) = (x + 3) (-4x^2 - 3x + 3)

We get stationary points when x = -3 or

x = (-1/8)( 3 ± √(9 - 4(-4)(3))) =  (-3 ± √57)/8  about -1.3 and 0.6 which are a local minimum and maximum respectively.

f''(x) = (-12x^2 - 30x -6)/3 = -4x^2 - 10x - 2

f''(-3) = -4(9)+ 30 - 2 = -8

Concave Down, Negative.   (-3,0) is a local maximum.

f''((-3 - √57)/8) = -4(-1.3)^2 - 10(-1.3) - 2 = 4.24

Concave up, positive, a CUP

(-3 - √57)/8, f((-3 - √57)/8) ) is a minimum.

f''((-3 + √57)/8) = -4(.6)^2 - 10(.6) - 2 = -9.44

CDN, ( ((-3 + √57)/8), f((-3 + √57)/8) ) is a maximum.

I didn't evaluate f((-3 ±√57)/8) which are around -3 and 1 but I leave that calculation to you.

6 0
3 years ago
a parabola has x intercepts of -1 and 3 it passes through the point (1,6) write the equation if the parabola
matrenka [14]

\boxed{f(x)=-\frac{3}{2}x^2+3x+\frac{9}{2}}

<h2>Explanation:</h2>

The Standard Form of the equation of a parabola is given by the form:

y=ax^2+bx+c

As y is a function of x, then we can write:

y=f(x)=ax^2+bx+c \\ \\ a, \ b, c \ Real \ Coefficients

Also, we can write f(x) in factored form as:

f(x)=a(x-x_{1})(x-(x_{2}) \\ \\ x_{1} \ and \ x_{2} \ Are \ the \ roots

In this case:

x_{1}=-1 \\ \\ x_{2}=3

So:

f(x)=a(x-(-1))(x-3) \\ \\ f(x)=a(x+1)(x-3)

We also know that the parabola passes through the point (1,6):

f(1)=6=a(1+1)(1-3) \\ \\ Isolating \ a: \\ \\ 6=a(2)(-2) \\ \\ 6=a(-4) \\ \\ a=-\frac{6}{4} \\ \\ a=-\frac{3}{2}

Finally, the equation of the parabola is:

f(x)=-\frac{3}{2}(x+1)(x-3)

Or applying Distributive Property:

f(x)=-\frac{3}{2}\left(x^2-2x-3\right) \\ \\ \boxed{f(x)=-\frac{3}{2}x^2+3x+\frac{9}{2}}

<h2>Learn more:</h2>

Piecewise-defined function: brainly.com/question/12169258

#LearnWithBrainly

3 0
3 years ago
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