What is the remainder of 1025 divided by 68

Mathematics

2 answers:

Nikitich [7]3 years ago

8 0

the full answer would be 15.07 the reminder of it would be the .07

vaieri [72.5K]3 years ago

6 0

Answer:

Step-by-step explanation:

We are given that two numbers are 1025 and 68

We have to find the remainder when 1025 is divided by 68

We have 1025=Dividend

68=Divisor

The relation between dividend, divisor and quotient is given by

Dividend= $divisor\times quotient+remainder$

a=bq+r

where a= dividend, b=Divisor, q=Quotient,r=Remainder

$1025=68\cdot (15)+5$

Compare the values then , we get

$a=1025,b=68,q=15,r=5$

Hence, remainder =5

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Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

sergejj [24]

Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let j be the inverse function of h.

Function h is given by:

$\displaystyle h(x) = y = 3x-2$

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

$\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}$

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

And:

$\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$