The value of a two-digit number exceeds twice the sum of its digits by 19. the tens digit is two less than the units digit. find the number.

Answer with Step-by-step explanation:

Let the ones digit of the number be y

and tens digit of the number be x.

The tens digit is two less than the units digit.

i.e. x=y-2

The value of the number exceeds twice the sum of its digits by 19.

i.e. 10x+y=2(x+y)+19

10(y-2)+y=2(y-2+y)+19

10y-20+y=2(2y-2)+19

11y-20=4y-4+19

11y-4y=20-4+19

7y=35

dividing both sides by 7, we get

y=5

Putting value of y in x=y-2, we get

x=3

10x+y=10×3+5

         =35

Hence, the two digit number is:

35

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9