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3 years ago

The unit digit in the square of 1294 is_______.

Mathematics

2 answers:

DaniilM [7]3 years ago

8 0

Answer:

Step-by-step explanation:

Furkat [3]3 years ago

3 0

The answer is 6 as unit digit of number is 4 when you square you will get the unit digit 6

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If a+b = 7, and a² +b²=25 then ab = ?

Rama09 [41]

a2+b2=25

or, (a+b)^2-2ab=25

or, (7)^2-2ab=25 [a+b=7]

or, 49-25=2ab

or, 24/2=an

•°• ab=12....

3 0

3 years ago

For which function is f(x) equal to f^1(x) ( answer choices in picture )

Sonja [21]

Answer:

C. $f(x)=\frac{x+1}{x-1}$

Step-by-step explanation:

Let's find the inverse of each of the given options.

Option A:

$f(x)=\frac{x+6}{x-6}\\y=\frac{x+6}{x-6}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+6}{y-6}$

Rewrite in terms of 'y'. This gives,

$x(y-6)=y+6\\xy-6x=y+6\\xy-y=6x+6\\y=\frac{6x+6}{x-1}$

The given function $y=\frac{6x+6}{x-1}\ne y=\frac{x+6}{x-6}$

So, option A is incorrect.

Option B:

$f(x)=\frac{x+2}{x-2}\\y=\frac{x+2}{x-2}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+2}{y-2}$

Rewrite in terms of 'y'. This gives,

$x(y-2)=y+2\\xy-2x=y+2\\xy-y=2x+2\\y=\frac{2x+2}{x-1}$

The given function $y=\frac{2x+2}{x-1}\ne y=\frac{x+2}{x-2}$

So, option B is incorrect.

Option C:

$f(x)=\frac{x+1}{x-1}\\y=\frac{x+1}{x-1}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+1}{y-1}$

Rewrite in terms of 'y'. This gives,

$x(y-1)=y+1\\xy-x=y+1\\xy-y=x+1\\y=\frac{x+1}{x-1}$

The given function $y=\frac{x+1}{x-1}\ equals\ y=\frac{x+1}{x-1}$

So, option C is correct.

Option D:

$f(x)=\frac{x+5}{x-5}\\y=\frac{x+5}{x-5}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+5}{y-5}$

Rewrite in terms of 'y'. This gives,

$x(y-5)=y+5\\xy-5x=y+5\\xy-y=5x+5\\y=\frac{5x+5}{x-1}$

The given function $y=\frac{5x+5}{x-1}\ne y=\frac{x+6}{x-6}$

So, option D is incorrect.

Therefore, only option C is correct.

7 0

3 years ago

jen uses 8.2 of blue paint and white paint to paint her bedroom walls. 4/5ths of this amount is blue paint, and the rest is whit

lara31 [8.8K]

Answer:

The amount of white paint Jen used to paint the walls in her room is:

1.64 pints.

Step-by-step explanation:

To solve the exercise you only have to pay attention to the statement, in the section that says that 4/5 parts of the total painting is blue, therefore, if 1 is the total painting, you must do a subtraction:

1 - 4/5 = 1/5

Since the remaining white paint is 1/5 of the total, you have two ways to solve the exercise: multiply the total paint (8.2 pints) by 1/5 or divide the number by 5, as shown below:

Amount of white paint = 8.2 pints * (1/5) = 1.64 pints.
Amount of white paint = 8.2 pints / 5 = 1.64 pints.

As you can see, the two methods provide a value of 1.64 pints, which corresponds to 1/5 of the total paint and is the amount of white paint used.

5 0

3 years ago

The area of a rectangle is 229.2 m2. If the length is 15 m, what is the perimeter of the rectangle

igor_vitrenko [27]

Answer:

$\large\boxed{P=60.56\ m}$

Step-by-step explanation:

The formula of an area of a rectangle:

$A=lw$

l - length

w - width

We have

$A=229.2\ m^2\\\l=15\ m$

Substitute:

$15w=229.2$ divide both sides by 15

$w=15.28\ m$

The formula of a perimeter of a rectangle:

$P=2(l+w)$

Substitute:

$P=2(15+15.28)=2(30.28)=60.56\ m$

8 0

3 years ago

Can the polynomial equation have exactly 1 real solution, including any repeated solutions? (Use the Fundamental Theorem of Alge

Kryger [21]

yes, there are infinitety many polynomial that have exactly one real root just like your example, to determine the real root first let the real root is a, and the complex roots are b±ic the polynomial satisfy

-9x³ + 19x² + 17 = -(x - a)(x - b - ic)(x - b + ic)

9x³ - 19x² - 17 = (x - a)(x - b - ic)(x - b + ic)

5 0

3 years ago

The unit digit in the square of 1294 is_______.​

The unit digit in the square of 1294 is_______.