How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed?

Anja simplified the expression StartFraction 10 x Superscript negative 5 Baseline Over Negative 5 x Superscript 10 Baseline EndF

Gwar [14]

The mistake that Anja made during the simplification of the considered expression is given by: Option C: She subtracted the coefficients instead of dividing them

<h3>What are coefficients?</h3>

Constants who are in multiplication with variables are called coefficients of those variables.

For example, in $10x^2$ we have 10 as coefficient of $x^2$

Those variables who have got no visible coefficient has 1 as their coefficient. Thus, $x^2$ has got its coefficient as 1. It is true since 1 multiplied with any number is that number itself.( $x^2 = 1 \times x^2$ )

<h3>What are some basic properties of exponentiation?</h3>

If we have $a^b$ then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

Exponentiation(the process of raising some number to some power) have some basic rules as:

$a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c$

For the considered situation, the expression that Anja is simplifying is:
$\dfrac{10x^{-5}}{-5x^{10}}$

Anja simplified it to $\dfrac{15}{x^{15}}$

She performed operations with variable 'x' correctly since

$\dfrac{x^{-5}}{x^{10}} = \dfrac{1}{x^5} \times \dfrac{1}{x^{10}} = \dfrac{1}{x^{15}}$

But coefficients will also get divided. Instead of dividing 10 by -5, she subtracted them (as 10 - (-5) = 10 + 5 = 15)

This was her mistake.

The correct simplification would be: $\dfrac{10x^{-5}}{-5x^{10}} = \dfrac{10}{-5} \times \dfrac{x^{-5}}{x^{10}} = -2 \times \dfrac{1}{x^{15}} = \dfrac{-2}{x^{15}} = -2x^{-15}$

Thus, the mistake that Anja made during the simplification of the considered expression is given by: Option C: She subtracted the coefficients instead of dividing them

Learn more about exponent and bases here:

brainly.com/question/847241

4 0

2 years ago

the door frame has measurements of 3 feet by 8 feet. What is the length of the largest table that can be brought in the house on

goldenfox [79]

8 ft. I’m not really sure though sorry

7 0

3 years ago

Find the value of x.

Reptile [31]

Answer:

3°

Step-by-step explanation:

20x + 5 = 9x - 2 + 40

Exterior angle is equal to the sum of interior angles

20x + 5 = 9x + 38

11x = 33

x = 3

8 0

3 years ago

Reflection across y = x<br> what does this mean

Tatiana [17]

Rule= (x,y) is now (y,x) so coordinates of (5,4) now would be (4,5). this is the rule for y=x problems so you take the coordinates and flip them for every point.

3 0

3 years ago

Solve the system by substitution math help. Please show every step.

Arlecino [84]

The idea here is to combine the equations into one in only one variable. The last equation is in only x and z so lets sub out y in the second.

-x - y - z = -8
8 - x - z = y

Substitute y with (8 - x - z) into the next equation.
-4x + 4(8 - x - z) + 5z = 7
-4x + 32 - 4x - 4z + 5z = 7
-8x + 32 + z = 7
The variable z is easiest to get alone; use that as substitution in the last equation.
z = 7 + 8x - 32
z = 8x - 25

Substitute z with (8x - 25)
2x + 2(8x - 25) = 4
2x + 16x - 50 = 4
18x = 4 + 50
18x = 54
x = 3

So use x = 3 in that last equation to find z.

2(3) + 2z = 4
6 + 2z = 4
2z = 4 - 6
2z = -2
z = -1

Now, use both x = 3 and z = -1 to find the final variable y.

-3 - y - (-1) = -8
-3 - y + 1 = -8
-2 - y = -8
-y = -8 + 2
-y = -6
y = 6

Solutions x,y,z = ( 3, 6, -1)

5 0

3 years ago