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3 years ago

In Exercise, use the properties of exponents to simplify the expression. 32(3- 2)

Mathematics

1 answer:

zavuch27 [327]3 years ago

4 0

Answer:

Step-by-step explanation:

We have given expression $3^2\times 3^{-2}$

We have to simplify the expression with use of property of exponent

According to property of exponent when two functions are multiplied with each other having exponent then their exponent are added to each other

So $3^2\times 3^{-2}=3^{2-2}=3^0$

Now according to exponent property if 0 is the exponent of any number then its result will be 1

So $3^0=1$

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What is necessary to write a number in scientific notation? Select all that apply. A. One factor is greater than 10. B. The numb

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Answer:

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3 years ago

Can someone please help me! I don’t understand how to do this!

Nutka1998 [239]

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Answer:

a. 4x^2 +16x -48 = 4x^2 +16x -48

b. -3x^2 +12x +36 = -3x^2 +12x +36

c. x^2 +12x +35 = x^2 +12x +35

Step-by-step explanation:

In general, you would prove this by transforming one of the expressions into the other. The easiest would be to transform the factored form into the vertex form, perhaps, as this would spare you trying to explain the magic of factoring.

Alternatively, you can transform both expressions into the same (standard) form. I believe that will be the easiest of all.

The product of two binomials is ...

(x +a)(x +b) = x(x +b) +a(x +b) = x^2 +bx +ax +ab

(x +a)(x +b) = x^2 +(a+b)x +ab . . . . after collecting terms

The square of a binomial is the same thing, but with b=a, so ...

(x +a)^2 = x^2 +2a +a^2

Using these forms, we can avoid showing all of the intermediate "work" of making the desired transformations.

a. 4(x -2)(x +6) = 4(x +2)^2 -64

4(x^2 +4x -12) = 4(x^2 +4x +4) -64 . . . . . expanding the products

4x^2 +16x -48 = 4x^2 +16x +16 -64 . . . . using the distributive property

4x^2 +16x -48 = 4x^2 +16x -48 . . . . . collect terms; expressions are equal

b. -3(x +2)(x -6) = -3(x -2)^2 +48

-3(x^2 -4x -12) = -3(x^2 -4x +4) +48

-3x^2 +12x +36 = -3x^2 +12x -12 +48

-3x^2 +12x +36 = -3x^2 +12x +36

c. (x +5)(x +7) = (x +6)^2 -1

x^2 +12x +35 = x^2 +12x +36 -1

x^2 +12x +35 = x^2 +12x +35

6 0

3 years ago

Read 2 more answers

1.Which system of linear inequalities is graphed? <br>

muminat

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3 years ago

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What is the IQR of 11,11.5,10.5,17,14.5,18,17,19

Vika [28.1K]

Ascending order :-

10.5 , 11 , 11.5 , 14.5 , 17 , 17 , 18 , 19

Median,

={(n/2)th + (n/2 +1)th}/2

={(4)th + (5)th}/2

=(31.5)/2

=15.75

I.Q.R.,

Median of lower half,

={(n/2)th + (n/2 +1)th}/2

={(2)th + (3)th}/2

=(22.5)/2

= 11.25

Median of upper half,

={(n/2)th + (n/2 +1)th}/2

={(2)th + (3)th}/2

=35/2

=17.5

I.Q.R. = 17.5 - 11.25 = 6.25

HOPE THIS WILL HELP YOU

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3 years ago

Read 2 more answers

Consider the arithmetic sequence:

Leona [35]

Answer:

If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is $\mathbf{d(n)=8+2n\:for\:n>1}$

Option D is correct option

Step-by-step explanation:

We are given the arithmetic sequence:

10, 12, 14, 16, ...

If n is an integer, which of these functions generate the sequence?

We need to find the nth term for the given sequence

The nth term for arithmetic sequence will be: $a_n=a_1+(n-1)d$

where aₙ is nth term, a₁ is first term and d is common difference

Looking at the sequence a₁ = 10 and d = 2

So, nth term will be:

$a_n=a_1+(n-1)d\\a_n=10+(n-1)2\\a_n=10+2n-2\\a_n=8+2n$

So, nth term is: $a_n=8+2n$

In the options below, the only correct answer is option D. so, we can write nth term as: $d(n) = 8 + 2n\: for\: n > 1$

So, If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is $\mathbf{d(n)=8+2n\:for\:n>1}$

Option D is correct option

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3 years ago

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