Rewrite (3x6) - (3x3) using distributive property

A and B because with the other three, they simplify to something else.

The function is not one-to-one function, hence the inverse doesn't exist for the whole domain of the function. But if we restrict the domain to [tex]x\in(-\infty,0][/tex] or [tex]x\in[0,\infty)[/tex], then we can give the inverse.

[tex]f(x)=x^2-4\\\\y=x^2-4\\\\x^2=y+4\\\\x=\sqrt{y+4} \vee x=-\sqrt{y+4}\\\\f^{-1}(x)=\sqrt{x+4}\vee f^{-1}(x)=-\sqrt{x+4}[/tex]

So, when [tex]D_{f(x)}:x\in(-\infty,0][/tex], the inverse is [tex]f^{-1}(x)=-\sqrt{x+4}[/tex] and when [tex]D_{f(x)}:x\in[0,\infty)[/tex], the inverse is [tex]f^{-1}(x)=\sqrt{x+4}[/tex].

The inverse of the function f(x) = x^2 - 4 is found by switching the x and y variables and solving for y. Because y is being squared, there are two solutions: y = ±sqrt(x + 4).

The inverse of a function f(x) is found by switching the x and y variables and solving for y. For the function f(x) = x^2 - 4, let us swap x and y, it becomes x = y^2 - 4. Next, solve for y. However, because y is being squared, there will be two solutions, one for the positive square root and other for the negative square root. Therefore, the inverse of the function f(x) = x^2 - 4 is y = ±sqrt(x + 4).

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Final answer:

The axis of symmetry of a parabola can be found by the formula x = -b/(2a), which uses the coefficients of the quadratic equation. This line runs vertically through the vertex of the parabola.

Explanation:

Finding the axis of symmetry for a quadratic equation based on its graph involves identifying the line that divides the parabola into two mirror images. The axis of symmetry is always a vertical line and can be found by looking at the vertex (the highest or lowest point) of the parabola. The equation for the axis of symmetry is x = h, where h is the x-coordinate of the vertex. If the quadratic equation is in the standard form y = ax² + bx + c, the axis of symmetry can be calculated using the formula x = -b/(2a).

For instance, if we have a quadratic equation like y = 2x² - 4x + 1, we can find the axis of symmetry by using the formula with a = 2 and b = -4 which gives us x = -(-4)/(2*2) = 1. Therefore, the axis of symmetry for this parabola is x = 1.

First let's write it out with just numbers

6×[tex]10^{5}[/tex]

Now solve!

Solve exponent first

10^5 = 100,000

Now multiply

6 x 100,000 = 600,000

600,000 is your answer

The number 6 x 10^5 in standard form equates to 600000. The conversion involves moving the decimal place the same number of steps as the power of ten indicates

The conversion of 6 x 10 to the power of 5 into standard form involves interpreting the exponent as the number of places to shift the decimal point. In this case, the decimal point will be moved five places to the right.

Thus, 6 x 10 is equivalent to 600000 in standard form.

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Answer:

Kim is 24 and her sister is 12.

Step-by-step explanation:

a) Xx2+X

I used the variable X because that represents Kim's sisters age, which you need to know in order to find out Kim's age. To get Kim's sisters age use a guess and check table or pick numbers until you get to the correct answer.

b) 12x2=24

24+12=36

My solution is Kim is 24 and her sister is 12.

Given

The expression is given in the question

[tex]=(x^{\frac{4}{3}}\times\ x^{\frac{2}{3}})\ ^{\frac{1}{3}}[/tex]

Find the expression is equivalent to the above expression.

To proof

As expression is given in the question

[tex]=(x^{\frac{4}{3}}\times\ x^{\frac{2}{3}})\ ^{\frac{1}{3}}[/tex]

By using the properties

product of powers property tells us that when you multiply powers with the same base you just have to add the exponents.

i.e

[tex]x^{a} .x^{b} = x^{a +b}[/tex]

Now using this in above

we get

[tex]=x^{\frac{6}{3}\times\frac{1}{3}}[/tex]

Also by using the property

[tex](x^{a} )^{b} = x^{ab}[/tex]

We get[tex]=x^{\frac{6}{9}}[/tex]

Therefore expression becomes

[tex]= x^{\frac{2}{3}}[/tex]

Hence proved

Answer:

155.82 miles

Step-by-step explanation:

You multiply 6 and 25.97 to get your answer.

the answer is 155.82 miles

Hey there!

The only thing we can do to simplify this expression is to combine 5a and 2a, the two like terms in the expression.

Our final answer is 7a + 9.

Hope this helps!

We are given

Marta is making a quilt in the shape of a square

The length of one edge of the quilt is 2g^2h^3

so, we get

[tex]s=2g^2h^3[/tex]

now, we know that

area of square = length *length

so, we get

[tex]A=s^2[/tex]

now, we can plug values

and we get

[tex]A=(2g^2h^3)^2[/tex]

we can simplify it

[tex]A=2^2(g^2)^2(h^3)^2[/tex]

[tex]A=4g^4h^6[/tex].............Answer

2x-3=4x+8     Equation

-3=6x+8         Add 2x to opposite side

-11=6x            Subtract 8.

x= -6/11          Answer

Answer:

500,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

if the hundred is 500+ round it up...if smaller than 500 round down. (:

i believe your answer is c. because the x value goes first in a coordinate. hope this helps!

Answer:

0.24 with a line over the 24. The line means that it is repeating.

Explanation,

There is not much to explain it's just simple divison.

The correct answer is 4a^2 + 3ab

In order to find this, we can write the equation out as described and then follow the order of operations.

3a^2 - 2ab + 3b^2 - (-a^2 - 5ab + 3b^2) ----> Distribute the negative

3a^2 - 2ab + 3b^2 + a^2 + 5ab - 3b^2 ----> Combine like terms

4a^2 + 3ab

The subtraction -a² - 5ab + 3b² from 3a² -2ab + 3b² is -a(4a + 3b)

Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.

Simplification is to make something easier to do or understand and to make something less complicated.

Given

-a² - 5ab + 3b² and 3a² -2ab + 3b² are the two expression.

-a² - 5ab + 3b² from 3a² -2ab + 3b², we will have

-a² - 5ab + 3b² - (3a² -2ab + 3b²)

On simplifying,

-a² - 5ab + 3b² - 3a² + 2ab - 3b²

-4a² - 3ab

-a(4a + 3b)

Thus , the subraction is -a(4a + 3b).

More about the subtraction link is given below.

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The lines are Perpendicular

Perpendicular lines are lines that directly bisect each other, forming 90° angles

~Rise Above the Ordinary

Hi, I'n Jenny and I'm a mathematician! I'd love to help you! :)

"which term describes lines that intersects at a 90 degree angle? "

My answer: perpendicular lines

Attached is more info on math lines

Message from ExperimentsDIYS:

Our team aims to please and if you have any question regarding your topic, we are here to help! We know that your education is very important. <3

(1/4)*(4*x+15) = 24 // - 24

(1/4)*(4*x+15)-24 = 0

1/4*(4*x+15)-24 = 0

1/4*(4*x+15)-24 = 0

x-81/4 = 0

x-81/4 = 0

x-81/4 = 0 // + 81/4

x = 81/4

x = 81/4

hope I helped

Solution

Leased cost for 3 years  = $3000 + 250 *36                    [ 3 years = 36 months]

= 3000 + 9000

Leased the car for 3 years cost you = $12,000

The residual value = $10,000

Assume that you bought the car and used for 3 years and sold for $10,000

Cost of the car = $24,000

Sold after 3 years for $10,000

Your expense in 3 years = $24,000 - 10, 000 = $14,000

By comparing these two options, leasing the car will benefit you since it cost only $12,000.

Therefore, lease car is less expense.

The cost for buying the car and selling it after three years would be $14,000.

That is the answer. :)

Thank you.

Perimeter of a rectangle can be represented by 2* length + 2 * width

We can represent the width with the variable x

We can represent the length by the expression 3x-1

So, now we can make a forumla and solve

2(3x-1) + 2(x) = 30

6x-2+2x = 30

8x = 32

x = 4 is the width of the rectange.

Now we find the length

3(4)-1

11 = Length

The width of the rectangle is 4 inches and its length is 11 inches.

A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

The Perimeter of rectangle is -

P = 2(x + y)

The Area of rectangle is -

A = xy

We can write -

P = 2x + 2y

Py = 2xy + 2y²

Py = 2A + 2y²

2y² - Py + 2A = 0

y = ± (P² - 16A)/4

Given is a rectangle that has a perimeter of 30 inches. Its length is one less than three times its width

Assume the length to be [x] inches and width be [y] inches. Then, we can write -

[x] = 3[y] - 1

and

2(x + y) = 30

2(3y - 1 + y) = 30

2(4y - 1) = 30

8y - 2 = 30

y = 4 inches

then -

x = 12 - 1

x = 11 inches

Hence, the width of the rectangle is 4 inches and its length is 11 inches.

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Solution:

The outlier is 17

With Outlier

4 + 5 + 5 + 7 + 9 + 17 = 47

47 / 6 = 7.83333333...

Without Outlier

4 + 5 + 5 + 7 + 9 = 30

30 / 5 = 6

Mean With Outlier - 7.8333...

Mean Without Outlier - 6

Answer - 3. It will decrease

Answer:

17

Step-by-step explanation:

Hi there!!

Here is the answer =

Step 1 : simplify 10^2 to 100

Step 2 : 35.5 ÷100

Answer confirmed = 0.355

Hope this helps you!!!

Final answer:

Dividing 35.5 by 10 to the power of 2 (which is 100) results in 0.355, achieved by moving the decimal point two places to the left.

Explanation:

To calculate 35.5 divided by 102, you need to understand the concept of exponents. The expression 102 means 10 multiplied by itself twice, which equals 100.

Now, dividing 35.5 by 100, you move the decimal point two places to the left because dividing by a power of 10 shifts the decimal point to the left for each zero in that power. Therefore, when 35.5 is divided by 102 it will be equal 0.355.

The amount is written in improper fraction.

To know, which amount is greatest, we will convert these improper fraction to proper decimal form values by division method and then we will compare the values.

A. [tex]\frac{33}{4}=8.25[/tex]

B. [tex]\frac{22}{3}=7.33[/tex]

C. [tex]\frac{78}{9}=8.66[/tex]

D. [tex]\frac{43}{5}=8.60[/tex]

Hence, the greatest amount is option C. [tex]\frac{78}{9}[/tex]

Assume that the width=w

22=2w+2(w+1)

22=2w+2w+2

22=4w+2

20=4w

w=5

The dimensions are 4 by 5.

The dimensions of the rectangle photograph are 5.5 inches (width) by 6.5 inches (length), calculated by setting the given perimeter equal to twice the sum of the length and the width, and then solving for the width and length.

The perimeter of a rectangle is the sum of all its sides. Given that the perimeter of the photograph is 22 inches, you can work out the length and width using algebra. Let's denote the width of the photograph as 'x' (in inches). Thus, the length is 'x + 1' since it is one inch more than the width. Since the rectangle has two equal lengths and two equal widths, its perimeter can be represented as 2*(length + width) or 2*(x + x + 1). Setting this equal to 22 (the perimeter), we get 2*(2x + 1) = 22. Solving for 'x' gives us the width, which is 5.5 inches. The length is therefore 6.5 inches, being 1 inch more than the width. Therefore, the dimensions of the rectangle are 5.5 inches by 6.5 inches.

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-2x^3 - 2x^2 + 12x

Because we can pull out a common factor, we'll do that first to simplify the expression.

-2x(x^2 + x - 6)

Now, let's see if we can split the middle term.

Display factors of -6.

-6 * 1

-1 * 6

-3 * 2

3 * -2 (these digits satisfy the requirements for splitting the middle term)

Split the middle term.

-2x(x^2 + 3x - 2x - 6)

Group terms in pairs of two.

-2x((x^2 + 3x) - (2x - 6))

Factor each binomial.

-2x((x(x + 3)) - (2(x + 3)))

Rearrange the terms.

-2x(x - 2)(x + 3) is the fully factored form of the provided trinomial.  

The factorization of the trinomial -2x^3-2x^2+12x includes first factoring out the common factor -2x, and then further factoring of the trinomial within the parenthesis results in the final factorization as -2x(x-2)(x+3).

The trinomial in this question is -2x^3-2x^2+12x. The process we use to factor this trinomial would be to first factor out the greatest common factor (GCF) for all the terms. In this case, the GCF is -2x.

So, if we factor out -2x, we get: -2x(x^2+x-6).  We can continue to factor the trinomial (x^2+x-6) inside the parenthesis then. We find that it factors to (x-2)(x+3).

Thus, the final factorization of the original trinomial is -2x(x-2)(x+3).

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3 + (-7)

yyyyyyyyyyyyyyyy

The addition form will be equal to 3 + (-7).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

Given that:-

= 3 − 7

The additional form of the above expression will be:-

=3 + (-7)

Therefore the addition form will be equal to 3 + (-7).

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12 - 3 = 9

So Nemili has 9 more red triangles than blue triangles.

Hope this Helps!!

Hey there!:

- 10 e + 15 = 95 - 30 e

subtract  15 from both sides:

- 10 e + 15 - 15 = 95 - 30 e - 15

Simplify :

- 10 e  = - 30 e + 80

Add 30 e to both sides:

- 10 e + 30 e  = - 30 e + 80 + 30 e

Simplify:

20 e = 80

e = 80 / 20

e = 4

hope that helps!