Which of the following sets contain all roots of the polynomial

she uses 1/12 of the paper

She uses ¹/₁₂ of the sheet of paper to make the flower

Order of Operations in Mathematics follow this following rule :

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem!

Let :

Total Area of Paper = X

Given:

Mrs. Sheppard cuts 1/2 of a piece of construction paper

[tex]\texttt{Cutting Piece Area of Paper} = \frac{1}{2} \times \texttt{Total Area of Paper}[/tex]

[tex]\texttt{Cutting Piece Area of Paper} = \frac{1}{2} \times X[/tex]

[tex]\texttt{Cutting Piece Area of Paper} = \boxed {\frac{1}{2} X}[/tex]

She uses 1/6 of the piece to make a flower

[tex]\texttt{Area of Paper for Making Flower} = \frac{1}{6} \times \texttt{Cutting Piece Area of Paper}[/tex]

[tex]\texttt{Area of Paper for Making Flower} = \frac{1}{6} \times \frac{1}{2} X[/tex]

[tex]\texttt{Area of Paper for Making Flower} = \frac{1 \times 1}{2 \times 6}X[/tex]

[tex]\texttt{Area of Paper for Making Flower} = \boxed {\frac{1}{12}X}[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent

The expression simplifies to[tex]\( \left(\frac{2}{3}\right)^8 \), representing \( \frac{2^8}{3^8} \), or \( \frac{256}{6561} \).[/tex]

Sure, here's a detailed stepwise solution with explanation:

1. **Understand the problem**: We're asked to simplify the expression  [tex]\( \left(\frac{2}{3}\right)^2 \cdot \left(\frac{2}{3}\right)^6 \).[/tex]

2. **Apply the exponent property**: According to the exponent property [tex]\(a^m \cdot a^n = a^{m+n}\),[/tex] when multiplying two expressions with the same base, we add their exponents.

3. **Calculate the exponents**:

  - The first expression  [tex]\( \left(\frac{2}{3}\right)^2 \) has an exponent of 2. - The second expression \( \left(\frac{2}{3}\right)^6 \)[/tex] has an exponent of 6.

4. **Add the exponents**:

[tex]- \(2 + 6 = 8\).[/tex]

5. **Combine the expressions**:

  - By applying the exponent property, we get  [tex]\( \left(\frac{2}{3}\right)^{2+6} = \left(\frac{2}{3}\right)^8 \).[/tex]

6. **Final result**:

  - The simplified expression is [tex]\( \left(\frac{2}{3}\right)^8 \), which represents \( \frac{2^8}{3^8} \).[/tex]

  - This can also be expressed as [tex]\frac{256}{656\1} \),[/tex] where 256 is the numerator and 6561 is the denominator.

7. **Explanation of the result**:

  - The simplified expression represents the result of raising  [tex]\( \frac{2}{3} \)[/tex] to the power of 8, which is obtained by multiplying the expression by itself 8 times.

  - It can be interpreted as the fraction [tex]\( \frac{256}{6561} \)[/tex] , which is the result of raising 2 to the 8th power in the numerator and 3 to the 8th power in the denominator.

C

the equation of a parabola in ' vertex form ' is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

the vertex of g(x) = (1, - 3) and a = 1

g(x) = (x - 1)² - 3

[tex]f(x)=4x-11\\\\\text{Put the value of x = 5 to the equation of the function}\\\\f(5)=4(5)-11=20-11=9[/tex]

1/4n - 7 = -1

Hope this helps and was fast enough!

The phrase 'Seven less than one-fourth of a number is -1' translates into the mathematical equation: 1/4x - 7 = -1.

The subject of your question is Mathematics, and based on the content, it seems like it's geared toward a Middle School level. 'Seven less than one-fourth of a number is -1' can be translated into the equation: 1/4 x - 7 = -1, where 'x' represents the number in question.

To achieve this, the phrase 'one-fourth of a number' translates into 1/4x in mathematics and 'seven less' means you subtract seven from that quantity (hence, -7). Hence, the equation becomes '1/4x - 7'. This equals -1, according to your statement, so the final equation is 1/4x - 7 = -1.

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1. ∠1 ≅ ∠3                                              1. given

  ∠1 and ∠6 are supplementary angles

  ∠3, ∠4, and ∠5 are supplementary angles

2. m∠1 = m∠3                                        2. definition of congruency

3. m∠1 + m∠6 = 180°                             3. definition of supplementary angles

   m∠3 + m∠4 + m∠5 = 180°

4.  m∠3 + m∠4 + m∠5 = m∠1 + m∠6     4. transitive property

5.  m∠3 + m∠4 + m∠5 = m∠3 + m∠6     5. substitution property

6.  m∠4 + m∠5 = m∠6                             6. subtraction property of equality

S+ST = RT  

3x+1 + 2x-2 = 64  

5x = 65  

x = 13

To divide x^3 - 3x^2 by x - 2, use long division. The quotient is x^2 - x - 4.

To divide x^3 - 3x^2 by x - 2, we can use long division. Here are the steps:

Therefore, the quotient of x^3 - 3x^2 divided by x - 2 is x^2 - x - 4.

The value of [tex]\( k \)[/tex] is 2.

Which gives a remainder of 0, indicating [tex]\( x - 2 \)[/tex] is a factor of the polynomial [tex]\( x^3 - 3x^2 - 10x + 24 \)[/tex]. The complete synthetic division process for [tex]\( k = 2 \)[/tex] would then be:

 2 |  1   -3   -10   24

 |      2    -2   -24

   ---------------------

     1   -1   -12    0

The quotient of the division is [tex]\( x^2 - x - 12 \)[/tex] with a remainder of 0.

complete question given below:

The distance between the spokes of the wheel will be πr / 8 units.

Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

A wheel has 16 spokes. Then the angle between the two spokes is calculated as,

θ = 2π / 16

Let 'r' be the radius of the wheel. Then the distance between the spokes will be given as,

Arc = ((2π / 16)/2π) 2πr

Arc = 2πr / 16

Arc = πr / 8

The distance between the spokes of the wheel will be πr / 8 units.

More about the arc length of the sector link is given below.

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Answer:

True.

Step-by-step explanation:

Consecutive square numbers can be written as:

1^2, 2^2, 3^2, 4^2, 5^2 ...

The sequence of the numbers being squared in odd, even, odd, even...

Squaring an odd number yields an odd. Squaring an even yields an even. The difference between an odd and even number is always odd. Since consecutive perfect squares are odd, even, odd... then the difference is always odd.

Answer:

The answer is: True.

Step-by-step explanation:

A perfect square number in math is an integer that can be expressed as the product of a number by itself.

The difference between each square and consecutive number, if it starts with 0, is all odd numbers, in ascending order.

The answer is: True.

The number zero (0) belongs to the following sets:

5/6+2 3/4

= 10/12 + 2 9/12

= 2 19/12

= 3 7/12

Hope that helps

Mixed Number Form:[tex]3\frac{7}{12}[/tex]

Step by step: [tex]\frac{5}{6} + 2\frac{3}{4}[/tex]

= [tex]\frac{5}{6} + \frac{11}{4}[/tex]

= [tex]\frac{43}{12}[/tex]

Answer: [tex]3\frac{7}{12}[/tex]

It will be greater, since there are 16 ounces in a pound. You can say that the new amount will be 16 times the amount of pounds there is.

When you convert pounds to ounces, the number of ounces will always be greater. This is due to the fact that 1 pound equals 16 ounces.

If you convert pounds to ounces, the number of ounces will be greater than the number of pounds. This is because 1 pound equals 16 ounces. For instance, if you have 2 pounds, and you want to convert it into ounces, you would multiply the 2 pounds by 16 (the conversion factor), which would give you 32 ounces. Therefore, the number of ounces is always going to be greater than the number of pounds when you're converting pounds into ounces.

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We are given

nine less than three times a number is forty

we know that

we always start our order of operation from left to right

This sentence represents equality

Let's assume that number as 'x'

Left side is :

3x-9

Right side is :

40

so, we can write as

[tex]3x-9=40[/tex].............Answer

Answer:

6.875

Step-by-step explanation:

We have been given that after a storm Michael measured 6 7/8 inches of snow. We are asked to show this amount  as a decimal.

We can represent our improper fraction as a whole and a part as:

[tex]6\frac{7}{8}=6+\frac{7}{8}[/tex]

Let us convert [tex]\frac{7}{8}[/tex] as a decimal.

[tex]6+\frac{7}{8}=6+0.875=6.875[/tex]

Therefore, the amount as a decimal would be 6.875.

Answer:

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

It is rational because it isnt a decimal or fraction

Pls rate me 5 stars and thank me :D

Answer:

Amount invested at 7% = 16000

Amount invested at 9% = 12000

Step-by-step explanation:

Let x be the amount invested at 7% and y be the amount invested at 9%.

Since the total amount invested is $28000, therefore, we can set up the first equation as:

[tex]x+y=28000[/tex]

Secondly, we are give that sum of two investments is $2200. Therefore, we can write the second equation as:

[tex]0.07x+0.09y=2200[/tex]

Now we need to solve these two equations to get the values of x and y.

First of all, we multiply the second equation with 100 in order to get rid of decimal values.

[tex](0.07x+0.09y)*100=2200*100\\7x+9y=220000[/tex]

Let us use substitution method here. First of all we will solve for y from first equation and plug that into second equation.

[tex]y=28000-x[/tex]

[tex]7x+9(28000-x)=220000\\7x+252000-9x=220000\\-2x=-32000\\x=16000[/tex]

Therefore, amount invested at 7% is $16000 and amount invested at 9% is 28000-16000=$12000.

The population of a town y years after 1970 is;

31,787 + 1,735y.

From the results above;

y represents the number years

So the population increased by 1,735 people each year after 1970.

Population after y years = 31,787 + 1,735y

The correct choice is 'A.'

The answer to this equation would be 7.21

the answer is 7.21.

You have to divide 9 by 2.5, which is 3.6

The answer is $3.60 per pound of chicken breasts

Steps:

isolate " x "  for -2x + 2y  + 3z  = 0 ;    x = -  ( - 3z - 2y ) / 2

Subsititute : x = -  ( - 3z - 2y ) / 2

- 2 * (  - ( - 3z - 2y ) / 2 ) - y + z = - 3

2 * ( -  ( - 3z - 2y ) / 2 ) + 3y  + 3z  =5

isolate " z " for  :  - 2  ( -  ( - 3z - 2y ) / 2 ) - y+ z = - 3 ;  z = - ( - 3 +  3y / 2 )

subsititute  z = - ( - 3 + 3y / 2 ) :

2* ( - ( -3* ( - ( - 3 +3y / 2 ) - 2y / 2  ) + 3y  + 3  ( - ( - 3 + 3y / 2 ) = 5

isolate y for 2 ( -( - 3 ) - 3 + 3y / 2 ) - 2y / 2 ) + 3y + 3 ( - ( - 3 + 3y / 2 ) = 5

y = 1

for z =  - ( - 3+ 3y ) / 2

subsititute y = 1

z = - ( - 3 + 3  * 1 ) / 2

z =  0

For x  = - ( - 3z - 2y ) / 2

subsititute y = 1

subsititute z = 0

x = -  ( - 3 *0 - 2 * 1 ) / 2

x =  1

x = 1  , y =  1  , z = 0

Domain is (5, ∞), {x| x is greater than 5} for all integer n

Range is (-∞, ∞), {y| y belongs to Reals numbers}

[tex]F(x) = log (x - 5)[/tex]

Set up the equation for x

[tex]x - 5 > 0[/tex]

or,

x > 5

So the domain is all values of x greater than 5 to infinity.

Range is set of all correct or valid values of y.

Range = (-∞, ∞), {y| y belongs to Reals numbers}

I think the answer is 2 (D)   Hope this helps :D

Answer:

6

Step-by-step explanation:

divide every one by m^2

1:m^2+1

Step 1: Subtract 2x from both sides.7x−2x=2x−35−2x5x=−35   Step 2: Divide both sides by 5.‌5x5‌=‌−355‌x=−7 Answer: x = −7

Hope I helped.