The perimeter of the rectangular garden is 60 feet. Is the length of the garden is twice the width, what are the dimensions of the garden.

a = 14

distribute parenthesis on left side and simplify

8a - 6a - 15 = 13

2a - 15 = 13 ( add 15 to both sides )

2a = 28 ( divide both sides by 2 )

a = [tex]\frac{28}{2}[/tex] = 14

Divide the total amount traveled with the time it took.

21/3 = 7/1

Alba's average speed is 7 miles per hour

hope this helps

7 miles per hour.  21/3

Answer:

The answer is 115

Answer:

6 is a factor and 36 is neither and 48 is a multiple

Step-by-step explanation:

Answer: 18

Step-by-step explanation:

Well, the exponent is distributed to the 6 and g.

g cannot be changed and therefore remains as [tex]g^3[/tex]

[tex]6^3[/tex] can be simplified even further and into the number 216

Therefore, your answer should be:

[tex]216g^3[/tex]

When the highest exponent of any variable is three, then the the expression is termed as cubic expression.

Thus,the given expression is a cubic expression and the answer to the given expression is  [tex]216g^3[/tex].

Given expression has two components, a whole number and a variable.

Solving the expression [tex][6\rm g]^3[/tex]  :

[tex](6\times\ 6 \times6) g^3 = 216g^3[/tex]

Thus, the final value of the expression is [tex]216g^3[/tex].

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Jess buys a total of 17/16 pounds, which is equivalent to 1 1/8 pounds, of turkey and cheese combined.

Jess buys 5/8 pound of turkey and 7/16 pound of cheese. To find out how much turkey and cheese Jess buys in total, we need to add these two amounts together. Since both quantities are given in pounds, we can add them directly.

First, let's find a common denominator for the fractions 5/8 and 7/16. The common denominator is 16. Now we write 5/8 with the common denominator, which is the same as 10/16. With the fractions having the same denominator, we can add the numerators together:

(10/16) + (7/16) = (10+7)/16

17/16 pounds

So, Jess buys a total of 17/16 pounds of turkey and cheese. This is equivalent to 1 ⅛ pounds when expressed as a mixed number.

The answer to 20 x 9 x 5 is 900. You use multiplication property.

Hope this helps! :)

Answer: non-terminating decimals

Integers and whole numbers can be converted to fraction form. Example, the whole number 3 can be written as 3/1 which is rational. A rational number is any fraction of whole numbers (eg: 7/19). The denominator can never be zero.

All repeating decimals can be converted into a fraction. A number like 0.8888 with the 8s repeating forever converts to the fraction 8/9, which is rational

Non-terminating decimals are decimals that go on forever. If there is no pattern to the decimal sequence, then the decimals don't repeat and the number cannot be converted to a rational number. Something like pi = 3.14159... has no pattern to the decimal sequence. Therefore, a number like pi is irrational, which literally means "not rational", so numbers like pi aren't rational and are not part of the set of rational numbers.

Non terminating and non repeating decimals cannot be written in fraction from . So they are not included in set of rational numbers.

Given :

Lets take set of rational numbers that can written as a fraction of two numbers.

All integers are positive and negative numbers.

Rational numbers includes integers

Whole numbers starts from 0,1,2..........

Whole numbers are included in rational numbers

Repeating decimals can be written in fraction form .

Non terminating and non repeating decimals cannot be written in fraction from . So they are not included in set of rational numbers.

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Answer:

The teacher establishes 7 work stations in each of the classrooms.

Step-by-step explanation:

Each work station has 1/16 pounds of clay.

There are two classrooms with the same number of workstations.

The total amount of clay is 7/8

Then, we look for a number of work stations per classroom x, which multiplied by the number of classrooms (2) and multiplied by the amount of clay per work station (1/16) is equal 7/8.

Then we propose the following equation

[tex]\frac{1}{16}(2x) =\frac{7}{8}\\\\ \frac{2}{16}x = \frac{7}{8}\\\\ x = \frac{16 * 7}{8 * 2}\\\\ x = 7[/tex]

The teacher establishes 7 work stations in each of the classrooms.

Workstations  the teacher set up in each of the classrooms is is mathematically given as

x=7

Question Parameters:

An art teacher has a total of 7/8 pound of clay.

The teacher puts 1/16 pound of clay at each workstation.

The teacher sets up an equal number of workstations in each of 2 classrooms

Generally the equation for the  workstations is mathematically given as

1/16(x)=7/8

x=16*7/(8*2)

x=7

Therefore,workstations  the teacher set up in each of the classrooms is

x=7

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Answer:

4

Step-by-step explanation:

Answer:

The answer is 8 sides.

Step-by-step explanation:

A plane intersects a prism parallel to the base of the prism. The cross section is a polygon with eight sides. The base of the prism has also 8 sides.

The cross-section of a plane parallel to the base is the same shape as the base. The cross section is also an eight sided polygon, so, the base of the prism has 8 sides.

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 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.'

Let's assume

x is the age of 11th grade student

we are given

Rhonda  conducts a survey of the ages of  students in eleventh grade at her school.

On November 1, she finds the average  age is 200 months.

and

She also finds that  two-thirds of the students are within  6 months of the average age.

so, we can set up equation as

[tex]|x-200|=3[/tex]

now, we can solve for x

[tex]x-200=3, x-200=-3[/tex]

[tex]x-200=3[/tex]

[tex]x-200+200=3+200[/tex]

[tex]x=203[/tex]

[tex]x-200=-3[/tex]

[tex]x-200+200=-3+200[/tex]

[tex]x=197[/tex]

So, the minimum age of 11th grade student is 197 months

So, the maximum age of 11th grade student is 203 months

now, we are given age is 18 years

we will change into months

[tex]18 years=12*18 months[/tex]

[tex]18 years=216 months[/tex]

So, first of these students turn 18 is

[tex]=216 -203[/tex]

[tex]=13[/tex] months...........Answer

8 degrees per hour because 32/4 is 8. Hope that helped!

If there isn't any parenthesis it would be

-3n + 7 < 11

-3n < 4

n >  4 divided by 3

With parenthesis

-3(n+7) < 11

-3n - 21 < 11

-3n < 10

n > - 10 over 3

To find the LCM, you CAN divide the product of the two numbers by the GCF.

This is not a very well-known fact, but it is useful at times, especially when we are asked to calculate both the LCM and GCF.

For example, the GCF of 18 and 48 is 6, by inspection or by factors.

Therefore the LCM of 18 and 48 is 18*48/6=864/6=144.

It works because by definition the GCF is the products of all common factors between the two given numbers.  Dividing the product by the GCF will therefore remove the duplication of the common factors, leaving a number which contains the factors of each of the two numbers, thus a lowest common multiple.

Note that this method is not the only way to find LCM's.

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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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.

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 given triangle has two sides marked equal and hence is an isosceles triangle.In isosceles triangle base angles are equal <A=<B=50.

Sum of angles in any triangle is 180 degrees.

<A+<B+<C=180°

50+50+5y+10=180

Adding like terms :

110+5y=180

Subtracting 110 on both sides:

5y=70

Dividing both sides by 5:

y=14.

The isosceles triangle, with base angles both at 50 degrees, is solved for the variable y, resulting in y = 14. This value, when substituted, gives angle C as 65 degrees.

The triangle in question is an isosceles triangle, meaning that two of its sides are of equal length. Consequently, the base angles, denoted as angle A and angle B, are also equal, and both are given as 50 degrees. In any triangle, the sum of its angles equals 180 degrees, so for this isosceles triangle:

[tex]\[ \angle A + \angle B + \angle C = 180^\circ \][/tex]

Substituting the known values:

50 + 50 + 5y + 10 = 180

Combining like terms:

110 + 5y = 180

To isolate the variable term, subtract 110 from both sides:

5y = 70

Now, divide both sides by 5 to find the value of y:

y = 14

In conclusion, the value of y is determined to be 14. This signifies that in the given isosceles triangle, angle C is represented as 5y + 10, which becomes 65 degrees. Therefore, the solution provides a comprehensive understanding of the triangle's angle distribution.

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Answer:

Step-by-step explanation:

[tex]\frac{2}{3} n[/tex] [tex]+ 8[/tex][tex]=\frac{1}{2} n[/tex] [tex]+2[/tex]

I am sprry bit I am not sure if I got it right but 560 centimeters if you group the sum of each side and multiply it like 2(2+12)*2(4+6), maybe I switched the multiplications around

Remark

You have to make an assumption here. I know of no other way to do the problem than by making the assumption that 10 * 14 figure is a rectangle. If that is not true, the problem is not solvable.

Step One

Find the length of the shaded area.

The length will be the length of the hypotenuse of a right triangle formed by the two smaller sides = the hypotenuse.

a = 4

b = 12

c = ????

Length

L = square root (a^2 + b^2)

L = √(4^2 + 12^2)

L = √(16 + 144)

L = √160    =  √(4*4 * 10)

L = 4√(10)

Width

The width is done the same way.

a = 6

b = 2

w = c = ??

w = √(6^2 + 2^2)

w = √(36 + 4)

w = √40

w = √(2 * 2 * 10)

w = 2 √ 10

Area

Area = L * W

Area = 4√10 * 2√10

Area = 8 * 10

Area = 80

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