what was the initial amount of water in a barrel, in liters, if x liters remain after y liters were spilled and 6 were added?

The simplified expression, 36a + 42b - 18a + 6 by combining the like terms is 18a + 42b + 6

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).

To simplify an expression means to write an equivalent expression which contains no similar terms.

Therefore, let's simplify the expression by combining the like terms.

36a + 42b - 18a + 6

Like terms can be defined as terms that contain the same variables raised to the same power.

36a + 42b - 18a + 6

combining the like terms

36a - 18a + 42b + 6

Therefore, the simplified expression is 18a + 42b + 6

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Answer:

[tex]2 {d}^{2} + 5d - 7 [/tex]

[tex](2d + 7)(d - 1)[/tex]

we can do a triangle to solve the apothem

the upper angle is equal to 360 divided by 8 since 360 ​​is a complete turn and an octagon is composed of 8 equal triangles, so is 45

now we take a triangle from the triangle to apply trigonometric ratios and solve a

the upper angle of the new triangle is the half of the original so is 45/2

now i will use the trigonometric ratio of tangent

where alpha is the angle, O the opposite side drom the angle and a the adjacent side from the angle

so replacing

and solve for a

the aphotem is 8.4

and the formula of the area of the octagon is

where a is the aphotem and l the measure f each side so 7

replacing

the area is 235.2 square units

The expression that equals 3C+3D in standard form is:

x²+7x+1

Given:

C = -x+2

and D = x²+8x-1

we are asked to find out an expression which equals 3C+3D in standard form.

based on the conditions, formulate:

3C+3D

substitute C and D values.

⇒ 3(-x+2) + 3(x²+8x-1)

Apply multiplicative distribution law:

⇒ open the parenthesis.

⇒ -3x+6+3x²+24x-3

calculate the product or quotient

⇒ arrange the like terms.

⇒ 3x²+21x+3

⇒ Reduce the terms.

⇒ x²+7x+1

Hence we get the equation in standard form.

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[tex]\frac{325}{520}[/tex] fraction of the workforce kept their jobs

What is the Percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

What is Percentage change?

The percentage increase is calculated by subtracting the original number from the new number, dividing that result by the original number, and multiplying that result by 100.

where growth in number equals new number minus initial number.

Similar to how a percentage increase is calculated, a percentage reduction is calculated by subtracting a new number from the original number, dividing that new number by the original number, and multiplying that result by 100.

decreasing number where original number - new number

In other words, there is a percentage decline if the response is negative.

Here, It is given:

In January 520 workers were employed;

In the end, 195 employees were redundant;

So, The fraction of the workforce who kept their job:-

The fraction of the workforce who kept their job=[tex]\frac{520-195}{520}[/tex]

The fraction of the workforce who kept their job=[tex]\frac{325}{520}[/tex]

Hence,

The fraction of the workforce who kept their job=[tex]\frac{325}{520}[/tex]

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The mean number of miles that the employees in a department live from work is 24.

What is a z-score?

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The z-score is given as

x = 29

s = 3.6

z = -1.5

Then the mean will be

[tex]-1.5 = \frac{29-u}{3.6}[/tex]

μ = 29 - 5.4

μ = 23.6 ≅ 24

Hence the answer is the mean number of miles that the employees in a department live from work is 24.

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Using mathematical operations, we can conclude that the pound of pork the girl brought was 11.2 pounds.

So, the pounds of pork the girl bought:

Calculate pork as:

Therefore, using mathematical operations, we can conclude that the pound of pork the girl brought was 11.2 pounds.

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The reduce algebraic fraction is [tex]\frac{y^2 + 1}{y + 3}[/tex]

Algebraic fraction are simply fractions with algebraic expressions on the top and/or bottom

We follow the step to reduce to algebraic fraction

[tex]\frac{y^3 - 3y^2 -3 }{y^2 - 9}[/tex]

Simplify the numerator

[tex]\frac{ (y - 3) )(y^2 + 1 )}{y^2 -9}[/tex]

Factor out the greatest common factor from each group

[tex]\frac{(y^3 -3y^2 ) = y -3}{y^2 - 9}[/tex]

Find out greatest common factor (GCF) from each group

[tex]\frac{y^2 (y + 3) + 1 (y - 3)}{y^2 - 9}[/tex]

Simplify the denominator and rewrite 9 as [tex]3^{2}[/tex]

[tex]\frac{( y - 3 ) (y^2 + 1 ) }{y^2 - 3^2}[/tex]

Since both terms are perfect squares, factor using the difference of squares formula

[tex]a^{2}- b^2 = (a +b ) (a -b)[/tex] where a = y and b = 3

[tex]\frac{( y - 3) (y^2 + 1 )}{(y + 3 ) (y -3)}[/tex]

Evaluate the equation and rewrite the expression

[tex]\frac{y^2 + 1}{y + 3}[/tex]

Therefore, the reduce algebraic fraction is [tex]\frac{y^2 + 1}{y + 3}[/tex]

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When a polynomial is dived by x - a, to find the remainder, we can plug is x = a into the equation and find the remainder.

When it is divided by x + a, the remainder is found by plugging in x = -a.

Now, the polynomial here is:

It is divided by x + 5, so we need to plug in x = -5 to get the remainder, which is:

The remainder is - 41, 1st answer choice.

Answer: Width = 5.7 feet, Length = 10.5 feet

Step-by-step explanation:

Let the width be w. Then, the length is 2w-0.9.

[tex]w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5[/tex]

To earn at least $122.50 per day, Wing Ko must replace 5 watch bands

Here, we want to find the number of bands that Wing Ko must replace to earn at least $122.50 per day

Let the number of watch bands be x

Using mathematical relatio to represent this inequality, we have;

In the given isosceles triangle, the value of x is 10 units.

So, the value of 'x' will be:

Given triangle is an isosceles triangle. Then,

Therefore, in the given isosceles triangle, the value of x is 10 units.

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ANSWER:

4

STEP-BY-STEP EXPLANATION:

From a graph we can establish the following equation:

We solve for x:

The value of UV is equal to 4

Answer:

x>3 3/4

Step-by-step explanation:

you need to swap the sides and divide by 1.2

Answer:

-20x9= -180.    2 to the power of three =8  if you want the quotient it would be -22.5

Step-by-step explanation:

The rules of BODMAS are useful in calulating mathematical expressions involving many operators. The given expression can be simplified as a simple fraction 28 / 27.

The rules of BODMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.

The given expression can be written as,

4 / 5 ÷ 9 / 5 × 7 / 3

In the given expression there are three fractions separated by the sign of multiplication and division.

As per the rule of BODMAS, the division operator has the priority over multiplication operator.

Apply the rule mentioned above in the given expression to get,

4 / 5 ÷ 9 / 5 × 7 / 3

= 4 / 5 × 5 / 9 × 7 / 3

= 4 / 9 × 7 / 3

= 28 / 27.

Hence, the given expression is simplified to get the result as 28 / 27.

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The cost of the lemonade stand is $ 30.

The number of lemonade cups is x.

The price of each cup of lemonade is $ 0.25.

The cost function can be determined as,

Thus, option (A) is the correct option.

Answer:

2,6x +5 = y

Step-by-step explanation:

Don’t know if you wanted the equation, but this is how it’s written

Answer: 10.8 seconds

Step-by-step explanation:

[tex]-16t^2 +170t+40=10\\\\16t^2 -170t-30=0\\ \\ t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]

Answer:

$6.75 Per pound

Step-by-step explanation:

2.25 = 1/3

2.25 + 2.25 = 2/3

2.25 + 2.25 + 2.25 = 6.75 / 3/3

To calculate the unit race price per copy, we can divide $6.00 by 200 copies:

Each copy cost $0.03, to determine how much will cost 150 copies, we have to multiply the unit rate price by 150:

150 copies will cost $4.5

Answer:25

Step-by-step explanation:

1. you place the numbers in order from least to greatest so 1,1,3,8,12

2. then you add those all up

3.then you divide how many numbers there are together

1+1+3+8+12=25

then you divide by 5 because that's how many numbers are shown for the daily snow fall

HOPE THIS HELPS

Answer:

f(x) = (2x + 3)(2x + 1)

Explanation:

The form that best reveals the zeros of the function is:

f(x) = (x - a)(x - b)

Where a and b are the zeros of the function.

So, we need to apply the distributive property as:

Then, we can factorize the quadratic function as:

So, now we can identify the zeros of the function if we solve the following equation:

Therefore, the form that best reveals the zeros in the function is:

f(x) = (2x + 3)(2x + 1)

Perimeter of rectangular dog run is 32.34 units.

Given,

Vertices  of rectangular dog run are  [tex](2\frac{1}{3},7\frac{1}{2} ), (12,7\frac{1}{2}), (12,1), (2\frac{1}{3},1 )[/tex]

Let

[tex]A=(2\frac{1}{3},7\frac{1}{2} )=(\frac{7}{3} , \frac{15}{2} } )\\ \\B=(12,7\frac{1}{2})=(12,\frac{15}{2} )\\\\ C=(12,1)\\ \\D=(2\frac{1}{3},1 )=(\frac{7}{3},1)[/tex]

A, B,C and D be the vertices of the rectangular dog run as shown in figure.

In rectangle opposite sides are equal. thus, AB=CD and BC=AD

In this rectangle, AB is length and BC is width.

To find distance of  AB and BC use formula,

[tex]Distance=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

[tex]AB=\sqrt{(12-\frac{7}{3} )^2+(\frac{15}{2}-\frac{15}{2} )^2} = \sqrt{(\frac{36-7}{3} )^2} =\frac{29}{3}= 9.67[/tex][tex]Bc=\sqrt{(12-12 )^2+(1-\frac{15}{2} )^2} = \sqrt{(\frac{2-15}{2} )^2} =\sqrt{(\frac{-13}{2})^2} = 6.5[/tex]

To find perimeter of rectangular dog run use formula,

[tex]Perimeter =2(Length + Width)\\\\Perimeter =2(AB+BC)\\\\Perimeter =2(9.67+6.5)\\\\Perimeter=2(16.17)\\\\Perimeter=32.34[/tex]

Hence, perimeter of rectangular dog run is 32.34 units.

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The number of special necklaces that she can produce, using proportions, is obtained as follows:

4.

A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations to find the desired amounts in whichever context of a problem.

The requirements for each special necklace are listed as follows, from the problem:

The amounts purchased are given as follows:

The amount of round beads purchased is enough for:

30/4 = 7.5 special necklaces.

The amount of cube beads purchased is enough for:

24/5 = 4.8 special necklaces.

Hence the number of special necklaces that she can make is of:

4.

Because:

The complete problem is given by the image shown at the end of the answer.

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Answer:

1) B, 2) C

===========

As per definition, functions have only one y-value per x-value.

Let's test it with given sets and tables.

A)

x y

0 1

0 2

1 3

2 3

B)

x y

1 0

2 0

3 1

3 2

C)

x y

​​−1 −1

0 −1

2 0

3 2

D)

x y

−1 −1

−1 0

0 2

2 3

1) The set of ordered pairs that represents y as a function of x is;

B; {(−1, 1), (−2, 0), (−3, 4), (−3, 3)}

2) The table that represents y as a function of x is; Table 3

An ordered pair is defined as a composition of the x coordinate called the abscissa and the y coordinate called the ordinate having two values written in a fixed order within parentheses.

1) The first function given as  {(−1, 0), (−1, 1), (−2, 2), (0, 3)} ; This cannot be regarded as a function because the input x = - 1 is repeated with different output values.

The second function {(−1, 1), (−2, 0), (−3, 4), (−3, 3)} ; This cannot be regraded as a function because the input x = -3 is repeated with different output values.

The third function {(0, 0), (1, 1), (2, 2), (3, 3)};  This is a function because each input has unique output values.

The fourth function {(0, 0), (1, 0), (2, 4), (2, 3)} ;  This cannot be regraded as a function because the input x = 2 is repeated with different output values.

2) Table 1 cannot be regarded as a function because the input x = 0 is repeated with different output values.

Table 2 cannot be regarded as a function because the input x = 3 is repeated with different output values.

Table 3 is a Function because each input has unique output values.

Table 4 cannot be regarded as a function because the input x = -1 is repeated with different output values.

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The equation of the line 4 · x - y + 15 = 0 is parallel to the line y = 4 · x + 1.

In this problem we must determine the equation of a line that is parallel to the line y = 4 · x + 1 and that passes through the point (x, y) = (- 2, 7). Lines are represented by algebraic equations of the form:

y = m · x + b

Where:

Two lines are parallel if both share the same slope.

First, find the slope of the first line:

m = 4

Second, determine the intercept of the parallel line:

b = y - m · x

b = 7 - 4 · (- 2)

b = 7 + 8

b = 15

Third, write the resulting expression and find its standard form:

y = 4 · x + 15

4 · x - y + 15 = 0

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