which of the following can be added without altering any of the fractions?
a. 3x/x-1 + 8/x-1
b. 6x+1/4x-8 + 1/4x+1
c. 6x/x+6 + 6x/x-6
d. 6x/x-7 + x-7/6x

The line parallel to the given line 2x+3y=6 is 2x+3y=13.

The general equation of a line is y=mx+c where m is the slope of the line and c is the y-intercept.

The slope of the given line 2x+3y=6 is

3y=(-2x)+6

y=(-2/3)x+2

y=mx+c where m is the slope of the line

so the slope of the given line is (-2/3)

as the slope of two parallel lines is equal so the slope of the line parallel to the given line is also (-2/3)

(y-y1)=m(x-x1) where x1 is the x-coordinate and y1 is the y-coordinate.

Here x1=2 and y1=3

(y-3)=m(x-2)

y-3=(-2/3)x+4/3

3y-9=(-2x)+4

3y+2x=13

2x+3y=13

The line 2x+3y=13 is parallel to the given line 2x+3y=6.

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Answer:

To find the unit cost of her choice, divide $120 by 40 to get $3.00 per bouquet. This unit cost is more than the other deal.

Step-by-step explanation:

Answer:

2iiej

Step-by-step explanation:

1kejes191828wusnalao

The factors of 5x as calculated from the data given is found to be as 5, x and  1 .

On factorizing 5x we can write it as ,

5 x 1 x x .

Therefore the factors are 5 , 1 and x.

There are some integers which are positive and can divide a number completely leaving no remainders. Such integers are known as factors for a number. If we want to get a product by multiplying two numbers , we will have to multiply two factors. Each number is a multiplier of itself.

The prime factor is the factor of a given number that is also a prime number. Factors are numbers that are multiplied together to produce another number.

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B: (0, -1) , ( -4,0) , ( -2, -1) , (7, -7)

Image result for ordered pair definition

An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair’s numeric values can be integers or fractions.

The origin is the place where both axes cross. Every point on the coordinate plane is represented by an ordered pair (x, y), with the first element x referred to as the x-coordinate and the second element y referred to as the y-coordinate.

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Answer:

Step-by-step explanation:

[tex] {(2x)}^{3} [/tex]

= 2x × 2x × 2x (In expanded notation form) (Ans)

Answer:

2·2·2·x·x·x

Step-by-step explanation:

(2x)(2x)(2x) = 2·2·2·x·x·x = 8x³

The total hours did Brendan work that week is 669.86.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.

The collection of mathematical symbols that emerges from the right arrangement of numbers is known as a mathematical expression and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

The three different types of algebraic expressions are monomial, binomial, and polynomial.

The total hours did Brendan work that week is 669.86.

The complete question is: Brendan is an hourly worker and earns $15.25/hour. During a week's pay period, he worked the following hours and minutes:

Day Hours Minutes

Monday 8 45

Tuesday 7 52

Wednesday 8 0

Thursday 9 36

Friday 8 24

Using the hundredth-hour method, what is Brendan's gross pay for the week? The employer pays overtime for all time worked in excess of 40 hours per week.

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The area of the semicircle is, 6.28 unit².

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

BC is the diameter of the semicircle.

And, The area of rectangle ABCD is 20 and the length of line AB is 5.

Now, We have;

The area of rectangle ABCD is 20 and the length of line AB is 5.

Let the width of rectangle = x

So, We can formulate;

⇒ 20 = x × 5

⇒ x = 4

Here, the width of rectangle is the diameter of the semicircle.

So, The radius of semicircle = 4 / 2

                                            = 2 units

We know that;

Area of semicircle = π r

Where, 'r' is radius of semicircle.

Hence, We get;

⇒ Area of semicircle = π r

⇒ Area of semicircle = 3.14 × 2

                                 = 6.28 unit²

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Answer:

[tex]Tan(A+B)=\frac{264}{23}[/tex]

Step-by-step explanation:

From the question we are told that:

 [tex]SinA=\frac{28}{53}[/tex]

 [tex]CosB=\frac{3}{5}[/tex]

Let X be the adjective side to A

Let Y be the opposite side to B

Generally the equation for X is mathematically given by

 [tex]X^2=\sqrt{53^2-28^2}[/tex]

 [tex]X=45[/tex]

Therefore [tex]TanA[/tex]

[tex]TanA=\frac{28}{45}[/tex]

Generally the equation for Y is mathematically given by

 [tex]Y^2=\sqrt{5^2-3^2}[/tex]

 [tex]Y=4[/tex]

Therefore [tex]TanB[/tex]

[tex]TanB=\frac{4}{3}[/tex]

Generally the equation for [tex]Tan(A+B)[/tex] is mathematically given by

[tex]Tan(A+B)=\frac{TanA+TanB}{1-TanA*TanB}[/tex]

[tex]Tan(A+B)=\frac{\frac{28}{45}+(\frac{4}{3})}{1-(\frac{28}{45})*(\frac{4}{3})}[/tex]

[tex]Tan(A+B)=\frac{264}{23}[/tex]

Answer:

Step-by-step explanation:

because 2 + 2 is 4

If triple of a number added to its half part its equal to the difference between four times the number and 12 then the number is 24.

Two or more expressions with an Equal sign is called as Equation.

Let us consider the number be x

tripple of a number added to its half part

3x+x/2

Difference between four times the number and 12

4x-12

So tripple of a number added to its half part its equal to the difference between four times the number and 12

3x+x/2=4x-12

6x+x=2(4x-12)

Apply distributive property on RHS

7x=8x-24

Subtract 7x on both sides and add 24

24=x

Hence, if triple of a number added to its half part its equal to the difference between four times the number and 12 then the number is 24.

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Answer:

1 - 5 < y < 5

I hope you pass your assignment

The range of solutions for the given inequality is -5<y<5.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -6<1/3(6y + 12)<14.

Here, -6<(2y + 4)<14

-6<(2y + 4)

Subtract 4 on both the sides of an inequality, we get

-10<2y

Divide 2 on both the sides of an inequality, we get

-5<y

(2y + 4)<14

Subtract 4 on both the sides of an inequality, we get

2y<10

Divide 2 on both the sides of an inequality, we get

y<5

So, -5<y<5

Therefore, the range of solutions for the given inequality is -5<y<5.

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Answer:

The surface area is 1,070 ft².

We label points A=(x1,y1)=(1,1) A = (x1, y1) = (1,1) and A′=(x2,y2)=(3,3) A ′ = (x 2, y 2) = (3,3) to identify the centre of dilation. The centre of dilation's coordinates are then determined using the formula. (xo,yo) ( xo,yo) ( xo,yo )

When the scale factor exceeds 1, the dilation becomes an enlargement. If it falls within the range of 0 and 1, the dilation is a contraction. The point from which the image is dilated is known as the centre of dilation (or point of dilation).

The equation for the circle must be converted into standard form, (x h), in order to be able to determine the centre and radius.[tex](x-h)^2+(y-k)^2=r^2[/tex], where r is the radius and h and k are the coordinates for the centre.

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Answer:

86.4

Step-by-step explanation:

6x +12 + 4x + 44 = 180

10x +56 = 180

10x = 180 - 56

x = 12.4

180 - 4*12.4 + 44 =86.4

The transformation is shifted up 2 units.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=-2x+3.

Here, the slope m of a line is -2 and y-intercept is 3

A) If the function g(x)=f(x)+k, where k=2.

Now, g(x)=-2x+3+2

g(x)=-2x+5

Here, the slope m of a line is -2 and y-intercept is 5

B) The slope of both functions are same

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Shifted up 2 units

Therefore, the transformation is shifted up 2 units.

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Answer:

1 bucket

Step-by-step explanation:

3/4 buckets = 3/4 hours

multiply both sides by 4/3 to get one hour

(4/3) * (3/4) buckets = (4/3) * (3/4) hours

1 bucket = 1 hour

Answer:

x=6.3m

Step-by-step explanation:

Let the opposite side be y in 2nd triangle.

tan 27° = y/9

=> tan 27° X 9 = y

∴ y = 4.585m ≈ 4.59m

cos 43° = y/x

=> cos 43° = 4.59/x

=> cos 43° X x= 4.59

=> x = 4.59/cos 43°

∴ x =  6.276m ≈ 6.3m (corrected to 1 dp)

The corresponding equation of the proportional relationship will be;

⇒ y = - 1/4x

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The graph of a proportional relationship contains the point (-12, 3).

Now,

Let the equation of the proportion is,

⇒ y = kx

Where, 'k' is constant of proportion.

Since, The graph of a proportional relationship contains the point (-12, 3).

Hence, Substitute x = 0 12 and y = 3 in above equation we get;

⇒ 3 = k × - 12

⇒ 3 / (-12) = k

⇒ k = - 1/4

Thus, The equation of the proportion is,

⇒ y = - 1/4x

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Step-by-step explanation:

so, clearly, the triangles BCF and DCF are congruent.

that makes the line CF a bisector of the kite figure.

and so, both angles are identical halves of the total angle at C.

therefore,

3x + 13 = 13x - 7

13 = 10x - 7

20 = 10x

x = 20/10 = 2

So, Mathilda should mix 600 grams of OMT with 300 grams of WMT to sell the resulting mixture at Php 1.80 per gram.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

A unit is a quantity with a fixed magnitude that is used to gauge the sizes of other quantities that behave similarly.

The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grams (g). Milliliter (ml) and liter are used to measure volume (L).

Let x be the amount of OMT powder in grams. We know that the total amount of powder in the mixture is x + 300 grams since Mathilda is mixing x grams of OMT with 300 grams of WMT.

(x * Php 2 + 300 * Php 1) / (x + 300) = Php 1.80

Solving for x, we can get the amount of OMT powder in grams:

x = (300 * Php 1.80 - 300 * Php 1) / (Php 2 - Php 1.80) = 300 * (Php 1.80 - Php 1) / (Php 2 - Php 1.80) = 600

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Answer:

1376x-736

Step-by-step explanation:

Take 32 and multiply it by 43. By multiplying vertically, distribute the multiplication of 3 (from 43) times both the 2 and 3 of 32 (right to left)

3 x 2=6; 3 x 3=9:

32

x

43

--------

96

Then, distribute the multiplication of 4 (from 43) times both the 2 and 3 of 32 (right to left) and leave a zero under the last number of your previous answer while moving the distribution of numbers forward.

4 x 2=8; 4 x 3=12

32

x

43

--------

   96

+

1280   <----(this is the zero you must leave under your previous set)

After distributing each number of 43 to each number of 32 while multiplying, add your answers together vertically from right to left and bring down the x:

  96

+

1280

----------

1376x

Now do the same for 32 x -23 after learning vertical multiplication to get -736

Your final answer put together is 1376x-736

The expression written by Regina is y + 9, which means adding nine to some number y. None of the given expressions are equivalent to this expression.

The expression written by Regina is y + 9, which means adding nine to some number y. None of the given expressions are equivalent to this expression. In order for two expressions to be equivalent, they must have the same value when the same values are plugged into them. For example, if y is equal to 5, then y + 9 would be equal to

14, while (9. 3 • 4) + y

would be equal to

27, (9+ y (3 = 4))

would be equal to 17, and

(y + 9)(3 = 4)

would be equal to 21. As these values are not equal, the given expressions are not equivalent to the one written by Regina.

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Answer:

Y=54x−2y=54x−1

I hope this helps you!

The decimal form of the -1 1/12 is obtained by finding the sum of -1 and -1/12 (-1/12 = -0.08[tex]\overline{3}[/tex] a recurring decimal), which is the option A

A. -1.08[tex]\overline{3}[/tex]

A recurring decimal is a decimal that has a digit or a group of digits that is continuously repeated in the decimal.

The specified expression, -1 1/12, can be presented as follows;

[tex]-1\dfrac{1}{12}[/tex]

The value of the specified expression in decimal form is therefore;

[tex]-1\dfrac{1}{12}= -1+\left( - \dfrac{1}{12}\right)[/tex]

[tex]- \dfrac{1}{12} = -0.08\overline{3}[/tex]

The fraction -1/12, therefore consist of a recurring decimal, with the 3 in the thousandth place after the 8 being the part that repeats.

Therefore, the value of the expression, [tex]-1+\left( - \dfrac{1}{12}\right)[/tex] is -1 + (-0.08[tex]\overline{3}[/tex])

-1 + (-0.08[tex]\overline{3}[/tex]) = -1.08[tex]\overline{3}[/tex]

The specified expression is therefore;

[tex]-1\dfrac{1}{12}[/tex] = -1 + (-0.08[tex]\overline{3}[/tex]) = -1.08[tex]\overline{3}[/tex]

The correct option is option A

The option C. -1.[tex]\overline{083}[/tex] is incorrect, the correct option is option A

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70% of those who went to the music concert and the play also did so.

A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The word "%" stands in for it.

In addition to being stated as a decimal or a fraction, a percentage is a number that indicates how many out of 100 it is. Three for the price of one! Simply enter the % as the numerator and 100 as the denominator to convert the percentage to a fraction.

We know that 350 people attended the drama play.

50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.

We know that 250 people attended the music concert.

The percentage of the people who attended the music concert even attended the drama play would be 175 ÷ 250 · 100% = 70%

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70% of those who went to the music concert and the play also did so.

Hence, the option A is correct.

In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage. In order to get the percentage of a given number, divide the number by the total and multiply by 100. The percentage is a chunk out of one hundred. One out of 100 is referred to as a percentage. The symbol for it is "%".

A % is a number that, in addition to being expressed as a decimal or a fraction, also specifies how many out of 100 it is. For the price of one, get three! To convert a percentage to a fraction, just enter the% as the numerator and 100 as the denominator.

We know that 350 people attended the drama play.

50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.

We know that 250 people attended the music concert.

The percentage of the people who attended the music concert even attended the drama play would be 175 ÷ 250 · 100% = 70%

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