the amount of sales tax paid on a purchase is proportional to the price of the item. suppose the sales tax rate is 6.25%. if p is the price of the item and t is the sales tax, which equation represents this?

a)Percentage increase is 23.07%.

b)Percentage increase is 28.5%.

Percentage is a relative value that represents hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is

([tex]\frac{value}{total value}[/tex])100%.

Given Data

Percentage increase = [tex]\frac{final value - starting value}{starting value}[/tex]× 100

a) Cost = $65

New cost = $70

Difference = 5

Equating,

Percentage increase = [tex]\frac{70-65}{65}[/tex] × 100

Percentage increase = [tex]\frac{15}{65}[/tex] × 100

Percentage increase = 23.07%

Percentage increase is 23.07%.

b) Cost = $45

New cost = $35

Equating,

Percentage increase = [tex]\frac{45-35}{35}[/tex] × 100

Percentage increase = [tex]\frac{10}{35}[/tex] × 100

Percentage increase = 28.5%

Percentage increase is 28.5%.

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Answer:

[tex]4r - 9s = k \\ ➪4r = 9s + k \\➪ r = \frac{9s + k}{4} [/tex]

Hope it helps

The equation that represents the line is,

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

We are asked to find the equation that represents the line shown in the figure.

We need the slope of the line and a point on the line to find the equation of the line.

The equation of a line can be written in the slope-intercept form given below as,

 y-y₁ = m(x-x₁),

where m is the slope of the line and (x₁, y₁) is a point on the line.

From the figure we can find two points on the line which are (x₁ ,y₁) = (2, -3) and (x₂, y₂) = (-2, -6).

Hence slope, m = (y₂-y₁)/(x₂-x₁)

                          = (-6- -3)/(-2-2)

                          = 3/4

So the equation that represents the line is

 y - -3 = 3/4(x-2)

⇒ y+3 = 3/4(x-2)

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y = -5/2x-8 is the slope-intercept form for the lines that passes through the point (-6,7) and parallel to 5x+2y = 10.

Given that, the line 5x+2y = 10 passes through the point (-6,7) and is parallel to the given equation. Now, we have to write an equation in the slope-intercept form.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as: y = mx + b.

where, m is the slope of the line and b is the y-intercept of the line.

Let's proceed to find the equation.

5x+2y = 10

2y = -5x+10

y = -5/2x+10/2

y = -5/2x+5

Now, comparing with y = mx+b (slope-intercept form)

m = -5/2 and b = 5

As the two lines are parallel with each other then the slope of other line will also be same as m = -5/2

Now, the line passing through the point (-6,7)

⇒ x₁ = -6 and y₁ = 7

y-y₁ = m(x-x₁) ..........(1)

putting values in equation (1), we get

y-7 = -5/2(x-(-6))

⇒ y-7 = -5/2(x+6)

⇒ y = -5/2x-15+7

⇒ y = -5/2x-8

This is the slope-intercept form for the lines that passes through the point (-6,7) and parallel to 5x+2y = 10.

Hence,  y = -5/2x-8 is the required answer.

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Answer:

5) a) x=55

Step-by-step explanation:

x=55

2x + 15 = 110 + 15

=125

Answer:

-3(4x + 1) = 21 given

4x + 1 = -7 Division Property of Equality

4x = -8 Subtraction Property of Equality

x = -2 Division Property of Equality

Answer:

see explanation

Step-by-step explanation:

prove by solving the equation

- 3(4x + 1) = 21 ( divide both sides by - 3 )

4x + 1 = - 7 ( subtract 1 from both sides )

4x = - 8 ( divide both sides by 4 )

x = - 2

thus solution is x = - 2

Answer:

Step-by-step explanation:

- 4 ≤ 3 , then f(- 4) = [tex]\frac{1}{2}[/tex] ( - 4) + 1 = - 1

2 ≤ 3 , then f(2) = [tex]\frac{1}{2}[/tex] (2) + 1 = 2

3 ≤ 3 , then f(3) = [tex]\frac{1}{2}[/tex] (3) + 1 = 2.5

5 > 3 , then f(5) = 9×5 - 4 = 41

Answer:

$71.39

Step-by-step explanation:

So we can go ahead and add the extra money they paid (sales tax and tip).

15% + 6% = 21%

Then we can find 21% of 59 then that will be our extra money we're paying.

59 × 0.21 = 12.39

Then we add that amount to our 59 to get the total amount.

59 + 12.39 = 71.39

Answer: 8x + -31 + 5y + 35 + 6x + 3 = 180. Reorder the terms: -31 + 35 + 3 + 8x + 6x + 5y = 180.

Answer: 40

Step-by-step explanation:

The smallest number that all three numbers go into evenly is 40.

Therefore the LCM of 8, 11, and 20 is 40.

Answer:

440

Step-by-step explanation:

To find the Least common multiple (L.C.M) of 8, 11 and 20, it means that:

8 = 2,2,2

11 = 1, 11

20= 2,2,5

LCM of 8,11,20 = 2× 2 × 2 × 11 × 5

= 440

the numerical value of x in fraction and decimal form are 11/2 and 5.5 respectively.

A midpoint is simply a point that divides a line segment into two equal halves.

Given the data in the question;

Since that T is the midpoint of segment SU, segment ST and segment TU are two equal halves of of segment SU.

Segment ST = Segment TU

Plug in the given values and solve for x

14x - 6 = 12x + 5

14x - 12x = 5 + 6

2x = 11

x = 11/2

x = 5.5

Therefore, 11/2 or 5.5 is the numerical value of x.

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Answer:

The length of the radius is 10.7cm

Step-by-step explanation:

[tex]v = \pi {r}^{2} h[/tex]

6480=(22r*180)/7

6480*7=3960r

r=

[tex]r = \sqrt{45360 \div 396} [/tex]

If we define x as the number of goals that she needs to do, we can write the inequality:

x  ≥ 10.

And to graph that we need to use a closed dot at x = 10.

We know that Lesley wants to have an average of 4 games per day.

Until now she played:

Now we assume that on game 5 she does x goals, and if we want the average to be 4 or larger, then we can write:

(6 + 1 + 0 + 3 + x)/5  ≥ 4

Now we need to solve that inequality, we can rewrite:

(6 + 1 + 0 + 3 + x)/5  ≥ 4

(10 + x)/5  ≥ 4

(10 + x) ≥ 4*5

(10 + x) ≥ 20

x ≥ 20 - 10

x ≥ 10

So she needs to do at least 10 goals on the next game.

Now, when graphed we will have an open or a closed circle? In the inequality we have the symbol " ≥ " so x = 10 is a solution, then we need to use a closed circle.

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Answer:

x = 132°

Step-by-step explanation:

Sum of interior angles = (n - 2) x 180, where n is number of sides of the polygon.

Sum = (6 - 2) x 180 = 720°

sum = 160 +75 + 132 + 113 + 108 + x

sum = 588 + x

720 = 588 + x

x = 720 - 588

x = 132°

:)

SOMEONE HAS A PET WATER BUFFALO.

THE GIVEN STATEMENT IS INDICATING THAT NOT EVEN ONE PERSON HAS A PET WATER BUFFALLO SO THE NEGATION SHOULD INDICATE THERE IS SOMEONE WHO DOES HAVE A PET WATER BUFALLO.

HOPE THIS HELPS

Answer:

b is -4

Step-by-step explanation:

we're given:

|2b + 2| = 6

substituting b for -4 :

|2(-4) + 2| = 6

|-8 + 2| = 6

|-6| = 6

any negative number between absolute value becomes positive.

Hence b is -4

On solving the simultaneous equations 3x+2y=7 and 2x-3y=-4 , the value of x is 1 and the value of y is 2  .

In the question,

it is given that the simultaneous equations are

3x+2y=7   ....(i)

and

2x-3y=-4    ...(ii)

to solve these equations ,

we multiply equation(i) with 2 and

multiply equation(ii) with 3 .

So , the equations become

6x+4y=14 ...(iii)

and

6x-9y=-12 ....(iv)

we subtract equation (iv) from  (iii) ,

So,

(6x+4y)-(6x-9y)=14-(-12)

Solving further ,

6x+4y-6x+9y = 14+12

4y+9y = 26

13y = 26

y = 26/13

y = 2

Substituting the value of y as 2 in equation (iii) , we get

6x+4(2) = 14

6x + 8 = 14

6x = 14-8

6x = 6

x=6/6

x=1

hence x=1 and y=2 .

Therefore , On solving the simultaneous equations 3x+2y=7 and 2x-3y=-4 , the value of x is 1 and the value of y is 2  .

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Answer 9 3/7

Step-by-step explanation:

[tex] \frac{30}{7} \times \frac{11}{5} \\ = \frac{330}{35} \\ = 9 \frac{15}{35} [/tex]

SIMPLIFIED WE GET:

[tex]9 \frac{3}{7} [/tex]

THE LAST OPTION IS THE ANSWER

The graph shown below represents the equation y =[tex]3\sqrt{x+6} -3[/tex]

Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.

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Answer:

8x6y12

Step-by-step explanation:

Correct option is B)

Put x=3y=4

(3x+4y):(5x+6y)=(3×3+4×4):(5×3+6×4)

                                      =(9+16):(15+24)

                                      =25:39

Hello!

What is the slope-intercept form:

 [tex]y = mx + b[/tex]

             [tex]m = \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-4}{0--2} =\dfrac{-5}{2}[/tex]  

               ⇒ where (x₂,y₂) and (x₁,y₁) are random points on the line

            ⇒ thus our y-intercept is '-1'

Thus our line's equation in slope-intercept form:

     [tex]y= -\dfrac{5}{2}x -1[/tex]

Hope that helps!

Answer: if the j is supposed to be there, the answer is -9+24j. if the j is not there then just -9+24.

Step-by-step explanation: we distribute the -3 to the 3 and the -8. (-3x3=-9) and (-3x-8=24). when you multiply for divide by a single negative it is negative. when there are two negatives the answer will come out positive.

The value of x if H is the midpoint of GJ is 31 units.

The midpoint is the middle point of a line segment.

It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

The midpoint is halfway between the two end points.

Therefore, H is the midpoint of GJ

Hence,

GJ = GH + HJ

GJ = 4x - 8

GH = 120

Therefore, GH and HJ are congruent because H is the midpoint of GJ

GH = HJ

Hence,

4x - 8 = 120 + 120

4x - 8 = 240

4x = 240 + 8

4x = 248

x = 248 / 4

x = 31

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The percentage of population of those knowing neither Hindi nor English is 43%.

The outcome of multiplying a given number by a percentage is the percentage. Since a percentage is a portion of a number or quantity, they are typically smaller than the actual number. There are instances, though, where the percentage exceeds the number. If the percentage is greater than 100%, this would occur.

A percentage is simply a certain proportion of a number.

Typically, the phrase "percent of" comes after the quantity.

So, 70% of 50 is 35, for instance.

50 is the quantity, 35 is the percentage, and 70% is the percent in this sentence.

The total percentage of population is represented by 100%, so let the population be 100

No. of population that knows only Hindi = 34 - 23

                                                                   = 11

No. of population that knows only English = 46 - 23

                                                                      = 23

No. of population that knows both = 23

The sum = 11 + 23 + 23

              = 57

No. of population that knows neither Hindi nor English = 100 - 57

                                                                                           = 43

And percentage = 43%

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The equation of the line passing through (0, 0) and (2, –3) is y = - 3 / 2 x

The equation of a line can be described as follows:

y = mx + b

where

Therefore, using (0, 0)(2, -3)

m = y₂ - y₁ / x₂ - x₁

m = -3 - 0 / 2 - 0

m = - 3 / 2

Therefore, the y-intercept is 0.

The equation of the line is y = - 3 / 2 x

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Answer:

∠1 = 103.9° ;  ∠2 = 27.8°

Step-by-step explanation:

Supplementary angles = 180°

So, Let the angles be 'x'

Then, x + x -27.8° = 180°

         2x - 27.8° = 180°

         2x = 180° + 27.8°

         2x = 207.8°

          x = 207.8°/2

          x = 103.9°

Therefore ∠1 = 103.9° ; ∠2 = 27.8°

I hope the answer is correct and has helped you!!!