A city has a 5% sales tax. A book costs $32.55 after tax. How much did it cost before tax?

Answer:

1/ Total percent of discount is 40%

2/ The original price is $520.70

Step-by-step explanation:

1/ We add a 25% discount on every TV store, a 10% discount on purchases, 5% discount for paying cash, so the total is a 40% discount.

2/ Now, let's find the original price

100% - 40% = 60%

We know that the 60% he has to pay is $371.93, so we have to find the 40% discount.

40% = 0.4

Take 371.93 times 0.4 = $148.77

Then we add both numbers together

148.77 + 371.93 = $520.70

The expression to represent the average change in temperature each minute is given as follows:

Mean = (4 x (-4) + 3 x (-3)+2 + 1)/10

Only numerical variables regardless of whether they are discrete or continuous can be used to determine the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it.

The average of all values is termed as mean value. Add all values given in data and divide with no. of values to get mean.

According to given condition the expression to represent the average change in temperature each minute is represented as:

Mean = (4 x (-4) + 3 x (-3)+2 + 1)/10

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Part A: Calculation of the limit at x = 3In order to find the limit of the function, we can factorize the numerator by factoring out (x-3).  Limit [tex][tex](x 3)\frac{(x^3 - 27)}{ (x-3)} )[/tex]Now, factorize x³ - 27 to get the difference of cubes. The

limit equation becomes,  Limit [tex](x 3) \frac{ (x-3)(x² + 3x + 9)]}{(x-3)}[/tex] Now, we can cancel out the term (x-3) from the numerator and denominator to get the limit equation as

Part B: Limit [tex](x 3) (x^2 + 3x + 9)[/tex]The limit of the function at x = 3 is the value of the function as x approaches 3. By plugging in x = 3 in the equation above, we get, Limit ([tex](x 3) (x^2 + 3x + 9) = (3)^2 + 3(3) + 9[/tex] = 27Part B: Equation of line through f(3) with slope = 27

The slope of the line is 27, and it passes through the point (3, f(3)). The equation of the line can be found using the point-slope form.  [tex]y - f(3) = 27(x - 3)[/tex]

Part C: Simplifying the equation, we get,[tex]y = 27x - 78[/tex] Part C: Graphical representation of the line and the function

The graph of the function f(x) is a parabola opening upward with a vertex at (3, 0). The slope of the line is positive, which means the line will have a positive y-intercept.

The line will intersect the y-axis at (0, -78).Both the graph of the function and the line pass through the point (3, 0). The line is tangent to the graph of the function at that point.

The slope of the line represents the instantaneous rate of change of the function at the point (3, 0). It is the same as the limit we calculated in Part A.

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Answer:

area = 27.5625, side length = 5.25

Step-by-step explanation:

21 is the perimeter of a square (given). We know a square has 4 equal sides, so 4s = p, where s is the side length and p is the perimeter of a square. Thus: 4s = 21 → s = 5.25

We also know that a square has a = s², where s is the side length and a is the area. Thus, a = 5.25² → a = 27.5625

According to the information given, the equation that represents the situation is 6c - 1200 = 240.

What is a quadratic equation?

Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

The total costs are:

 $240 in taxes and trips.

 6 nights at the hotel, each night with a cost of c, hence 6c

Then:

T = 6c + 240

The budget is of $1200, hence, since the total cost is equals to the budget:

T = 1200

6c + 240 = 1200

Rearranging:

6c - 1200 = 240

Hence, according to the information given, the equation that represents the situation is 6c - 1200 = 240.

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Answer:

the width of the flag is 310 ft and the length is 790 ft.

Step-by-step explanation:

Let "w" be the width of the flag and "l" be the length of the flag. We can set up the following equation to represent the problem:

2w + 2l = 2200

We know that the length of the flag is 480 ft greater than the width, so we can set up the following equation to represent this relationship:

l = w + 480

We can substitute the second equation into the first equation to solve for the width of the flag:

2w + 2(w + 480) = 2200

This simplifies to:

4w + 960 = 2200

Subtracting 960 from both sides gives us:

4w = 1240

Dividing both sides by 4 gives us:

w = 310

So the width of the flag is 310 ft.

We can use this value to find the length of the flag by substituting it into the equation l = w + 480:

l = 310 + 480

This simplifies to:

l = 790

So the length of the flag is 790 ft.

Therefore, the width of the flag is 310 ft and the length is 790 ft.

a)

Step-by-step explanation:

we only need to look at the point, where y = 0.

that is clearly at x = 3.

which function gives y = 0 as result, when x = 3 ?

only a)

y =

[tex] \sqrt[3]{3 - 3} [/tex]

the cubic root of 0 is 0.

as 3 is not equal to the cubic root of 3, b), c) and e) are out.

and d) is

[tex]y = \sqrt[3]{3 + 3} [/tex]

the cubic root of 6 is NOT 0.

so, only a) is the only right answer.

The system of equations, 2x − 7y = −15 and 4x − 14y = 30, has no solution.

To find the solution to the system of equations, we can plot the line of the two equations on a graph, then find the coordinate of the point where both lines of the equations intersect each other.

Alternatively, we can solve simultaneously as shown below:

2x − 7y = −15 --> eqn. 1

4x − 14y = 30 --> eqn. 2

Rewrite eqn. 1:

2x − 7y = −15

-7y = -15 - 2x

y = 15/7 + 2/7*x

Substitute the value of y into eqn. 2:

4x − 14(15/7 + 2/7*x) = 30

4x - 30 - 4x = 30

0 - 30 = 30

0 - 30 + 30 = 30 + 30

0 = 60 [not true]

This means that the system has no solution. If we graph both lines, the two lines of the equations will not intersect each other at any point.

The graph below shows the graph of both lines of the system of equations, meaning that it has no solution.

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For the given equation of variable condition, the cost of the bench is $450.

What is the equation of variable?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

Given, A garden table and a bench cost $964 combined.

i.e. G + B = $964 .............. (i)

and, the garden table costs $64 more than the bench

i.e. G = B + $64 ............. (ii)

From eq (i) and (ii), we get

B + $64 + B = $964

or, 2B = 964 - 64 = 900

or, B = 900/2 = 450

Hence, the cost of the bench is $450.

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Answer:

72 in^3

Step-by-step explanation:((3*3*6)/3  ) * 4

The frequency distribution table starting with score 26 will be illustrated as:

Class interval Number of data.

26 - 31. 2

32 - 37. 4

38 - 43. 0

44 - 49. 1

Based on the information illustrated, let's assume that the numbers that we have include 27, 26, 45, 32, 35, 37, 36.

It should be noted that frequency distribution are portrayed as frequency table me chart. It shows the actual number or observations.

In this case, the class width is 26 - 31, 32 - 37, etc. The frequency distribution is illustrated above.

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Answer:

Line A

Step-by-step explanation:

Any line facing towards the left side of the coordinate plane will have a negative slope.

Line C is facing towards the right

Line D and B doesn't have a slope

A is the only right answer

Answer:

0.262 hectares

Step-by-step explanation:

To find the size of each property, you need to divide the total area of the land by the number of properties. In this case, the total area of the land is 1.31 hectares, and it is being divided into 5 properties, so the size of each property is:

Property size = 1.31 hectares / 5 properties = 0.262 hectares/property

Therefore, each property will be 0.262 hectares in size.

The solution is Option C.

The number of pints of fresh berries is 6 pints and is calculated by the equation 3 ( f + 2 ) = 24

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of pints of fresh berries be represented as f

Now , the number of pints of berries Samantha got initially = 2 pints

So , the total number of berries Samantha got = f + 2

The cost of 1 pint of berries = $ 3

The total amount Samantha paid for the berries = $ 24

Now , the equation will be

Total amount Samantha paid for the berries = cost of 1 pint of berries x ( total number of berries Samantha got )

Substituting the values in the equation , we get

24 = 3 ( f + 2 )   be equation (1)

On simplifying the equation , we get

Divide by 3 on both sides of the equation , we get

f + 2 = 8

Subtracting 2 on both sides of the equation , we get

f = 6 berries

Hence , the equation is 3 ( f + 2 ) = 24

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Answer:

3/7 ; -7

Step-by-step explanation:

1)

(7-4)/(10-3)

3/7

2) -7 because is the number that multiplies x

Answer: 2.2 | 4.2 | 4.1

Step-by-step explanation:

The quadratic equation does not have solutions where both x and y are integers.

Here we have the following quadratic equation:

2x^2 + 5y^2 = 14

We want to check that we can't solve this equation with x and y integers, to see that, we can start by isolating one of the variables:

2x^2 + 5y^2 = 14

5y^2 = 14 - 2x^2

y^2 = (14 - 2x^2)/5

y = ±√((14 - 2x^2)/5)

Now, trivially:

(14 - 2x^2)/5

Is not an integer for any integer value of x, and this happens because 5 is not a factor of 14, thus, for any integer value of x the value of y that we get is non integer, then there aren't two integers that solve the quadratic equation.

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Explanation:

The equation y - b = m(x - a) is a mathematical formula that describes the relationship between the x and y coordinates of a point on a line. The equation is called "point-slope form" because it uses the coordinates of a point on the line (point a) and the slope of the line (m) to describe the line.

The equation has three parts: y, b, and m(x - a).

The y part of the equation represents the y-coordinate of a point on the line. This value can change depending on the x-coordinate of the point.

The b part of the equation is the y-coordinate of a known point on the line. This value is fixed and does not change.

The m(x - a) part of the equation represents the slope of the line and the x-coordinate of the known point on the line. The slope is represented by m, and the x-coordinate of the known point is represented by a.

To use the equation to find the y-coordinate of a point on the line, you first need to know the x-coordinate of the point and the values of b, m, and a. Then, you can substitute these values into the equation and solve for y.

For example, if the x-coordinate of a point on the line is 5, the y-coordinate of a known point on the line is 2, the slope of the line is 3, and the x-coordinate of the known point is 1, then the y-coordinate of the point can be calculated as follows:

y - 2 = 3(x - 1)

y = 3x - 3 + 2

y = 3(5) - 3 + 2

y = 15 - 3 + 2

y = 14

Therefore, the y-coordinate of the point with x-coordinate 5 is 14.

In summary, the equation y - b = m(x - a) is a mathematical formula that describes the relationship between the x and y coordinates of a point on a line. The equation uses the coordinates of a known point on the line and the slope of the line to describe the line, and you can use it to find the y-coordinate of a point on the line if you know the x-coordinate of the point and the values of b, m, and a.

Five times the sum of some number plus 3 is equal to 9 times the number minus 9.

5 (x + 3) = 9x - 9

expand left side:

5x + 15 = 9x - 9

subtract 15 from both sides:

5x + 15 - 15 = 9x - 9 - 15

5x = 9x - 24

subtract 9x from both sides:

5x - 9x = 9x - 24 - 9x

-4x = -24

divide both sides by -4:

-4x/(-4) = -24/(-4)

x = 6

Answer: 2560

Step-by-step explanation:

m= -8

n=4

p= -12

4(7mp+3p)+4n= 4((7 x -8 x -12)) +4(4)= 2560

Answer:

125.5cm³. (your answer is correct)

Step-by-step explanation:

Volume = cross-sectional area×height

= πr²×h

= (3.14)(2²)×10

= 3.14×4×10

= 125.6cm³

Answer:

I dont understand

Step-by-step explanation:

Step-by-step explanation:

When you are looking for a no that DIVIDES the no, then you have to find HCF. When you are looking for a no that is DIVISIBLE, then you have to find LCM (mathematical explaination)

Answer:

x = 2

y = 6

Step-by-step explanation:

5x-4=y

We add 4 and subtract y from both sides

5x - y = 4

Now we have 2 equation

5x - y = 4

-2x + 2y = 8

Let's find the x first! We time the first equation by 2

10x - 2y = 8

-2x + 2y = 8

Now add both equations

8x = 16

x = 2

Now let find the y by put 2 back in the x

-2(2)+2y=8

-4 + 2y = 8

2y = 12

y = 6

Answer: $355

Step-by-step explanation:

First, find the total of cheques she writes out by taking 558 + 453 = $1011

Then add 78 to it because she is overdrawn by $78 at the end, so we now have $ 1089.

Then we take 1089 - 734 = $355

So, her cheque account balance before she received her pay was $355

Answer:

112.5°

Step-by-step explanation:

The corner of the square that remains is a 90° angle.

The opposite corner started as a 90° angle that was folded in half into two 45° angles. Then each 45° angle was folded in half into two 22.5° angles. Then you put two 22.5° angles together to make a 45° angle.

So far we have two opposite angles measuring 90° and 45°.

The quadrilateral is a kite. The other two opposite angles are congruent.

The sum of the measures of the angles of a quadrilateral is 360°.

360° - 90° - 45° = 225°

225°/2 = 112.5°

The correct statement is end behavior is decreasing to the left and increasing to the right, which statement must be true about the function is The order is odd and the leading coefficient is negative.

As x approaches infinity it is detected by its limit. On the left side, it is given by:

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