Back in 1997, Sally paid $11,448 for a new automobile. This amount included
the 6% sales tax. What was the price of the automobile without the tax? (Please show step by step)

Based on the information given, the number is 13

From the information given;

Let the number be x

We have that;

3(my number) + 10 = my number + 36

Substitute the number as x, we have;

3x + 10 = x + 36

collect like terms

3x - x = 36 - 10

2x = 26

Make 'x' the subject of formula

x = 26/ 2

x = 13

The number is 13

Thus, based on the information given, the number is 13

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You find a book that costs $16.75 and you must pay 4% sales

tax. You use a $25 gift card then only $7.58 is left on the gift card after you buy the book.

A sales tax is a government-imposed consumption tax levied on the purchase of goods and services. A traditional sales tax is assessed at the point of sale, collected by the retailer, and passed on to the government. A firm is liable for sales taxes in a given jurisdiction if it has a nexus there, which can be a physical location, an employee, an affiliate, or some other presence, depending on the rules in that country.

We must 4% sales tax on $16.75 book

Sales tax = 16.75 × 0.04

               = 0.67

The total cost = 16.75  + 0.67

                       = $17.42

He uses a $25 gift card, so he is left with

= 25 - 17.42

= 7.58

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Answer:

20

Step-by-step explanation:

We can solve for the unknown base using Pythagorean's theorem.

Remember Pythagorean's theorem goes as such:

[tex]a^2+b^2=c^2[/tex]

Where a and b are the two legs and c is the hypotenuse. We know one leg and the hypotenuse so we can insert our known values and solve for the unknown.

[tex]15^2+b^2=25^2\\225+b^2=625\\b^2=400\\b=20[/tex]

Or using trigonometry:

Note this is a 45-45-90 triangle, therefore all angles are known.

I'll use the sin function with the B angle.

[tex]sin(45)=\frac{b}{25} \\25*sin(45)=b\\17.67=b[/tex]

I'm assuming this problem was not made for trig, although the answer is still close.

Answer:  Theorem 4 says that the columns of B do NOT span R4. Further, using Theorem 4, since 4(c) is false, 4(a) is false as well, so Bx = y does not have a solution for each y in R4.

Step-by-step explanation:

Yes, the column b span r4. Yes, the equation has a solution for each y in r4.

Matrix is defined as a set of numbers consisting of rows and columns elements.

It consists of rows and columns.

The dimensions of the matrix are determined by m×n.

Given matrix,

[tex]\begin{bmatrix} &1 &3 &-2 &2\\ &0 &1 &1 &-5\\ &1 &2 &-3 &7\\ &-2 &-8 &2 &-1\\\end{bmatrix}[/tex]

R3  → R1

R3→R4+2R1

[tex]\begin{bmatrix} &1 &3 &-2 &2 \\ &0 &1 &1 &-5 \\ &0 &-1 &1 &5 \\ &0 &-2 &-2 &3\\\end{bmatrix}[/tex]

R3→R3+R2

R4→R4+2R2

[tex]\begin{bmatrix} &1 &3 &-2 &2 \\ &0 &1 &1 &-5 \\ &0 &-0 &2 &0 \\ &0 &-0 &0 &7\\\end{bmatrix}[/tex]

This is the row echelon form of B. It has four independent columns and the dimension of r4 is 4.

column of B spans r4.

Row of matrix = 4

No of columns of matrix = No of rows of the matrix.

and the columns of B span r4.

thus we can conclude that the columns of b span r4 and the equation

bx =d y have a solution for each y in r4.

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Answer: its A. ^^

Step-by-step explanation:

The statement describing the comparison correctly is "There is a gap in the data and an outlier in both graphs" option (A) is correct.

Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.

It is given that:

The two-bar graph is given in the picture.

From the data given in the picture.

Both plots contain an outlier and a data gap.

Thus, the statement describing the comparison correctly is "There is a gap in the data and an outlier in both graphs" option (A) is correct.

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The coordinates of one point in the solution set are (0, 0)

The system of inequality is given as

y < 5/6x + 4

-5x + 6y >-6

The graph that completes the question is added as an attachment

From the question, we also have the graph that represents the inequalities in the above system of inequality

As a general rule, the shaded region in a system of inequality represents the solution set

From the attached graph, the point (0, 0) is in the shaded region

Hence, the coordinates of one point in the solution set are (0, 0)

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If a store owner wants to develop a new snack mix by mixing chocolate and trail mix, then the number of pounds of chocolate costing $20.10 per pound that should be mixed with 25 pounds of trail mix costing $2.80 per pound to create a mixture worth $8.41 per pound is equal to 11.99.

The pounds of chocolate needed to create a mixture worth $8.41 per pound can be calculated using an algebraic expression.

An algebraic expression can be defined as an expression consisting of both numbers and letters.

If x = the unknown pounds of chocolate

An algebraic expression can be given as,

20.10x + 2.80(25) = 8.41(x + 25)

Solving for x,

20.10x + 70 = 8.41x + 210.25

Rearranging,

20.10x - 8.41x = 210.25 - 70

11.69x = 140.25

x = 140.25 ÷ 11.69

x = 11.99

Hence, 11.99 pounds of chocolate costing $20.10 per pound should be mixed with 25 pounds of trail mix costing $2.80 per pound to create a mixture worth $8.41 per pound.

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The percentage is the hundredth of any digit or value between 1 to 100 so 35% of 900 will be 315.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The x percentage of any random y digit is given as;

⇒ (x/100) × y

Therefore,

35% of 900 →

(35/100) × 900

⇒ 35 × (900/100)

⇒ 35 × 9

⇒ 315

Hence " The 35% percentage of the amount 900 will be 315".

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The given question is not in English, English translation follows;

What is 35% of 900?

The three types of congruence transformations are rotation, reflection, and translation is TRUE.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

A triangle will remain congruent if we rotate it by any angle in either a clockwise or counterclockwise manner.

If we transform by any amount either horizontal or vertical then it will remain the same so it will be congruent.

A triangle will remain the same if we mirror it on any axis, making it congruent.

Hence "The three types of congruence transformations are rotation, reflection, and translation is TRUE".

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A) The equation for a line that passes through the points (8, 2) and (6, 10) is:

y = -4*x + 34

B) line that has a slope of -2 and that passes through the point (-3, 5)

y = -2*x - 1

A) First we want to find the equation for a line that passes through the points (8, 2) and (6, 10).

Remember that a general linaer equation is of the form:

y = m*x + s

Where m is the slope and s is the y-intercept.

If the line passes through (a, b) and (c, d), then the slope is given by:

m = (d - b)/(c - a)

Then in this case, the slope is:

m  =(2 - 10)/(8 - 6) = -8/2 = -4

Replacing that we get:

y = -4*x + s

To find the value of s we use the fact that the line passes through (8, 2), this means that:

2 = -4*8 + s

2 + 32 = s

34 = s

The linear equation is:

y = -4*x + 34

B) Now we want to find a line that has a slope of -2 and that passes through the point (-3, 5)

Here we already know the slope, so we can write:

y = -2*x + s

Again, to find the value of s, we replace the values in the point in the linear equation:

5 = -2*-3 + s

5 = 6 + s

5 - 6 = s = -1

We conclude that this linear equation is:

y = -2*x - 1

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and

Find amount of tax against each paycheck:

The explicit formula for a geometric sequence is [tex]a_{n}[/tex] =[tex]a_{1}^{r-1}[/tex]

The sequence is:

  1, 2, 4, 8..........

The formula for a geometric sequence,

                   [tex]a_{n}[/tex] = [tex]a_{1}^{r - 1} }[/tex]

                   a, ar, [tex]ar^{2}[/tex], [tex]ar^{3}[/tex]

r = common ratio

n = number of sequences in a series.

Let us understand by the sequence,

Here r = 2 , a = 1

Therefore by putting these values in the equation we get,

[tex]a_{n}[/tex] = [tex]a_{1}r^{n-1} }[/tex]

   = a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex], ........

   1, 2, 4, 8 .........

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A quadratic polynomial can be written using the sum and product of its zeroes as: x² + (α+β) + αβ = 0 Where α and β are the roots of the equation. ☛ x² + ( 0+√5)x + 0 = 0 .

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hi

slope formula is :    y2-y1 / x2-x1  

you can reverse it if you want.   :    y1-y2 / x1 -x2

m =   0- (-2)  / 3 - (-1) =  2/ 4 = 1/2

Answer:1/15

Step-by-step explanation:

Assuming it is multiplication, multiply the numerators: 3 * 2 = 6

Multiply the denominators: 10 * 9 = 90

Put them together for 6/90 and simplify for 1/15

The Spinners landing on green is 10%, blue is 40%,  yellow is 15% and red is 35%.

Given,

Green–6: The spinner lands on green with a relative frequency of 6/60.

Blue – 24: Spinners landing on blue have a relative frequency of 24/60.

Yellow – 9: The spinner's relative landing frequency on yellow is 9/60.

Red – 21:  The spinner lands on red with a relative frequency of 21/60.

Then the simplified fraction, decimal, and percentage are as follows:

When the spinner lands on green, it does so relatively often, especially 6/60

Simple Fraction: 1/10

0.1 in decimal

percent equals 10%

The spinner's landing on blue occurs with a relative frequency of 24/60

Simple Fraction: 2/5

Decimal: 0.4.

percent equals 40%

The spinner's relative frequency of landing on yellow is 9/60

Simple Fraction: 3/20

Decimal: 0.15

Percentage equals 15%

The spinner typically lands on red with a relative frequency of 21/60

Simple Fraction: 7/20

Decimal: 0.35

Percentage: 35%

Hence, the spinners landing on green is 10%, blue is 40%,  yellow is 15% and red is 35%.

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Answer:

The value of x is 12 if the value of f^-1(x) = 2.

Step-by-step explanation:

It is given that f(x) = 4(x + 1), which is an inverse function.

Now,

First of all, let us understand what is a function and an inverse function;

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

On the other hand;

A function that may reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1." Here, (-1) should not be confused with an exponent or a reciprocal.

Now, let us consider the first part of the question;

We have to calculate the value of x when f^-1(x) = 2 given that f(x) = 4(x+1) is the function;

=> f(x) = 4(x + 1)

=> 4(y + 1) = x

=> x = 4y + 4

=> y = (x - 4)/4

=> f^-1(x) = (x - 4)/4

Hence, f^-1(x) = (x - 4)/4 is the inverse of f(x).

Now, let us put the value of f^-1(x) = 2 in the equation so obtained;

=> f^-1(x) = (x - 4)/4  

=> 2 = (x - 4)/4

=> 8 = (x - 4)

=> x = 12

Hence, the value of x is 12 if the value of f^-1(x) = 2.

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Answer:

= 0.25m/s

Step-by-step explanation:

The formula of finding the speed, v is given by

[tex]v \: = \frac{change \: in \: distance \: d}{change \: in \: time \: t} [/tex]

The change in distance from the graph is

∆d = (8 - 6)

= 2 m

The change in time from the graph is

∆d = (20 - 12)

= 8s

Substituting to our formula, we have

[tex]v \: = \frac{2m}{8s} \\ = \frac{1}{4} \frac{m}{s} \\ = 0.25 {m}s^{ -1 } [/tex]

Therefore, the speed v, of the journey between 12 and 20 second is 0.25m/s.

The dimensions are 3 inches, 10 inches, and 13 inches.

It should be noted that the diagonal is the longest side. This will be solved by using Pythagoras theorem.

Therefore,

(2x + 6)²

4x²+ 24x + 36

Reduce to lowest term

x² + 6x + 9

x² + 3x + 3x + 9

x(x + 3) - 3(x + 3)

(x - 3) = 0

x = 0 + 3 = 3

Therefore x = 3

Therefore the dimensions will be:

x = 3

2x + 4 = 2(3) + 4 = 10

2x + 6 = 2(3) + 6 = 12

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2x and 72

Step-by-step explanation:

pls don't use this I don't want you to get a bad grade if it is wrong

Answer: 4x+24

Step-by-step explanation: 8x+40-4x-16

The equation when the accountant charges a fee of $120 to complete a company's taxes. The accountant also charges an additional $40 per hour to complete the taxes is 120 + 40h.

From the information, it should be noted that the

accountant charges a fee of $120 to complete a company's taxes. The accountant also charges an additional $40 per hour to complete the taxes.

Let the number of hours be represented by h.

Therefore, the expression to describe the problem will be:

= 120 + (40 × h)

= 120 + 40h

The equation is 120 + 40h.

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Answer:

7.519*10 power 3 is the answer.

The equation in point-slope form of the line having the given slope m = 2 that contains the given point (4, -9) is 2x - y = 17

It is given that,

Slope is the measure of the steepness of a line.

Equation is the mathematical statement made up of two expressions joined together by the equal sign. For instance 3x - 5 = 16

The slope of a one point line = m = 2

The point through which the line passes = (4, -9)

We need to find the,

The equation in point-slope form of the line having the given slope that contains the given point

The formula which will be used,

(y-y1) = m(x-x1)

where, (x1,y1) = (4, -9) and m = 2

putting the values in the formula, we get

[y - (-9)] = 2. (x-4)

y + 9 = 2x - 8

y - 2x = -17

2x - y = 17

Hence, the equation in point-slope form of the line having the given slope that contains the given point is 2x - y = 17

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Answer:

F

Step-by-step explanation:

Wrong answers

A. current price not doubled

B. price before is 150%, not current price

C. price is reduced by 33.3%, not 25%

D. price is 66.6% of price before

E. price before is 1.5 times greater, not current price

G. price is now 66.6% of price before

H price is 66.6%, not 75%

Answer:

the answer should be 5 sorry if wrong

Answer:

5

Step-by-step explanation:

y=xx5

By the symmetric property of congruence is  ∠FSJ ≅∠UPR.

It is required to find the solution.

Symmetry is defined as a proportionate and balanced similarity that is found in two halves of an object, that is, one-half is the mirror image of the other half. A 2D shape is symmetrical if a line can be drawn through it and either side is a reflection of the other.

Given:

The symmetric property is if y = x then x = y. The order of what is on the left or right side of the equation does not matter. It's like saying 2+3 = 5 is the same as 5 = 2+3.

According to given question we have,

This idea can be extended to congruences because congruent angles have the same measure.

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.

So, ∠UPR ≅∠FSJ, then ∠FSJ ≅∠UPR.

Therefore, by the symmetric property of congruence is  ∠FSJ ≅∠UPR.

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The probability that the card drawn has a composite number written on it is 1/2

The sample space is given as

S  = {1, 2....3}

The list of composite numbers from 1 to 12 is 4, 6, 8, 9, 10, 12

So, we have

Composite = 6

The probability that the card drawn has a composite number written on it is

P = Composite/Sample size

So, we have

P = 6/12

Simplify

P = 1/2

Hence, the probability that the card drawn has a composite number written on it is 1/2

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