Colton works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commision on top of his base salary equal to 10% of his total sales for the week. How much would Colton make in a week in which he made $1075 in sales? How much would Colton make in a week if he made xx dollars in sales?

Answer:

x = 15

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 9² + 12² = 81 + 144 = 225 ( take square root of both sides )

x = [tex]\sqrt{225}[/tex] = 15

Answer:

x = 15

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the given values into Pythagoras Theorem and solve for x:

[tex]\implies 9^2+12^2=x^2[/tex]

[tex]\implies 81+144=x^2[/tex]

[tex]\implies 225=x^2[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{225}[/tex]

[tex]\implies x=15[/tex]

By solving system of linear equation we get Cost for 1 cheeseburger $5 and 1 cups of lemonade $2

A system of linear equations is a collection of two or more linear equations that have the same variables. A linear equation is an equation in which the highest power of the variable is 1. In other words, the equation is a straight line when graphed.

Here is an example of a system of linear equations:

3x + 2y = 19

2x + 4y = 18

This is a system of equations problem, where we can use the information provided to set up two equations and then solve for the unknown variables. Let x be the cost of one cheeseburger and y be the cost of one cup of lemonade.

From the information provided, we know that:

3x + 2y = 19 (the cost of 3 cheeseburgers and 2 cups of lemonade is $19)

2x + 4y = 18 (the cost of 2 cheeseburgers and 4 cups of lemonade is $18)

To find the cost of one cheeseburger and one cup of lemonade, we can solve this system of equations. One way to do this is by substitution.

3x + 2y = 19

we get

[tex]x=\frac{19-2y}{3}[/tex]

substituting x in equation 2x+4y=18

we get

 [tex]2(\frac{19-2y}{3})+4y=18[/tex]

[tex]38 - 4y + 12y = 54\\8y = 16\\y = 2[/tex]

substituting y in equation 3x+2y=19

[tex]3x+2(2)=19\\3x=19-4\\3x=15\\x=5[/tex]

The cost of one cup of lemonade is $2

The cost of one cheeseburger is $5

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Step-by-step explanation:

I'm pretty sure it's 19200? or maybe im writing is wrong

Answer:

After 24 years population of the city will be 27000.

exponential function.

Step-by-step explanation:

in picture

Answer: look it up :)

Step-by-step explanation: click new tab. then type 'the sum of a number and 9'. the first or second result will come up with your answer, n+9 is the one I got.

Answer: x+9 or n+9

Step-by-step explanation: sum refers to addition you can put x for "a number"  thus you get x+9 as your expression or n+9 for your teacher but both are variables so it doesn't matter if it's j, y, u, or p what's there functionality wise but your teacher might want it a certain variable like n

Therefore , the solution of the given problem of equation comes out to be a.60 , b.20 and c.21.

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

Given : 9(x - y) = 30,

or (x-y) =30/9

To find :  

a) 18(x - y) = ?

=> 2(9(x - y))

=> 2(30)

=> 60

b)6x - 6y = ?

=> 6(x-y) = 6(30/9)

=> 2*30/3

=> 20

c) 9(x-y)-9

=> 30 -9

=>21

Therefore , the solution of the given problem of  equation comes out to be a.60 , b.20 and c.21.

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The cost of renting the car for one day and driving 200 miles is $54.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, In some cities you can rent a car for $18 per day and $0.20 per miles.

Establishing the equation for finding total cost y for x miles and d days

y = 18d + 0.2x

For 200 miles, the cost =

y = 18×1+0.20×200

y = 18+40

y = $54

Hence, the cost of renting the car for one day and driving 200 miles is $54.

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Total amount paid by Donna is $16,689.6 and interest paid is $789.6.

The cash up front paid by the buyer in real estate transactions and other significant purchases is known as a down payment on a house. For a property being used as a primary residence, down payments, which are typically a percentage of the purchase price, can range from as little as 3% to as much as 20%.

According to question:

Given,

Price of car= $15,900

Down Payment=$4800

number of months=12 x 4=48 month

Monthly payment=$245.70

Total amount Donna paid = Down payment+ all monthly installment

Total amount = $4800+ 48 x 247.70 =$16,689.6

Interest Paid = $16,689.6 - $15,900 = $789.6

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Answer:

15+5=v

Step-by-step explanation:

Solve

1. Add the numbers

15+5 = v

20 = v

2. Move the variable to the left

20 = v

v = 20

3. Solution

   v = 20

Therefore , the solution of the problem of probability comes out to be  

Probability = 0.25 or 25% that he will pass using this random option picking method.

Probability is the likelihood or potential for something to event.  For instance, there is only one way to get a head and a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) must equal 12. Classical: (equally likely results) (equally probable outcomes) S, the sample location (the collection of all distinct outcomes that could occur), Definition of Relative Frequency and Subjective Probability.

Here,

Given : t the end of each week there is a 5 questions multiple choice test.

and

Has 4 options.

Probability that he will pass using this random option picking method.

=> Probability = Favourable events / Total no of outcomes

=>  Probability = 1 /4

=> Probability = 0.25 or 25%

Therefore , the solution of the problem of probability comes out to be  

Probability = 0.25 or 25% that he will pass using this random option picking method.

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Answer:

no solutions

Step-by-step explanation:

   -9x-2y=5

- (-9x-2y=11)

-9x-(-9x) - 2y-(-2y) = 5 - 11  ==> subtract the top two equations

-9x + 9x - 2y + 2y = -6  ==> subtracting by a negative number is equivalent

                                       to adding by a positive number

(-9x + 9x) - 2y + 2y = -6

0 - 2y + 2y = -6

0 - 0 = -6

0 [tex]\neq[/tex] -6  ==> Hence, there is no solutions.

The three ways to purchase a vehicle include: (1) On lease  (2) On hire purchased and (3) On cash basis

A vehicle can be purchased on the following ways:

Lease:  This involves granting the user access on the property over a period of time before he could make payment

Hire purchase:  In this method, the buyer deposits first initial money while he agrees with the seller to make the payment of the balance on installment basis

Cash:  In this method the buyer pays cash at prompt or on the point of purchase

Advantages include:

It places the buyer on good life without cash

He enjoys the luxurious life

Disadvantages:

He can run away with the vehicle

The seller looses in cash of accident taking the life of the buye

Additional expenses include

Cost of maintenance

Repairs

Fueling

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The Value for x and y as follow:

A) x=2 and y=-8

B) x = -2 and y = 5

C) x = -9/4 and y= -5/2

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Given:

A) 9x- 2y = 34...............(1)

5x+ 2y = -6..............(2)

Adding equation (1) and (2) we get

9x -2y = 34

5x + 2y = -6

_____________

14x = 28

x= 28/14

x= 2

and, 5x +2y= -6

5(2) + 2y= -6

2y = -6 -10

y = -8

B) x+ 6y = 28.....................(3)

2x -3y = -19................(4)

Multiply equation (2) by 2 we get

4x - 6y = -38.......................(5)

Adding equation (3) and (5), we get

x + 6y = 28

4x- 6y = -38

___________

5x = -10

x= -2

and, x+ 6y= 28

-2 +6y= 28

6y= 30

y=5

C) 8x -6y = -3................(6)

6x -5y = -1......................(7)

Multiply equation (6) by 5 and equation by (6), we get

40x - 30 y = -15

36 x - 30y = -6

-       +           +

____________

4x = -9

x= -9/4

and, 8x - 6y = -3

8(-9/4) - 6y = -3

-18 - 6y= -3

-6y = 15

y = -5/2

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Answer:

Step-by-step explanation:

read the data numbers

it's none of the above its 27.5

Answer:316.8

Step-by-step explanation:

Answer:316.8

Step-by-step explanation:

Answer:

[tex]\dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]

Step-by-step explanation:

Given expression:

[tex](a^{10}b^{0}cde^{3})^{-2}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{(a^{10}b^{0}cde^{3})^{2}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{1}{a^{(10 \times 2)}b^{(0 \times 2)}c^2d^2e^{(3 \times 2)}}[/tex]

Simplify:

[tex]\implies \dfrac{1}{a^{20}b^{0}c^2d^2e^{6}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^0=1:[/tex]

[tex]\implies \dfrac{1}{a^{20}(1)c^2d^2e^{6}}[/tex]

[tex]\implies \dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]

The correct option regarding which of the sentences represents a trigonometric identity is given as follows:

b. None of the equations are identities.

A trigonometric identity is a relation that is true for all possible angle measures of [tex]\theta[/tex]

The first relation is given as follows:

[tex]4\cos{\theta}\tan{\theta}\sec{\theta} = 4[/tex]

The tangent and secant equations are given as follows:

Hence:

4cos(x)tan(x)sec(x) = 4cos(x) x sin(x)/cos(x) x 1/cos(x)

4cos(x)tan(x)sec(x) = 4sin(x)/cos(x)

4cos(x)tan(x)sec(x) = 4tan(x).

Meaning that the first statement is not an identity.

The second relation is given as follows:

[tex]\frac{9\sec^{2}{\theta}}{\cos^{2}{\theta}} - \frac{\tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]

With a single denominator, we have that:

[tex]\frac{9\sec^{2}{\theta} - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]

The secant identity is given as follows:

[tex]\sec^2{\theta} = 1 + \tan^2{\theta}[/tex]

Hence:

[tex]\frac{9\sec^{2}{\theta} - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]

[tex]\frac{9(1 + \tan^2{\theta}) - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]

[tex]\frac{9 + 8\tan^2{\theta}}{\cos^{2}{\theta}} = 2[/tex]

Is also a false statement, hence neither is an identity and option B is correct.

The statements are given by the image presented at the end of the answer.

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For the given graph, the domain and range of the relation equals [-4, 6].

A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the objects x and y come from different sets, then the objects are said to be connected. One kind of relation is a function.

In other words, the ordered pair collection, where the ordered pair is made up of an object from each set, is used to define the relationship between the two sets. As an illustration, consider the set notation symbols (-2, 1), (4, 3), and (7, -3) with curly brackets.

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The piecewise-defined function for this graph will be y = -(3/5)x - 4/5 for x < 2 and y = (5/2)x - 7 for x ≥ 2.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The equation of the line that passes through (-3, 1) and (2, -2) is given as,

(y + 2) = [(- 2 - 1) / (2 + 3)](x - 2)

y + 2 = - (3/5)x + 6/5

y = -(3/5)x - 4/5

The equation of the line that passes through (2, -2) and (4, 3) is given as,

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

y + 2 = (5/2)x - 5

y = (5/2)x - 7

The piecewise-defined function for this graph will be y = -(3/5)x - 4/5 for x < 2 and y = (5/2)x - 7 for x ≥ 2.

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The next step in the series is, shown in Option C.

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

Given that;

There are three steps are shown.

Now, In first step, only one line shown.

In second line the line is left to first line.

And, So on.

Hence, The next step in the series is, shown in Option C.

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Answer:

6/7

Step-by-step explanation:

36/42 = 36:6/42:6 = 6/7

Answer:

b

Step-by-step explanation:

i think i say c because a is 30 degrees and c is 90 the whole triange needs to be 180 so b would be 60 also you see one side is 10 the other side also known as b is also 10 they have to be the same length and a is five because half of 10 is 5

The given polynomial is a factor of P(x) because P(-5)=0.

The Remainder Theorem states that if a synthetic division of a polynomial by x = a results in a zero remainder, then x = an is a zero of the polynomial (thanks to the Remainder Theorem), and x an is also a factor of the polynomial (courtesy of the Factor Theorem).

The Factor Theorem states that x - c is only a factor of P(x) when P(c) = 0.

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Therefore ,the top limit of the normal class of three parts of mean class 10th is therefore 60, and the median class is 40–60.

Simply average a collection of three or more numbers yields the phrase "mean." The median method, which employs the maximum of a group of products, and the arithmetic average approach, which uses the sum of both the series' values, are two ways to determine the mean for just a given set of numbers.

Given:

Grades received:

X   f   fi   xi

0-20,     10  15   150

20-40,  30  18   540

40-60, 50 21   1050

60-80, 70 29 2030

80-100 90 p   90p

Total: 3770 + 90p + 83p

Mean (3770 plus 90 pi)/(83 plus pi) = 53

=> 3770 + 90p = 83 * 53 + 53p

=> 37p = 629

=> p = 17

17 students received scores in the 80–100 range.

f = 29 and modal class 60-80

minimum of modal class 60

=> 60 + 20 * 8/20

=>68

68 is the modal marks value.

=> ∑fixi = 3770 + 90p = 3770 + 90(17) = 5300

=> 100/2 = 50

60 is the maximum median class for 3 phases of class 10 with a median class of 40–60.

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Answer:

9.583 hours

Step-by-step explanation:

multiply both of them and divide by 60 youll get. how long it will take for u to complete an anime

a) The angular speed of the saw blade in radians per minute is;

460.77 radians per minute.

b) The linear speed (in feet per minute) of the saw teeth as they contact the wood being cut is; 7.46 * 10⁻⁴ ft/min

a) Angular speed is defined as the speed of the object in rotational motion

The formula of the angular speed is; ω = θ / t

where;

ω is the angular speed

θ is the angular rotation

t is the time taken.

We are given;

In one revolution, the angle made is 2π radian.

In 4400 revolutions = 2π * 4400 radian

= 8800π radians

We know that ,

1 hour = 60 minute.

Thus;

Angular speed = 8800π/60

= 460.77 radians per minute

b) The relationship between the linear speed and angular speed in a uniform circular motion is given by the formula;

s = rω

where;

s is the linear speed

r is the radius

ω is the angular speed.

radius = 8 ¼ -inch/2 = 33/8 inches

Conversion from inches to feet gives;

33/8 inches = 0.34375 ft

Thus;

s =  0.34375/460.77

s = 7.46 * 10⁻⁴ ft/min

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Answer:

y = 1/3x - 7

Step-by-step explanation:

start with the point-slope form:

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

substitute the values of (x,y) into the formula:

(y-(-5)) = 1/3(x-6)

y+5 = 1/3x - 2

now write in slope-intercept form:

y = 1/3x - 2 - 5

y = 1/3x - 7