the-sales-tax-t-on-a-purchase-is-a-function-of-the-amount-a-of-the-purchase-the-sales-tax-rate-in-th

Question

The sales tax $t$ on a purchase is a function of the amount $a$ of the purchase. The sales tax rate in the city of East chester is 8$\% .$ 
a. Write a rule in function notation that can be used to determine the sales tax on a pur- chase in East chester.
b. What is a reasonable domain for this function?
c. Find the sales tax when the purchase is $\$ 5.00 .$
d. Find the sales tax when the purchase is $\$ 16.50 .$

Emma Chickles · Accepted Answer

and this problem were asked to describe the sales tax T as a function of the price of the product A were given of the sales tax rate is 8% so the sales tax is a function of a 0.8 times a. Now he has to find the domain of the function. Since it&#x27;s impossible to have a negative price, it makes sense that the lower limit of the domain is syrup, and there&#x27;s no upper limit now. Asked to find sales tax if the price is five, so something the value of five into A This is your Quincy or eight times five. This is equal to 0.4 summer. Similarly, we can find the sales tax when the prices equals 16.5 by substituting the value of 16.5 into a, and this is equal to 1.32

Ankit Gupta · Answer

we have been doing that TX with amount off sales text Just so the exes seals X. Okay, so service text Andi the question we have been given that it&#x27;s the sales techstars on the purchase x dollars. So for purchase X dollars will be just the excel sticks. And to find the tax, we take 8% off the participants 8% off purchase price on that purchase Prizes X so well, look it by 100 multiplied by X hands, The T X consult Toby, it takes divided way under. This is the real representation. No, we will move towards the sitting part that is, to find the numerical representation numerical representation. For that, we&#x27;ll make a table off X, add the export different value. So if we put different values, what we get, then your access you definitely notice actually, because 20 on when it is one, it is 800 similarly for values for values off four, will you get the value of zero point? Great. When they put their eight, it will be 0.64 Now, this particular thing gives the numerical numerical representation of the same novel moved towards the graphical representation. So we will be just a plotting these values on def implored these values What? We get the gate Something graph like this? No one thing eunuchs toe noted down here is that first, this is our X axis Onda, This is our why access, which is representing? No. Are you okay on this? Is the graphical representation on one of what? Anything is that it&#x27;s only having the values for X greater than other questions. It&#x27;ll because your approach is off X cannot be negative. Hence, it is only considering this particular area that is positive. Xxx which is? I like it. Okay, so this particular thing will be the graphical representation off the given the question.

Ankit Gupta · Answer

So it is given to me that the sales tax rate they don&#x27;t decks is equal. Toe 7.5 divided by 100 7.5% that is 7.5 divided. 100 on a party is over off X dollars. So if I have toe write a function, then I&#x27;ll write FX Equal toe 7.5 divided by 100 but declared by X so fxc Koldo 7.5 divided by 100 x so sales tax on but $86 in place. I&#x27;ll just put exit corridor $86. So I know I hope a physics is a horrible 1.5 divided by 100. Glad way. So that comes out to be $6.45. So that is my sales tax. Therefore, sales taxes. The caldo explained for $5. Thank you

Melissa Salvador · Answer

And here we have an equation. Foot back says we&#x27;re income in between 8350. And 33,940. So part area of those problems asking for the domain. So if they tell us that this equation Onley works for on those two numbers and that means that Ordina Maine is gonna go from 8350 to 33,150 including both of those numbers. No. Corby&#x27;s asking how many taxes if we have an income, uh, 20,000. So that put in 20,004 X. So we put all of this, that calculator, and we get that we would have to pay, um, 2582.5 dollars as our taxes. Okay, Marcie is asking, what is the independent and dependent variable? So the independent is the one that&#x27;s changing. So what is changing would be the incumbent we have, and the taxes depend on the income. So that would be your dependent variable. Thank you. Right now, party is asking us to graft this. So we are going to good right here. You kind of just graph it. We&#x27;re gonna go 34 by it says in the thousands off dollars, right. And then we&#x27;re gonna go like threes here. 369 It will 15. 18 in one before by 27. When? 30. This would be also in the Thompsons of dollars. So no, what we&#x27;re going to do then, IHS kind of like, figure out where we&#x27;re gonna put of this equation. So we&#x27;re told that it goes from 8350 to, um, 33,000, 950. So what, we can dio kind of just love those numbers into our equations and see what we get. So every plug in, um, 8350 as our income we get I am, Yeah, 800. Um, 35 rocks are cats, is so let&#x27;s love that point. So 80,350 with can be kind of all right there, right before the 9000 and before the 1000 and taxes? No. If we plug in the 33,150 of income you get that we would pay for thousands of 175 of taxes so 33 will be after that 30,000 and then 4000 would be before the flag 1000. So kind of so over there. And so that right there will be dollar line. And so this is the point 8350 835. And this is the point 33 9 could be and one of 6 75 Okay, now, Part E is asking if we pay, um, 3707. Let me write those 3707 in 50 cents as attacks is how much is our income? So we put your number, and then we&#x27;re going to then be solving for X. Okay, so we subtract the 835 on both sides and get, um, 2872 point but and that&#x27;s we&#x27;re going to be dividing by the 0.15. And then we get 1000. Oh, sorry. 19,000 one, 150. It is equal to x minus 8240. And we add that and we get that income this 27,400 it is equal to X. And so those are your answers

Yifan Xu · Answer

All right. This question has two parts. The first part is to find a mathematical linear motto that gives them out of cell. Why, in terms of the retail price X are so let us right on the general form of this motto. It&#x27;s gonna be why equals K x were The main aim is to find the K here. And since we&#x27;re given a pair of white Annex where it&#x27;s gonna be 11. 40 So text eco&#x27;s k times the price 189 point 90 Nice and are so no, we can sew for the K. It&#x27;s gonna be 11 and four over 180 I 1800.99 All right, so now we can write on the enemy our motto Explicitly. We just plug this cape back. All right, so this Ah, the mathematical motto are at the second part of this question is to use this mater to find this so tax own a purchase of six aim $0.99. So if we have six under 39 0.9 and I of purchase, we&#x27;re gonna multiply. But this case because the X here is this value right over 109.9 and I and then we can get this so stacks being approximately 380 0.40.

Ankit Gupta · Answer

the next function he is, he&#x27;s given point was five x minus 97 5 Unless you&#x27;re buying fight Thank the exhibition the next. You know that. Thanks. Me. Okay. Off. Single person who district the Russian coming eight X dollars. Okay, exit, pretend go in normal. And, uh, this in cultured being between nine thousands and dolar Go. He started 19. Okay, What inclusive. So this emotion in the West Barnidge What? That domain on telling attention. So it&#x27;s weird to find so domain. No, it should be Nine years. 752 6900. Okay, so So no be park. We need to bar the x bill for single let person. Okay, so it is given they get home. So gross income. It&#x27;s dirty pigments. Excess given note That says I could tell you dollars, so that will be boring. 15 then minus nine doodle seven. Place less. News seven. Bind. So no, simply fight. You&#x27;ll get 1 68.5 was my needle seven boy. What? Right there. Then you&#x27;ll get through 546 point through, but Okay, so next part we need to bed, which very well is independent and dependent so income income, it means X independent and two years defend. So golden hour expansion. Okay, so he x is very this multi like 25 in the bracket X 1907 by two point was, like less nine years on 15 face on you get minus four. So we need to call this function. So this is ok. Oh, get real easy as incoming increase. They said this pointed night leaders and this is six out of $900. Okay, so this portion, from this point, up to this point, right? Or you can really see any sovereign coming in reading tests. Also inflating with so electrocution immunity to find out the truth. Gross income on next. You took places 56. I never saved. You know the point late. I mean, I know that X. Okay, so 15 x minus nine Do does like by five is equal to 36.5. So you get a point with my X minus nine. You toes, it doesn&#x27;t take you don&#x27;t out inside. It&#x27;s a protected with 16 points having now divided by point. So you get nine years five one a four life and this bless Nice. You play late, so you get roles. 500

Problem

A muffin shop's weckly profit is a function of th…

Problem 16 Medium Difficulty

Answer

a) $t=8 \% \times a=0.08 \times a$
b) $\mathbb{R}^{+}$
c) $t=\$ 0.40$
d) $t=\$ 1.32$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Alayna H.

Caleb E.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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a) $t=8 \% \times a=0.08 \times a$b) $\mathbb{R}^{+}$c) $t=\$ 0.40$d) $t=\$ 1.32$

Algebra 2 and Trigonometry

Alayna H.

Caleb E.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Alayna H.

Caleb E.

Maria G.

Kristen K.

a) $t=8 \% \times a=0.08 \times a$
b) $\mathbb{R}^{+}$
c) $t=\$ 0.40$
d) $t=\$ 1.32$

Ann Xavier Gantert

Algebra 2 and Trigonometry