1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Natali [406]
2 years ago
11

Gunther's starting weight is 248 pounds, and he plans to lose 2 pounds each week. Use a linear equation to determine Gunther's w

eight after 10 weeks. What linear equation??
NEED HELP ASAP DUE TODAY!!! PLEASE AND THANK YOU :)
Mathematics
1 answer:
n200080 [17]2 years ago
8 0

Answer:

......

Step-by-step explanation:

With these types of problems, it's best to label the unknowns and figure out an equation for what we want to find. Here, we're interested in weight in pounds, which I'll call W, as a function of the number of weeks that have gone by, which I'll call n. So if we can get an equation that relates W to n, we can answer the question of "how many weeks to reach 175 pounds?" by plugging in W = 175 to our equation and solving to find out what value of n gives us that.

Suppose Alex weighs P pounds at the start of his diet. We don't know what P is yet, but we'll aim to find its value later with the information the question gives us.

After 1 week, Alex will lose 2 pounds and will weigh P - 2 pounds

After 2 weeks, Alex will lose another 2 pounds and weigh (P - 2) - 2 = P - 4 pounds

After 3 weeks, Alex will weigh (P - 4) - 2 = P - 6 pounds

You can see the pattern here: after every week, knock off 2 pounds. So in general after n weeks, Alex will lose 2n pounds from his start weight, and he will weigh P - 2n

That gives the equation W = P - 2n, or equivalently

W = -2n + P

We can recognize this as a linear equation, which takes the form y = mx + b, where:

- x is the independent variable,

- y is the dependent variable (the thing that changes as a function of x),

- m is the slope (how much y changes for every unit change in x), and

- b is the y-intercept (that is, the value of y when x = 0).

In our equation W = -2n + P, the number of weeks n is the independent variable, weight W is the dependent variable (it varies as a function of the number of weeks), -2 is the slope (because Alex weight 2 pounds less for every week that goes by), and P - whose value we don't know yet - is Alex's starting weight (i.e., the value of W when n = 0).

To find the value of P, we can use the information in the question that after 6 weeks, Alex weighs 205 pounds. In other words, when n = 6, W = 205. Plug that into our equation and get:

205 = P - 2*6

We can solve that for P:

205 = P - 12

Add 12 to both sides:

P = 205 + 12 = 227

So Alex weighs 227 pounds when he starts the diet, and we have

W = -2n + 227

This is the linear equation the question is asking for.

To find how many weeks Alex needs to reach his target weight of 175 pounds, set W = 175 in the equation and solve it for n:

175 = -2n + 227

Move the -2n over to the other side:

2n + 175 = 227

Subtract 175 from both sides:

2n = 227 - 175

2n = 52

Divide both sides by 2:

2n/2 = 52/2

n = 26

So if he keeps losing 2 pounds per week, Alex will reach his target weight of 175 pounds after 26 weeks.

Of course in real life weight loss doesn't necessarily work like in this question (usually, the rate of loss slows down closer to the goal and the body adapts to eating less). But for the purposes of this question and with this simple linear model of weight loss, Alex would reach his goal weight in half a year.

You might be interested in
Ethan writes
Alex_Xolod [135]
A
1/3 is equal to .33333333333 (which 3 repeats forever)
I hope this helped!
8 0
2 years ago
Read 2 more answers
Find the value of c so that (x-2) is a factor of the polynomial p(x)
blagie [28]

Answer:

<h2>c = 2</h2>

Step-by-step explanation:

\text{If}\ (x-a)\ \text{is a factor fo polynomial}\ w(x),\ \text{then}\ a\ \text{is a root of plynomial}\ w(x):\\\\w(a)=0.\\\\\text{We have}\\\\\text{the polynomial}\ p(x)=x^3-4x^2+3x+c\\\\\text{the factor of the polyniomial}\ p(x):(x-2)\\\\x=2\ \text{is the root of polynomial}\ p(x).\ \text{Therefore we have the equation:}\\\\2^3-4(2^2)+3(2)+c=0\\8-4(4)+6+c=0\\8-16+6+c=0\\-2+c=0\qquad\text{add 2 to both sides}\\c=2

3 0
3 years ago
On Monday the temperature was 6.c overnight it fell to -2.cby how many degrees did it fall
ahrayia [7]
Find the difference between the 2 numbers.
6 - (-2) = 8
So it fell 8.c.
7 0
3 years ago
Maya rode her bike to the park and back. if the trip was 3 3/4 miles each way how far did she ride in all?​
DaniilM [7]
She read 7 1/2 miles. You multiply 3 3/4 by 2
5 0
2 years ago
5. answer please and thank u
Murljashka [212]

Answer:

x^3 - 2x + 4

Step-by-step explanation:

4x^2 - 2x + 6x - 10 + desiredsidelength = x^3 + 4x^2 + 2x - 6.

desiredsidelength = x^3 - 2x + 4

5 0
2 years ago
Other questions:
  • PLEASE HELP ME ASAP OR I WILL FAIL:(
    13·2 answers
  • A florist is making flower arrangements with 32 roses and 40 tulips. Each arrangement must be identical. What is the greatest nu
    5·1 answer
  • Ples helpe me its math
    10·2 answers
  • What are the coordinates of Point W?
    14·2 answers
  • If shelia earned 36 points for the ducks, how many points did she earn for each frog?
    10·2 answers
  • You spending $144 for new sweaters,T-Shirts and pants.Sweaters cost $28,T-Shirts (t) cost $14 and pants (p) cost $23,each.Which
    11·1 answer
  • The quantities xxx and yyy are proportional. xxx yyy 5.85.85, point, 8 5.85.85, point, 8 7.57.57, point, 5 7.57.57, point, 5 11.
    5·2 answers
  • The mean score was 72. The standard deviation was 7 percentage-points. Based on this information, what is the best
    15·1 answer
  • G(n)=n2 + 2; Find g(3)<br> g(3)=______
    6·2 answers
  • Solve the equation below
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!