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mestny [16]
2 years ago
13

The question is in the picture i attached. the right answer gets brainlist :) <3

Mathematics
1 answer:
sergeinik [125]2 years ago
7 0

Answer:

∠ 4 = 130°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ 4 is an exterior angle of the triangle , so

∠ 4 = ∠ 1 + ∠ 2 ( substitute values )

11x + 9 = 6x + 6 + 4x + 14 , that is

11x + 9 = 10x + 20 ( subtract 10x from both sides )

x + 9 = 20 ( subtract 9 from both sides )

x = 11

Then

∠ 4 = 11x + 9 = 11(11) + 9 = 121 + 9 = 130°

your friend may have only calculated ∠ 1

∠ 1 = 6x + 6 = 6(11) + 6 = 66 + 6 = 72°

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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.

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