Find the length of the radius of the circle, which is inscribed into a right trapezoid with lengths of bases a and b.

Answers

Answer 1

Answer:

Answer:

r = (ab)/(a+b)

Step-by-step explanation:

Consider the attached sketch. The diagram shows base b at the bottom and base a at the top. The height of the trapezoid must be twice the radius. The point where the slant side of the trapezoid is tangent to the inscribed circle divides that slant side into two parts: lengths (a-r) and (b-r). The sum of these lengths is the length of the slant side, which is the hypotenuse of a right triangle with one leg equal to 2r and the other leg equal to (b-a).

Using the Pythagorean theorem, we can write the relation ...

((a-r) +(b-r))^2 = (2r)^2 +(b -a)^2

a^2 +2ab +b^2 -4r(a+b) +4r^2 = 4r^2 +b^2 -2ab +a^2

-4r(a+b) = -4ab . . . . . . . . subtract common terms from both sides, also -2ab

r = ab/(a+b) . . . . . . . . . divide by the coefficient of r

The radius of the inscribed circle in a right trapezoid is r = ab/(a+b).

_____

The graph in the second attachment shows a trapezoid with the radius calculated as above.

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The cost of having a package delivered has a base fee of $10.80. Every pound over 5 lbs cost an additional $0.41 per pound. Write an equation that expresses the cost C in terms of w, the total weight in pounds of a package weighing over 5 lbs. a. C = 10.8w + 0.41 c. C = 0.41(w - 5) + 10.8 b. C = 0.41w + 10.8 d. C = 0.41w + 12.85

Answers

Answer:

c. C = 0.41(w - 5) + 10.8

Explanation:

(w - 5) will represent the number of pounds over 5. For example, for a weight of 6 pounds, 6-5 = 1 is the number of pounds over 5.

The cost is $0.41 for each pound over 5, so that cost can be represented by ...

... 0.41(w - 5)

This charge is in addition to the base charge of $10.80, so the total cost will be ...

... C = 0.41(w - 5) + 10.80

Which choice is equivalent to the product below?Vovino
O A. 4,/25
B. 2V50
O C. 5,2
O D. 10
SUBMIT

Answers

$√(2) . √(10) . √(5) \n = √(2 * 10 * 5) \n = √(100) \n = 10$

Answer:

D.10

Hope you could get an idea from here.

Doubt clarification - use comment section.

10

2*10*5= 100
Square root of 100 is 10

brody is working two summer jobs, making $10 per hour babysitting and making $15 per hour cleaning tables. In a given week, he can work a maximum of 13 total hours and must earn at least $150. If x represents the number of hours babysitting and y represents the number of hours cleaning tables, write and solve a system of inequalities graphically and determine on possible solution.

Answers

The solution is x = 9 and y = 4, meaning Brody would work 9 hours babysitting and 4 hours cleaning tables to satisfy both conditions (total hours ≤ 13 and total earnings ≥ $150).

Given:

Brody can work a maximum of 13 hours: x + y ≤ 13

Brody must earn at least $150: 10x + 15y ≥ 150

These are the two inequalities we need to solve graphically.

Graph the first inequality: x + y ≤ 13

This inequality represents the total number of hours Brody can work, which cannot exceed 13 hours. We'll plot the line x + y = 13 and shade the region below it.

Graph the second inequality: 10x + 15y ≥ 150

This inequality represents the total earnings Brody needs to make, which should be at least $150. Let's simplify it to 2x + 3y ≥ 30. We'll plot the line 2x + 3y = 30 and shade the region above it.

Now, let's find the point where the shaded regions of both inequalities overlap. This point will represent the feasible solution where Brody's working hours and earnings satisfy both conditions.

Solving the system of inequalities graphically, you will find the point of intersection. However, since I can't create a graphical representation here, I'll explain how to calculate the solution point algebraically:

First, solve the equation x + y = 13 for y:

y = 13 - x

Now substitute this value of y into the equation 2x + 3y = 30:

2x + 3(13 - x) = 30

2x + 39 - 3x = 30

-x = -9

x = 9

Now substitute the value of x back into the equation y = 13 - x:

y = 13 - 9

y = 4

So, the solution is x = 9 and y = 4, meaning Brody would work 9 hours babysitting and 4 hours cleaning tables to satisfy both conditions (total hours ≤ 13 and total earnings ≥ $150).

To know more about inequalities:

brainly.com/question/20383699

#SPJ3

Graph y≤13−x (shading down)

graph y≥10− 3/2x (shading up)

fruit-o-rama sells dried pineapple for$0.25 per ounce. mags spent a total of $2.65 on pineapple. How many ounces did she buy?

Answers

If you divide what she spent (2.65) buy the price per ounce (0.25) , you should come up with 10.6 ounces, which is the amount she bought.

Hope this helps :)

Divide the amount paid by the cost per ounce to find the number of ounces.

($2.65) / ($0.25/oz) = 10.6 oz

Answer: She bought 10.6 ounces

What is the value of P+Q+R+S?