You buy 3.17 pounds of peaches, 1.45 pounds of apples, and 1.85 pounds of oranges. What is your total bill?

Three cell phones towers can be modeled by the points X(6,0), Y(8,4), and Z(3,9). Determine the location of another cell phone t

Marat540 [252]

Answer:

The location of the new cell phone tower is $(h,k) = (3,4)$ , and the equation of the circle is $x^{2}+y^{2} -6\cdot x - 8\cdot y = 0$ .

Step-by-step explanation:

The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:

$x^{2} + y^{2}+A\cdot x + B\cdot y +C = 0$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$A$ , $B$ , $C$ - Circunference constants.

Given the number of variable, we need the location of three distinct points:

$(x_{1},y_{1}) = (6,0)$

$36 +6\cdot A + C = 0$

$(x_{2},y_{2}) = (8,4)$

$80 + 8\cdot A + 4\cdot B + C = 0$

$(x_{3},y_{3}) = (3,9)$

$90 + 3\cdot A + 9\cdot B + C = 0$

Then, we have the following system of linear equations:

$6\cdot A + C = -36$ (2)

$8\cdot A +4\cdot B + C = -80$ (3)

$3\cdot A + 9\cdot B + C = -90$ (4)

The solution of this system is:

$A = -6$ , $B = -8$ , $C = 0$

By comparing the general form with the standard form of the equation of the circunference is:

$A = -2\cdot h$ (5)

$B = -2\cdot k$ (6)

$C = h^{2}+k^{2}-r^{2}$ (7)

Where:

$h$ , $k$ - Coordinates of the center of the circle.

$r$ - Radius of the circle.

If we know that $A = -6$ , $B = -8$ and $C = 0$ , then coordinates of the center of the circle and its radius are, respectively:

$h = -\frac{A}{2}$

$k = -\frac{B}{2}$

$r = \sqrt{h^{2}+k^{2}-C}$

$h = 3$ , $k = 4$ , $r = 5$

The location of the new cell phone tower is $(h,k) = (3,4)$ , and the equation of the circle is $x^{2}+y^{2} -6\cdot x - 8\cdot y = 0$ .

3 0

2 years ago

PROBLEM SOLVING A game of bowling has ten frames. After five frames, your friend’s bowling score is 65 and your bowling score $x

Elodia [21]

Considering the situation described, we have that:

a. x = 65 - 8 = 57.

b. You won the game, as you scored 137 and your friend 130.

<h3>What is the equation for the situation after five frames?</h3>

Your friend's score is of 65, and your score of x is 8 less than your friend, hence the equation is:

x = 65 - 8 = 57.

<h3>What are the final scores?</h3>

Your friend score doubled, hence his/her final score is:

2 x 65 = 130.

Your score increased by 80, hence your final score is:

57 + 80 = 137.

You won the game, as you scored 137 and your friend 130.

More can be learned about equations at brainly.com/question/25537936

#SPJ1

8 0

10 months ago

Find (f • g) when f(x) = x^2 + 5x + 6 and g(x) = 1/x+3

Nikitich [7]

Answer:

option D

Step-by-step explanation:

$f(x) = x^2 + 5x + 6$

$g(x)= \frac{1}{x+3}$

(fog)(x) = f(g(x))

Plug in g(x) in f(x)

We plug in 1/x+3 in the place of x in f(x)

$f(g(x))= f(\frac{1}{x+3})= (\frac{1}{x+3})^2 + 5(\frac{1}{x+3}) + 6$

To simplify it we take LCD

LCD is (x+3)(x+3)

$\frac{1}{(x+3)(x+3)}+5\frac{1*(x+3)}{(x+3)(x+3)}+\frac{6(x+3)(x+3)}{(x+3)(x+3)}$

$\frac{1}{x^2+6x+9}+\frac{(5x+15)}{x^2+6x+9}+\frac{6x^2+36x+54}{x^2+6x+9}$

All the denominators are same so we combine the numerators

$\frac{1+5x+15+6x^2+36x+54}{x^2+6x+9}$

$\frac{6x^2+41x+70}{x^2+6x+9}$

Option D is correct

8 0

2 years ago

Read 2 more answers

Solve. −425=x−114 What is the solution to the equation? Enter your answer as a simplified mixed number in the box. FIRST PERSON

Maksim231197 [3]

Answer:

-311

Step-by-step explanation:

−425 = x − 114

=> x = -425 + 114

=> x = -311

Therefore, -311 is our answer.

Hoped this helped.

8 0

2 years ago

Need help with working perimeter and area please

SVETLANKA909090 [29]

Answer:

Area = 228 m²

Perimeter = 60 m

Step-by-step explanation:

The figure given shows a rectangle that has a cut triangular portion.

✔️Area of the figure = area of rectangle - area of the triangular cut portion

= L*W + ½*bh

Where,

L = 20 m

W = 12 m

b = 20 - (8 + 8) = 4 m

h = 6 m

Plug in the values

Area = 20*12 - ½*4*6

Area = 240 - 12

Area = 228 m²

✔️Perimeter = perimeter of rectangle - base of the triangular cut portion

= 2(L + W) - b

L = 20 m

W = 12 m

b = b = 20 - (8 + 8) = 4 m

Plug in the values

Perimeter = 2(20 + 12) - 4

= 2(32) - 4

= 64 - 4

Perimeter = 60 m

5 0

3 years ago

You buy 3.17 pounds of peaches​, 1.45 pounds of apples​, and 1.85 pounds of oranges. What is your total​ bill?

You buy 3.17 pounds of peaches, 1.45 pounds of apples, and 1.85 pounds of oranges. What is your total bill?