Perform the indicated operation. 3/a

You are given the following equation: (x+3)^2 + (y+9)^2 = 144 What is the<br> (h,k)

qwelly [4]

Answer:

Step-by-step explanation:

Equation of circle: (x - h)² + (y -k)² = r²

(x+ 3)² + (y + 9)² = 144

(x+ 3)² + (y + 9)² = 12²

h = -3 ; k = -9

6 0

3 years ago

The junior and senior class officers are sponsoring a homecoming dance. The total cost for the facilities and catering is $45 pe

larisa86 [58]

Answer:

Domain is (0,∞)

Range is (45, ∞)

Step-by-step explanation:

Let x represents the number of persons and f(x) represents the average cost per person,

∵ Fixed cost = $ 2500

Also, additional cost is $ 45 per person,

So, the total cost for x persons ( in dollars ) = fixed deposit + additional cost for x persons,

= 2500 + 45x

$\text{Average cost for x persons}=\frac{\text{Total cost}}{x}$

$\implies f(x)=\frac{2500+45x}{x}$

Which is a rational function,

∵ A rational function is defined for all real numbers except those for denominator = 0

Denominator of f(x) = x

So, f(x) is defined for all real numbers except x ≠ 0,

Now, the cost can not be negative,

⇒ x > 0

Hence, the domain for f(x) is (0, ∞)

Again,

$f(x)=45+\frac{2500}{x}$

If $x\rightarrow \infty$

$f(x)\rightarrow 45$

So, 45 < f(x) < ∞

i.e., range of f(x) is (45, ∞)

5 0

3 years ago

Find the area of this trapezoid. Be sure to include the correct unit in your answer. Continue 13 cm 20 cm 8 cm 5 cm 0 0/0 08 cm

kodGreya [7K]

Given:

• Upper Base of trapezoid = 8 cm

,

• Lower base = 20 cm

,

• Length of one leg (also height) = 5 cm

,

• Length of other leg = 13 cm

Let's find the area of the trapezoid.

To find the area of the trapezoid, apply the formula:

$A=\frac{a+b}{2}*h$

Where:

A is the area

a is the length of upper base = 8 cm

b is the length of the lower base = 20 cm

h is the height = 5 cm

Plug in the values for a, b, and h to find the area, A:

$\begin{gathered} A=\frac{8+20}{2}*5 \\ \\ A=\frac{28}{2}*5 \\ \\ A=14*5 \\ \\ A=70\text{ cm}^2 \end{gathered}$

Therefore, the area of the trapezoid is 70 cm^2

8 0

1 year ago

A business shows a profit of $110 for selling 20 leather wallets. How much profit would the business make if they sold 35 wallet

NeX [460]

Answer:

Sales of 35 leather wallets will give profit of $192.5

Step-by-step explanation:

If sales of 20 leather wallet gives $110

Sales of 35 leather wallet gives x

Cross multiply

20x = 110 x 35

20x = 3850

Divide both sides by 20

x = 3850/20

x = $192.5

4 0

3 years ago

Help please with this math ;-; I beg of you

RSB [31]

Answer:

49 - 9π

Step-by-step explanation:

Area of white portion = area of triangle - area of circle

To find the area of the triangle:

The area of a triangle can be calculated using this formula

$A=\frac{bh}{2}$ where b = base length and h = height

The height given is 7m and the base length given is 14m

That being said we plug in the given values into the formula

$\frac{14*7}{2} \\14*7=98\\\frac{98}{2} =49$

Hence, the area of the triangle is 49 sq meters.

To find the area of circle

( note that the area is in terms of pi; shown by the answer choices. )

Formula for area of a circle = $A=\pi r^2$

We are given the diameter ( 6m )

However, we need the radius

To convert diameter to radius we divide by 2

6/2 = 3 so the radius = 3m

Now we plug in 3 into the formula

$A=\pi 3^2\\3^2=9\\A=9\pi$

Remember we do not apply pi because the answer should be in terms of pi.

Now we subtract the two

Area of white portion = 49 - 9π

Hence, the answer is A

7 0

3 years ago

Read 2 more answers

Perform the indicated operation. 3/a - 5 + a + 2/a =