7 people went to the movies the number of sdults was one more than the number of children write and solve an equation

The following equation describes a circle.

Simora [160]

Answer:

Center = (5, -2) and radius = √33

Step-by-step explanation:

The equation of a circle is given by the formula;

(x-a)² + (y-b)² = r² ; where (a,b) is the center of the circle and r is the radius of the circle.

In this case;

2x² - 20x + 2y² + 8y =40 ;

Dividing both sides of the equation by 2 we get;

x² - 10x + y² + 4y = 20

we can then use the completing the square on both x and y terms.

x² - 10x + y² + 4y = 20

x² + 2(-5)x + 25 + y² + 2(2) y + 4 = 20 +9 + 4

In standard form we get;

(x-5)² + (y+2)² = 33

Therefore;

Center = (5, -2) and radius = √33

3 0

3 years ago

Tulky draws 4 ten sticks and less than ten circles to make what number

11111nata11111 [884]

I would try -50 i really dont get what your asking but i did -10 -40=50

3 0

3 years ago

Write an equation of the line that passes through (18,2) and is parallel to the line 3y-x=-12 .

uysha [10]

Answer:

$y = \frac{1}{3}x-4$

Step-by-step explanation:

Step 1: Solve for y in the first equation

$3y - x = -12$

$3y - x + x = -12 + x$

$\frac{3y}{3} = \frac{x}{3} - \frac{12}{3}$

$y = \frac{1}{3}x - 4$

Step 2: Determine the important aspects

We know that our line is parallel to the other line that has a slope of 1/3 which means that our slope is also going to be 1/3. We also know that our line crosses the point (18, 2) which means that we can use the point slope form to determine our equation

Point Slope Form → $(y-y_1) = m(x - x_1)$

Step 3: Plug in the information and solve

$(y-2) = \frac{1}{3}(x - 18)$

$y - 2 = \frac{1}{3}x - 6$

$y - 2 + 2 = \frac{1}{3}x - 6 + 2$

$y = \frac{1}{3}x-4$

Answer: $y = \frac{1}{3}x-4$

7 0

2 years ago

(a) Show that the volume of a metal sphere of radius 15 cm is 14140 cm”, correct to 4 significant

Sladkaya [172]

Answer:

a) The volume of the sphere is approximately 14,137.16694 which is 14,140 cm³ correct to 4 significant figures

b) The volume of water required to fill the tank is approximately 103,670 cm³

Step-by-step explanation:

a) In the question, the radius of the sphere, r = 15 cm

The formula for the volume, 'V', of a sphere is given as follows;

$V = \dfrac{4}{3} \times \pi \times r^3$

Where;

r = The radius of the the sphere

V = The volume of the sphere

Plugging in the value for the radius, 'r', of the sphere, in the equation for, 'V', we get;

$V = \dfrac{4}{3} \times \pi \times 15^3 \approx = 14,137.16694$

Therefore;

The volume of the sphere to 4 significant figures is V ≈ 14,140 cm³

b) The parameters of the cylindrical tank are;

The height of the cylindrical tank, h = 60 cm

The radius of the cylindrical tank, r = 25 cm

The volume of a cylinder, V = π·r²·h

∴ The volume of the cylindrical tank without water, ' $V_t$ ', is given as follows;

$V_t$ = π × (25 cm)² × 60 cm ≈ 117809.72451 cm³

The volume of water, $V_{water}$ , required to fill the tank with the sphere of volume 'V' placed inside is given as follows

$V_t$ = V + $V_{water}$

∴ $V_{water}$ = $V_t$ - V

From which we get;

$V_{water}$ ≈ 117809.72451 cm³ - 14,140 cm³ = 103,669.72451 cm³ ≈ 103,670 cm³

The volume of water required to fill the tank, $V_{water}$ ≈ 103,670 cm³.

8 0

3 years ago

How do you find out if a like is parallel, perpendicular, or coincidental when theres 2 equations

finlep [7]

The slope intercept form of the equation of a line is given as:

y = mx + c

where m = the slope of the line

c = the y - intercept of the line

1) Two line are parallel if they have the same slope

That is:

$\begin{gathered} \text{If the equation for line 1 is: y = m}_1x+c_1 \\ \text{If the equation for line 2 is: y = m}_2x+c_2 \\ \text{Then, line 1 is parallel to line 2 if m}_1=m_2 \end{gathered}$

2) Two equations are perpendicular if the slope of one is the negative inverse of the other.

$\text{That is : m}_1=\text{ }\frac{-1}{m_2}$

3) Two equations are coincidental if they have the same slope and the same y intercept

$\begin{gathered} \text{That is: m}_1=m_2_{} \\ \text{and c}_1=c_2 \end{gathered}$

8 0

1 year ago