Please help find the area (not cm) i’ll give brainliest

The equation of a circle is (x + 6)^2 + (y - 4)^2 = 16. The point (-6, 8) is on the circle.

pantera1 [17]

Answer:

y = 8 is the equation of tangent.

Step-by-step explanation:

The equation of the tangent to the circle at (-6,8) is of the form:

y = mx + c

where m is the slope of the tangent and c is the y-intercept.

The point (-6,8) lies on the circle and the tangent line as well.

Hence (-6,8) satisfies the line equation:

8 = m(-6) + c ⇒ c-6m = 8 -------------1

We know that slope of two perpendicular lines are related as:

$m_{1}\times m_{2}=-1$

At any point on the circle, the normal line at a point is always perpendicular to the tangent line at that point.

Hence :

$m_{normal} \times m_{tangent}=-1$

We can find the slope of the normal at point (-6,8) as it passes through the centre of the circle (-6,4) by using the two-points formula for slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{8-4}{-6+6}$

= ∞

Slope of the normal is infinity and hence slope of tangent is -1/∞ = 0

Hence m=0

Putting m=0 in equation 1 we get:

c = 8

The equation of tangent line at (-6,8) is:

y = 8

6 0

3 years ago

Ten members of the academic team went to a local restaurant after their contest. Each meal combo that came with soda cost $6.75,

Aneli [31]

Answer:

7 ordered with Soda;

3 ordered with water

Step-by-step explanation:

Given

$m \to$ With water

$n \to$ With Soda

So:

$m + n =10$ --- total

$5m + 6.75n = 62.25$ -- cost

Required

Find m and n

$m + n =10$

Make m the subject

$m = 10 - n$

Substitute $m = 10 - n$ in $5m + 6.75n = 62.25$

$5(10-n) +6.75n = 62.25$

$50-5n +6.75n = 62.25$

Collect like terms

$-5n +6.75n = 62.25 - 50$

$-5n +6.75n = 12.25$

$1.75n = 12.25$

Solve for n

$n = 12.25/1.75$

$n = 7$

$m = 10 - n$

$m = 10 - 7$

$m =3$

8 0

3 years ago

a bag contains Stephanie five marbles, some red some blue. The ratio of red marbles to blue ones is 3:2. how many red marbles ar

Nikolay [14]

Answer:

There are 3 red marbles.

Step-by-step explanation:

The ratio of red marbles to blue marbles is 3:2, so for every two blue marbles there are three red marbles. This means that there are three red marbles for every four marbles in the bag. Therefore, if there are five marbles in the bag, there must be three red marbles and two blue marbles.

7 0

2 years ago

Plot 9/10 and 1 2/5 on the number line below

HACTEHA [7]

First one is 9/10 second is 1 2/5

6 0

3 years ago

Answer quickly plz

Rainbow [258]

Answer:

The observation I can make for the values of pi for circles A and B is that the value of pi remains the same whether we find pi using the circumference of the circle or the Area of the circle, the value of pi remains the same for both circles.

Pi = π = 3.14

Step-by-step explanation:

Part A: Using the formula for circumference, solve for the value of pi for each circle. (4 points)

The formula for the circumference of circle when Diameter is given = πD

π = Circumference / Diameter

For Circle A :

Circle A has a diameter of 7 inches, a circumference of 21.98 inches.

π = 21.98 inches/7 inches

π = 3.14

For Circle B

The diameter of circle B is 6 inches, the circumference is 18.84 inches

π = 18.84 inches/6 inches

π = 3.14

Part B: Use the formula for area and solve for the value of pi for each circle. (4 points)

The formula for the area of the circle = πr²

Circle A has a diameter of 7 inches, an area of 38.465 square inches.

r = Radius = 7 inches ÷ 2

= 3.5 inches

π = Area / Radius²

π = 38.465 in²/(3.5 inches)²

π = 3.14

For Circle B

The diameter of circle B is 6 inches, and the area is 28.26 square inches.

r = Radius = 6 inches ÷ 2

= 3 inches

π = Area / Radius²

π = 28.26 in²/(3 inches)²

π = 3.14

Part C: What observation can you make about the value of pi for circles A and B? (2 points)

The observation I can make for the values of pi for circles A and B is that the value of pi remains the same whether we find pi using the circumference of the circle or the Area of the circle, the value of pi remains the same for both circles.

8 0

3 years ago