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3 years ago

The general form of a circle is given as x^2 + y^2 + 4x - 12y + 4 = 0.

1 answer:

7 0

If you can rewrite the formula as (x-a)² + (y-b)² = r², the center is at (a,b) and the radius is r.

If you work out this equation, and map it to the original, you will find that the +4x term hints that a = 2 (double product) and -12y hints that b=-6, and r=6.

So, the formula can be written as (x+2)² + (y-6)² = 6² and the center is at (-2,6) and the radius is 6.

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PLS HELP ASAP

ale4655 [162]

Correct answer is : Area of triangle is $15\sqrt{3} sq.units$

Solution:-

We can do it in 2 methods.

Method 1:-

Given that AB=6, BC=10 and m∠B = 120

Then area of triangle = $\frac{1}{2}XbaseXheight$

Let us assume AB is base and D is an altitude from C onto AB.

Then sin(60)= $\frac{CD}{BC}$

CD = BC sin(60)

Hence height = $10*\frac{\sqrt{3}}{2}$ = $5\sqrt{3}$

Hence area of ΔABC = $\frac{1}{2} X6X5\sqrt{3} = 15\sqrt{3}$ sq.units

Method2:-

Area of triangle = $\frac{1}{2} acsin(B)$

Here a= BC=10, c=AB=6.

Hence area of triangle = $\frac{1}{2}X6X10sin(120) = 15\sqrt{3}$ sq.units

6 0

3 years ago

Find the value of X in this equilateral triangle.

Andrei [34K]

Answer:

x=4

Step-by-step explanation:

Since this is an equilateral triangle, all the sides are equal

6x = 4x+8 = 3x +12

Using the last 2 parts

4x+8 = 3x +12

Subtract 3x from each side

4x-3x +8 =3x+12-12

x+8 = 12

Subtract 8 from each side

x+8-8=12-8

x = 4

7 0

4 years ago

Please help!! Need an explanation by tomorrow and I am super confused!

vovangra [49]

Answer:

x = 35

y = 7

Step-by-step explanation:

See how the image looks like two overlapping triangles. It is given that the triangles are congruent. Its easier to see whats what if you draw the triangles separately. I also flipped over the triangle on the right so they match. Record the given angle measures. Since A is 45° then D is also 45°. DBC is 30°, so we can find the missing angle in triangle DBC. Angles in a triangle add up to 180° so

C + 45 + 30 = 180

C + 75 = 180

C = 105°

This is angle DCB.

Now all the angles are marked. We can set up equations to find x and y. see image.

7 0

2 years ago

Carson throws a ball upward into the air the height of the ball is determined by h(t)= -16t^2 +60t+ 5.5. what is the height in f

Alex777 [14]

The ball was initially thrown from a height of 5.5 feet and 5.5 is y intercept that it throm from 5.5 feet.

6 0

4 years ago

Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is $z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$ .

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be $z (x) = \cos x$ the base formula, where $x$ is measured in sexagesimal degrees. This expression must be transformed by using the following data:

$T = 180^{\circ}$ (Period)

$z_{min} = -4$ (Minimum)

$z_{max} = 5$ (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of $2\pi$ radians. In addition, the following considerations must be taken into account for transformations:

1) $x$ must be replaced by $\frac{2\pi\cdot x}{180^{\circ}}$ . (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

$\Delta z = \frac{z_{max}-z_{min}}{2}$

$\Delta z = \frac{5+4}{2}$

$\Delta z = \frac{9}{2}$

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

$z_{m} = \frac{z_{min}+z_{max}}{2}$

$z_{m} = \frac{1}{2}$

The new function is:

$z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)$

Given that $z_{m} = \frac{1}{2}$ , $\Delta z = \frac{9}{2}$ and $T = 180^{\circ}$ , the outcome is:

$z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

8 0

3 years ago