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2 years ago

Which equation is equivalent to the given equation?

Mathematics

1 answer:

madam [21]2 years ago

4 0

Answer:

x² - x - 12 = 0

Step-by-step explanation:

0 = -x² + x + 12

→ Add x² to both sides

x² = x + 12

→ Minus x from both sides

x² - x = 12

→ Minus 12 from both sides

x² - x - 12 = 0

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Given right triangle ABC with altitude BD is drawn to hypotenuse AC. If AB=5 and AD=1, what is the length of AC ? (Note: the fig

Alex17521 [72]

Answer:

x = 24.99 or 25

Step-by-step explanation:

Using sin to figure out the angle of ABD, we can figure out the angle of CBD by subtracting it from 90°.

sin y = (1/5)

y = 11.54°

90 - 11.54 = 78.46°

Now using Pythagorean Theorem (a²+b²=c²) we can solve for line BD.

1² + b² = 5²

1 + b² = 25

b² = 24

b = √24

Now we can use tan to figure out the length of segment DC.

tan(78.46) = z/√24

z = 23.99

We can now combine the known length of segment AD and the length of DC to get x.

1 + 23.99 = 24.99 or about 25.

8 0

3 years ago

Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl

Wittaler [7]

Answer:

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

Step-by-step explanation:

The equation of a circle of radius $5$ centered at $(0,0)$ is:

$x^{2} + y^{2} = 5^{2}$ .

$x^{2} + y^{2} = 25$ .

Differentiate implicitly with respect to $x$ to find the slope of tangents to this circle.

$\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]$

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0$ .

Apply the power rule and the chain rule. Treat $y$ as a function of $x$ , $f(x)$ .

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0$ .

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0$ .

That is:

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0$ .

Solve this equation for $\displaystyle \frac{dy}{dx}$ :

$\displaystyle \frac{dy}{dx} = -\frac{x}{y}$ .

The slope of the tangent to this circle at point $(3, 4)$ will thus equal

$\displaystyle \frac{dy}{dx} = -\frac{3}{4}$ .

Apply the slope-point of a line in a cartesian plane:

$y - y_0 = m(x - x_0)$ , where

$m$ is the gradient of this line, and
$(x_0, y_0)$ are the coordinates of a point on that line.

For the tangent line in this question:

$\displaystyle m = -\frac{3}{4}$ ,
$(x_0, y_0) = (3, 4)$ .

The equation of this tangent line will thus be:

$\displaystyle y - 4 = -\frac{3}{4} (x - 3)$ .

That simplifies to

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

3 0

3 years ago

6. What is the greatest common factor of 12wr2 + 6wr – 6w ?

balandron [24]

Answer:

Step-by-step explanation:

5 0

3 years ago

What is x and what converse is used to find x

mrs_skeptik [129]

Answer:

Step-by-step explanation:

the third angle of the inner triangle is defined by using the rule that the sum of all angles in a triangle must be 180 degrees. let's call this angle a

180 = 48 + 16x + a

132 - 16x = a

and then we know that both angles, 28x and a together must also be 180, as they are complementing each other to cover the whole top of the base line.

so,

28x + 132 - 16x = 180

12x = 48

x = 4

8 0

3 years ago

Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (6,-5) lies on

Tom [10]

C i guesss because you just said it

4 0

3 years ago