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2 years ago

13

What is the vertex for this function? y = 3x^2 + 12x + 5

1 answer:

xz_007 [3.2K]2 years ago

8 0

That’s weird, it should be (-2,-7). Try (-2,7)

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What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?

ludmilkaskok [199]

The answer is Y=-5/2x-1

7 0

3 years ago

A triangle is placed in a semicircle with a radius of 7mm , as shown below. Find the area of the shaded region. Use the value 3.

timurjin [86]

We either need to see a picture of this and/or get more information about the measurements of the triangle. In general, the area outside of the triangle will be the area of the semi-circle minus the area of the triangle itself, or: 1/2*49*3.14 - 1/2 b*h of the triangle. That first part, which is the area of the semi-circle, works out to 76.93 So based on the info we have, it becomes 76.93 - 1/2*b*h of the triangle = area outside of triangle.

8 0

3 years ago

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

4 0

3 years ago

Simplify this expression. (2-5sqrt6)*3sqrt2<br> Please hurry taking a test.

a_sh-v [17]

Answer:

D

Step-by-step explanation:

7 0

3 years ago

Alphabet has how many letters?

LuckyWell [14K]

The alphabet has 26 letters

7 0

2 years ago

Read 2 more answers