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2 years ago

7

What is the slope of the line shown below? (9, 1) and (-3, -7

1 answer:

Dima020 [189]2 years ago

3 0

Answer:

The slope is 4

Step-by-step explanation:

I think it's right

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HELP 1-6 ME PLEASE (35 POINTS)

makvit [3.9K]

1. $1.90
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6. $2.25

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2 years ago

The ratio of witches to mummies at a Halloween party is 2:3.There are 12 witches at a party. How many mummies are there at the p

Kobotan [32]

Given the 2:3 ratio, we know there are 2 witches for every 3 mummies.

Cross multiply to solve the proportion for mummies.

(2/3) = (12/m)

2m = 36

m = 18

There were 18 mummies at the party.

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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

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

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2 years ago

Add 7/10 + (-17/20)....

r-ruslan [8.4K]

7/10 + (-17/20)

Make the denominators equal:

14/20 + (-17/20)

Add:

-3/20

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2 years ago

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Ulleksa [173]

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2 years ago