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3 years ago

15

Find the x intercept and the y intercept of the line 3x-6y=6.

1 answer:

svetoff [14.1K]3 years ago

7 0

X-2 y-1i think tell me if im wrong

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Estimate the percentage: 6,683 of 20,489<br> a. 0.3% c. 3%<br> b. 43.3% d. 33.3% Explain

Eduardwww [97]

Answer: B

Step-by-step explanation: B

6 0

2 years ago

Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

2 years ago

Three more than the quotient of a number and 5 is equal to 9

mars1129 [50]

Answer:

The number is 30.

Step-by-step explanation:

x/5+3=9

x/5=9-3

x/5=6

x=6*5

x=30

7 0

2 years ago

Sally's summer punch recipie is a combo of lemonade and fruit punch.

creativ13 [48]

Answer:

anything else?

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3 years ago

Josh is hiking Glacier National Park. He has now hiked a total of 17 \text{ km}17 km17, space, k, m and is 2 \text{ km}2 km2, sp

jeka94

Josh has hiked 17 km, which is 2 km away from being 1/2 done.
<span>In a equation, this might look like: 17 + 2 = (1/2)h </span>
<span>where h is the length of the hike. </span>
<span>and solve for h, h = 38 km

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
</span>

7 0

3 years ago

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