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VladimirAG [237]
3 years ago
16

Writing a Polynomial Expression to Represent Perimeter A family needs to build fencing around their rectangular home and square

swimming pool, depicted below. The total amount of fencing they need can be written as x + 10. If x = 5; The family needs yards of fencing for their home. The family needs yards of fencing for their pool.
Mathematics
2 answers:
IRISSAK [1]3 years ago
8 0
If you are given a rectangular home and a square swimming pool, with dimensions of Pool = 2x & home = (2 +5x) & (3+10x) The total amount of fencing they need can be written as x + 10. If x = 5; The family needs 5 yards of fencing for their home. The family needs 10 yards of fencing for their pool.
Anvisha [2.4K]3 years ago
6 0
The answers are as followed.
38
160
40
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Write the equation of a line with a slope of −1 and a y-intercept of −6. (2 points)
tatyana61 [14]

Answer:

y = -1x - 6

Step-by-step explanation:

Hi!

The format of the equation of a line is y = mx + b

m is the slope and b is the y-intercept

We just need to substitute in the values you gave for the variables and we get the answer,

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Someone help<br> 50 points + brainlist+ like +thank you<br> line segment measurement
Vika [28.1K]

\\ \bull\leadsto CD=DE

\\ \bull\leadsto 3x-6=2(x+1)

\\ \bull\leadsto 3x-6=2x+2

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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}.

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Vikentia [17]
The answer would be 3.

Hope this helps!
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