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Inga [223]
3 years ago
7

Use substitution to solve each system. 2y - 8 = 6x y = 3x + 2

Mathematics
2 answers:
Olegator [25]3 years ago
8 0
It looks like the problem you have displayed has no possible solutions.
lutik1710 [3]3 years ago
7 0
2y - 8 = 6x

2(3x + 2) - 8 = 6x

6x + 4 - 8 = 6x

6x - 4 = 6x

-4 = 0

this system has no solutions 
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Answer:

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Step-by-step explanation:

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Write three measurments using grams and three measurements using milligrams total 15.4 grams
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What is the value of f(-4) in the piecewise function f(x)= -x-5 for -5&lt;= x &lt;= -2; -x^2+1 for -2&lt;=x&lt;=2; (x-3)^2+2 for
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We first need to pick the correct piece to use. In this case, we will use f(x) = -x-5 because -5<=-4.

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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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What is the area and perimeter for these two shapes?
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A:
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