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3 years ago

Two angles that add up to 90° are called SUPPLEMENTARY angles. TRUE OR FALSE

Mathematics

1 answer:

svet-max [94.6K]3 years ago

3 0

Answer:

This is FALSE. Two supplementary angles add up to 180 degrees.

Step-by-step explanation:

Hope this helped! :-)

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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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2 years ago

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3 years ago

what are some tv shows a 12 year old watch on Netflix (im a mature 12 yr old and can watch almost anything)

Dmitriy789 [7]

Answer:

Umbrella Academy. Netflix. ...

The Baby-Sitters Club. Netflix. ...

Malibu Rescue. Netflix. ...

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Fuller House. Netflix. ...

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The Letter for the King. Netflix. ...

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The Half of It (2020) Director Alice Wu. ...

Mean Girls (2004) Film. ...

To All the Boys I've Loved Before (2018) Director Susan Johnson. ...

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Clueless (1995) Film. ...

The Edge Of Seventeen (2016) Film. ...

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2 years ago

Please explain me I can’t understand

valina [46]

Step-by-step explanation:

They are asking, like units are in the sum

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3 years ago

Matt is cutting quilt squares measuring 3 inches on each side. He wants to use them to make a rectangular wall hanging measuring

Andrei [34K]

Answer:

Matt will need 10176 square quilts to cover the wall

Step-by-step explanation:

To answer this perfectly, we will have to first convert everything to the same unit.

dimensions of the quilt squares = 3 inches

Length of the wall = 1 yard = 36 inches

Breadth of the wall = 212 feet = 2544 inches.

The next step, is to find the area of the wall that Matt is covering.

Area of wall = length X breadth = 36 X 2544 = $91584in ^{2}$

We will also find the area of the square quilts. This is given as length X length = $3^{2}$ = $9 in^{2}$

to get the number of square quilts that will cover that area, we will have to divide the area of the wall by the area of the quilts

= 91584 /9 = 10176 quilts

Matt will need 10176 quilts to cover the wall

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2 years ago