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3 years ago

What does “converse of the alternate interior angles theorem” mean?

Mathematics

1 answer:

babymother [125]3 years ago

3 0

Answer:

If alternate interior angles formed by two lines with an intersecting traversal are congruent , then these two lines are parallel.

Step-by-step explanation:

Hope this helps :)- Mark Brainiest Please! Thanks!

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Chloe drew a triangle with side lengths of 30 centimeters, 24 centimeters, and 18 centimeters. Juan drew a triangle with side le

vlada-n [284]

Answer:

A and B

Step-by-step explanation:

Each side in Chloe's triangle is 1.5 times the length of each side in Juan's triangle. Thus, they are 'similar' by the math definition of that word, by the SSS Rule for Similar Triangles.

That means they are different only in size. So, their angle measures are the same and they are the same shape.

A and B are true.

C is never true, because the sum of all 3 angles in a triangle is always 180°.

D is not true, because they are similar.

5 0

3 years ago

a snowplow has maximum speed of 40 miles per hour on a dry highway. It's maximum speed decreases by 1.2 miles per hour for every

vova2212 [387]

Step-by-step explanation:

The snowplow's speed is 40 mph minus the loss from the snow, which is 1.2 mph times the depth of snow in inches.

y = 40 − 1.2x

When y = 0:

0 = 40 − 1.2x

1.2x = 40

x = 33 ⅓

The snowplow stops moving when the snow is 33 ⅓ inches deep or more.

8 0

3 years ago

Finding Derivatives Implicity In Exercise, find dy/dx implicity. x2 - 3 ln y + y2 = 10

Veseljchak [2.6K]

Answer:

$\frac{dy}{dx}=-\frac{2xy}{2y^2-3}$

Step-by-step explanation:

We are given that

$x^2-3lny+y^2=0$

Differentiate w.r.t x

$2x-\frac{3}{y}\frac{dy}{dx}+2y\frac{dy}{dx}=0$

By using formula

$\frac{dx^n}{dx}=nx^{n-1}$

$\frac{d(lnx)}{dx}=\frac{1}{x}$

$\frac{dy^n}{dx}=ny^{n-1}\frac{dy}{dx}$

$\frac{dy}{dx}(-\frac{3}{y}+2y)+2x=0$

$\frac{dy}{dx}(-\frac{3}{y}+2y)=-2x$

$\frac{dy}{dx}=-\frac{2x}{-\frac{3}{y}+2y}$

$\frac{dy}{dx}=-\frac{2xy}{2y^2-3}$

Hence, the derivative of function

$\frac{dy}{dx}=-\frac{2xy}{2y^2-3}$

8 0

3 years ago

Write 0.216 as a rational number in lowest terms

lozanna [386]

Answer:

$=\frac{27}{125}$

Step-by-step explanation:

$0.216$

$\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}$

$\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000$

$=\frac{0.216\cdot \:1000}{1000}$

$=\frac{216}{1000}$

$216,\:1000$

$\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}$

$2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}$

$=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3$

$2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}$

$=2\cdot \:2\cdot \:2\cdot \:5\cdot \:5\cdot \:5$

$\mathrm{The\:prime\:factors\:common\:to\:}216,\:1000\mathrm{\:are\:}$

$=2\cdot \:2\cdot \:2$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8$

$=8$

$=\frac{8\cdot \:27}{8\cdot \:125}$

$\mathrm{Cancel\:the\:common\:factor:}\:8$

$=\frac{27}{125}$

Hence, the correct answer is $=\frac{27}{125}$

6 0

2 years ago

PLEASE HELP ME!!! ASAP!! ITS ALMOST DUE!!

Artyom0805 [142]

Answer:

I'm pretty sure it's the first one. If i'm wrong i am terribly sorry

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers